ORCID Profile
0000-0003-1042-6331
Current Organisation
University of Sydney
Does something not look right? The information on this page has been harvested from data sources that may not be up to date. We continue to work with information providers to improve coverage and quality. To report an issue, use the Feedback Form.
Research Topics
In Research Link Australia (RLA), "Research Topics" refer to ANZSRC FOR and SEO codes. These topics are either sourced from ANZSRC FOR and SEO codes listed in researchers' related grants or generated by a large language model (LLM) based on their publications.
Top 5 Research Topics
ANZSRC Field of Research (FoR)
Theoretical and Computational Chemistry | Quantum Chemistry | Quantum Chemistry | Atomic And Molecular Physics | Atomic and Molecular Physics | Supramolecular Chemistry | Software Engineering | Atomic, Molecular, Nuclear, Particle and Plasma Physics | Physical Organic Chemistry | Reaction Kinetics And Dynamics | Condensed Matter Modelling and Density Functional Theory | Degenerate Quantum Gases and Atom Optics
ANZSRC Socio-Economic Objective (SEO)
Chemical sciences | Application packages | Application Software Packages (excl. Computer Games) | Expanding Knowledge in the Chemical Sciences | Expanding Knowledge in the Physical Sciences | Physical sciences |
Related Links
Publications
Communication: Efficient counterpoise corrections by a perturbative approach
Publisher: AIP Publishing
Date: 26-08-2011
DOI: 10.1063/1.3632054
Abstract: We investigate the use of Hartree-Fock and density functional perturbative corrections for estimating the counterpoise correction (CPC) for interaction energies at the self-consistent field level. We test our approach using several popular basis sets on the S22 set of weakly bound systems, which can exhibit large basis set superposition errors. Our results show that the perturbative approaches typically recover over 95% of the CPC and can be up to twelve times faster to compute than the conventional methods and therefore provide an attractive alternative to calculating CPCs in the conventional way.
Extracting atoms from molecular electron densities via integral equations
Publisher: AIP Publishing
Date: 13-04-2004
DOI: 10.1063/1.1691401
Abstract: The observation that a molecular electron density is close to the superposition of its constituent atoms leads naturally to the idea of modeling a density by a sum of nuclear-centered, spherically symmetric functions. The functions that are optimal in a least-squares sense are known as Stewart atoms. Previous attempts to construct Stewart atoms by expanding them in an auxiliary basis have been thwarted by slow convergence with respect to the size of the auxiliary basis used. We present a method for constructing Stewart atoms via convolution integrals which bypasses the need for an auxiliary basis, and is able to produce highly accurate approximations to Stewart atoms.
Computation and analysis of molecular Hartree—Fock momentum intracules
Publisher: Informa UK Limited
Date: 10-06-2002
An investigation of the performance of a hybrid of Hartree-Fock and density functional theory
Publisher: Wiley
Date: 14-03-1992
Posmom: The Unobserved Observable
Publisher: American Chemical Society (ACS)
Date: 29-03-2010
DOI: 10.1021/JZ100216D
Highly Oxidized Ruthenium Organometallic Compounds. The Synthesis and One-Electron Electrochemical Oxidation of [Cp*RuIVCl2(S2CR)] (Cp* = η5-C5Me
Publisher: American Chemical Society (ACS)
Date: 16-11-2006
DOI: 10.1021/OM060866Z
Advances in methods and algorithms in a modern quantum chemistry program package
Publisher: Royal Society of Chemistry (RSC)
Date: 2006
DOI: 10.1039/B517914A
Abstract: Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.
Q-MP2-OS: Møller–Plesset Correlation Energy by Quadrature
Publisher: American Chemical Society (ACS)
Date: 23-01-2020
Abstract: We present a quadrature-based algorithm for computing the opposite-spin component of the MP2 correlation energy which scales quadratically with basis set size and is well-suited to large-scale parallelization. The key ideas, which are rooted in the earlier work of Hirata and co-workers, are to abandon all two-electron integrals, recast the energy as a seven-dimensional integral, approximate that integral by quadrature, and employ a cutoff strategy to minimize the number of intermediate quantities. We discuss our implementation in detail and show that it parallelizes almost perfectly on 840 cores for cyclosporine (a molecule with roughly 200 atoms), exhibits [Formula: see text] scaling for a sequence of polyglycines, and is principally limited by the accuracy of its quadrature.
Distribution of r12· p12in quantum systems
Publisher: Informa UK Limited
Date: 09-2013
The distribution ofr·pin quantum mechanical systems
Publisher: IOP Publishing
Date: 13-08-2009
Finite jellium models. I. Restricted Hartree–Fock calculations
Publisher: AIP Publishing
Date: 15-04-2005
DOI: 10.1063/1.1873552
Abstract: Restricted Hartree–Fock calculations have been performed on the Fermi configurations of n electrons confined within a cube. The self-consistent-field orbitals have been expanded in a basis of N particle-in-a-box wave functions. The difficult one- and two-electron integrals have been reduced to a small set of canonical integrals that are calculated accurately using quadrature. The total energy and exchange energy per particle converge smoothly toward their limiting values as n increases the highest occupied molecular orbital–lowest unoccupied molecular orbital gap and Dirac coefficient converge erratically. However, the convergence in all cases is slow.
Density functional triple jumping
Publisher: Royal Society of Chemistry (RSC)
Date: 2010
DOI: 10.1039/C0CP00242A
Abstract: We propose a density functional perturbative scheme to approximate the energy of a high-level DFT calculation at a significantly reduced cost. Our approach involves performing a primary SCF calculation using a crude functional, basis set and quadrature grid, followed by a single step using a more sophisticated secondary functional, basis and grid. Unlike the earlier dual-level DFT approach of Nakajima and Hirao, we use Roothaan diagonalization instead of perturbation theory to incorporate the effects of the secondary basis set. We show that energies at the popular B3LYP/6-311+G(3df,2p)/(75,302) level can be accurately estimated from primary calculations at the relatively economical BLYP/6-31G(d)/SG-0 level.
Optimal partition of the Coulomb operator
Publisher: American Physical Society (APS)
Date: 04-1997
Radial quadrature for multiexponential integrands
Publisher: Wiley
Date: 17-03-2003
DOI: 10.1002/JCC.10211
Abstract: We introduce a Gaussian quadrature, based on the polynomials that are orthogonal with respect to the weight function ln(2)x on the interval [0, 1], which is suitable for the evaluation of radial integrals. The quadrature is exact if the non-Jacobian part of the integrand is a linear combination of a geometric sequence of exponential functions. We find that the new scheme is a useful alternative to existing approaches, particularly for integrands that exhibit multiexponential behavior.
Performance of Gradient-Corrected and Hybrid Density Functional Theory: Role of the Underlying Local Density Approximation and the Gradient Correction
Publisher: American Chemical Society (ACS)
Date: 25-09-2012
DOI: 10.1021/CT300603D
Abstract: We have analyzed the performance of several widely used density functional theory procedures, namely B-P86, B-PW91, B-LYP, B3-P86, B3-PW91, and B3-LYP, for the E3 set of thermochemical properties. Each of these procedures employs a local density approximation (LDA) functional and a gradient correction for the correlation energy. We find that the VWN3 LDA functional in B-P86, B-PW91, B3-P86, and B3-PW91 leads to extremely large deviations from benchmark values for heats of formation (as large as -455.6 kJ mol(-1) for the B-PW91(VWN3) value for azulene!) and that VWN3 also gives significant errors in the calculated ionization energies and electron affinities. The PW91 gradient correction generally performs much better than P86 for heats of formation, and we propose that this is because P86 severely violates a uniform scaling condition that PW91 almost satisfies. Thus, of the procedures that we have examined, we recommend the use of the VWN5 or PW92 forms of LDA, preferably in combination with the PW91 gradient correction. Our results confirm previous findings that VWN3 is a more suitable LDA than VWN5 for B3-LYP, and we attribute this to fortuitous error cancellation between understabilization of molecules by LYP and overstabilization by VWN3.
Wave functions and two-electron probability distributions of the Hooke’s-law atom and helium
Publisher: American Physical Society (APS)
Date: 21-08-2003
Exact energy of the spin-polarized two-dimensional electron gas at high density
Publisher: American Physical Society (APS)
Date: 08-06-2011
Structures and stabilities of the dimer dications of first- and second-row hydrides
Publisher: American Chemical Society (ACS)
Date: 06-1989
DOI: 10.1021/JA00195A014
Empirical density functionals
Publisher: Elsevier BV
Date: 02-1998
Structures and stabilities of singly charged three-electron hemibonded systems and their hydrogen-bonded isomers
Publisher: American Chemical Society (ACS)
Date: 07-1988
DOI: 10.1021/JA00223A010
Probing the Reactivity of Photoinitiators for Free Radical Polymerization: Time-Resolved Infrared Spectroscopic Study of Benzoyl Radicals
Publisher: American Chemical Society (ACS)
Date: 21-11-2002
DOI: 10.1021/JA026099M
Abstract: A series of substituted benzoyl radicals has been generated by laser flash photolysis of alpha-hydroxy ketones, alpha-amino ketones, and acyl and bis(acyl)phosphine oxides, all of which are used commercially as photoinitiators in free radical polymerizations. The benzoyl radicals have been studied by fast time-resolved infrared spectroscopy. The absolute rate constants for their reaction with n-butylacrylate, thiophenol, bromotrichloromethane and oxygen were measured in acetonitrile solution. The rate constants of benzoyl radical addition to n-butylacrylate range from 1.3 x 10(5) to 5.5 x 10(5) M(-1) s(-1) and are about 2 orders of magnitude lower than for the n-butylacrylate addition to the counterradicals that are produced by alpha-cleavage of the investigated ketones. Density functional theoretical calculations have been performed in order to rationalize the observed reactivities of the initiating radicals. Calculations of the phosphorus-centered radicals generated by photolysis of an acyl and bis(acyl)phosphine oxide suggest that P atom Mulliken spin populations are an indicator of the relative reactivities of the phosphorus-centered radicals. The alpha-cleavage of (2,4,6-trimethylbenzoyl)phosphine oxide was studied by picosecond pump-probe and nanosecond step-scan time-resolved infrared spectroscopy. The results support a mechanism in which the alpha-cleavage occurs from the triplet excited state that has a lifetime less than or equal to the singlet excited state.
A generalized Poisson equation and short-range self-interaction energies
Publisher: AIP Publishing
Date: 24-06-2008
DOI: 10.1063/1.2945298
Abstract: We generalize the Poisson equation to attenuated Newtonian potentials. If the attenuation is at least exponential, the equation provides a local mapping between the density and its potential. We use this to derive several density functionals for the short-range self-interaction energy.
An optimal point-charge model for molecular electrostatic potentials
Publisher: Informa UK Limited
Date: 20-10-2005
A theoretical approach to molecular conformational analysis
Publisher: Elsevier BV
Date: 1985
Uniform electron gases. I. Electrons on a ring
Publisher: AIP Publishing
Date: 28-04-2013
DOI: 10.1063/1.4802589
Abstract: We introduce a new paradigm for one-dimensional uniform electron gases (UEGs). In this model, n electrons are confined to a ring and interact via a bare Coulomb operator. We use Rayleigh-Schrödinger perturbation theory to show that, in the high-density regime, the ground-state reduced (i.e., per electron) energy can be expanded as \\documentclass[12pt]{minimal}\\begin{document}$\\epsilon (r_s,n) = \\epsilon _0(n) r_s^{-2} + \\epsilon _1(n) r_s^{-1} + \\epsilon _2(n) +\\epsilon _3(n) r_s\\break + \\cdots\\,$\\end{document}ε(rs,n)=ε0(n)rs−2+ε1(n)rs−1+ε2(n)+ε3(n)rs+⋯, where rs is the Seitz radius. We use strong-coupling perturbation theory and show that, in the low-density regime, the reduced energy can be expanded as \\documentclass[12pt]{minimal}\\begin{document}$\\epsilon (r_s,n) = \\eta _0(n) r_s^{-1} + \\eta _1(n) r_s^{-3/2}\\break + \\eta _2(n) r_s^{-2} + \\cdots\\,$\\end{document}ε(rs,n)=η0(n)rs−1+η1(n)rs−3/2+η2(n)rs−2+⋯. We report explicit expressions for ε0(n), ε1(n), ε2(n), ε3(n), η0(n), and η1(n) and derive the thermodynamic (large-n) limits of each of these. Finally, we perform numerical studies of UEGs with n = 2, 3, …, 10, using Hylleraas-type and quantum Monte Carlo methods, and combine these with the perturbative results to obtain a picture of the behavior of the new model over the full range of n and rs values.
The structure and stability of the O2+2 dication: a dramatic failure of Møller—Plesset perturbation theory
Publisher: Elsevier BV
Date: 08-1991
Computation of molecular Hartree–Fock Wigner intracules
Publisher: AIP Publishing
Date: 14-01-2003
DOI: 10.1063/1.1532311
Abstract: The computation of molecular Wigner intracules from Hartree–Fock wave functions using Gaussian basis functions is described. The Wigner intracule is a new type of intracule that contains information about both the relative position and momentum of the electrons. Two methods for evaluating the required integrals are presented. The first approach uses quadrature while the second requires summation of an infinite series.
Self-Consistent Hartree-Fock-Wigner Calculations: A Two-Electron-Density Functional Theory
Publisher: American Chemical Society
Date: 13-03-2007
Correlation energy of anisotropic quantum dots
Publisher: American Physical Society (APS)
Date: 21-09-2011
A family of attenuated Coulomb operators
Publisher: Elsevier BV
Date: 10-1996
Gaussian Expansions of Orbitals
Publisher: American Chemical Society (ACS)
Date: 02-08-2012
DOI: 10.1021/CT300559T
Isomers of C24. Density functional studies including gradient corrections
Publisher: Elsevier BV
Date: 08-1994
Insights from Coulomb and exchange intracules
Publisher: Elsevier BV
Date: 07-2000
The performance of a family of density functional methods
Publisher: AIP Publishing
Date: 04-1993
DOI: 10.1063/1.464906
Abstract: The results of a systematic study of molecular properties by density functional theory (DFT) are presented and discussed. Equilibrium geometries, dipole moments, harmonic vibrational frequencies, and atomization energies were calculated for a set of 32 small neutral molecules by six different local and gradient-corrected DFT methods, and also by the ab initio methods Hartree–Fock, second-order Mo/ller–Plesset, and quadratic configuration interaction with single and double substitutions (QCISD). The standard 6-31G* basis set was used for orbital expansion, and self-consistent Kohn–Sham orbitals were obtained by all DFT methods, without employing any auxiliary fitting techniques. Comparison with experimental results shows the density functional geometries and dipole moments to be generally no better than or inferior to those predicted by the conventional ab initio methods with this particular basis set. The density functional vibrational frequencies compare favorably with the ab initio results, while for atomization energies, two of the DFT methods give excellent agreement with experiment and are clearly superior to all other methods considered.
Linear scaling density functional calculations via the continuous fast multipole method
Publisher: Elsevier BV
Date: 05-1996
Correlation energy of the spin-polarized uniform electron gas at high density
Publisher: American Physical Society (APS)
Date: 21-07-2011
Multiply-charged cations: remarkable structures and stabilities
Publisher: Walter de Gruyter GmbH
Date: 1988
Model calculations of isotope effects. 10. Temperature-independent isotope effects in hydrogen transfer. Do they signify a bent transition state?
Publisher: American Chemical Society (ACS)
Date: 05-1985
DOI: 10.1021/JA00296A022
Resolutions of the Coulomb operator: VII. Evaluation of long-range Coulomb and exchange matrices
Publisher: American Chemical Society (ACS)
Date: 16-01-2013
DOI: 10.1021/CT301110Y
Abstract: Use of the resolution of Ewald operator method for computing long-range Coulomb and exchange interactions is presented. We show that the accuracy of this method can be controlled by a single parameter in a manner similar to that used by conventional algorithms that compute two-electron integrals. Significant performance advantages over conventional algorithms are observed, particularly for high quality basis sets and globular systems. The approach is directly applicable to hybrid density functional theory.
Molecular integrals Over Gaussian Basis Functions
Publisher: Elsevier
Date: 1994
A simple yet powerful upper bound for Coulomb integrals
Publisher: Elsevier BV
Date: 1994
The nature of electron correlation in a dissociating bond
Publisher: AIP Publishing
Date: 10-06-2011
DOI: 10.1063/1.3599937
Abstract: We have constructed the unrestricted Hartree-Fock (UHF), restricted Hartree-Fock (RHF), and full configuration interaction (FCI) position and momentum intracules and holes for H⋅⋅⋅H at bond lengths R from 1 to 10 bohrs. We trace the recently discovered inversion of the UHF position hole at intermediate R to over-localization of the spin-orbitals, and support this by a correlation energy component analysis. The RHF and UHF momentum holes are found to be more complicated however their features are explained through decomposition of electron correlation effects. The UHF momentum hole is also found to invert and exhibits interesting behavior at large R. The RHF (but not UHF) and FCI momentum intracules exhibit Young-type interference patterns related to recent double photoionization experiments. Our analyses yield the most comprehensive picture to date of the behavior of the electrons during homolytic bond fission.
An ab initio study of anharmonicity and matrix effects on the hydrogen-bonded BrH:NH complex 3
Publisher: Informa UK Limited
Date: 10-1997
Empirical density functional and the adsorption of organic molecules on Si(100)
Publisher: American Physical Society (APS)
Date: 15-01-2003
An efficient algorithm for the generation of two-electron repulsion integrals over gaussian basis functions
Publisher: Wiley
Date: 19-06-2009
The stability of ‘food addiction’ as assessed by the Yale Food Addiction Scale in a non-clinical population over 18-months
Publisher: Elsevier BV
Date: 2016
DOI: 10.1016/J.APPET.2015.10.015
Abstract: The Yale Food Addiction Scale (YFAS) is a widely used tool to assess the behavioural indicators of addictive-like eating. No studies, however, have used a longitudinal design to determine whether these addictive-like eating behaviours are a stable or transient phenomenon in a community-based population. This study aimed to evaluate whether food addiction Diagnosis and Symptom scores as assessed by the YFAS remain stable over 18-months in a non-clinical population. Young adults aged 18-35 years were recruited from the community to a web-based survey in 2013. The survey included demographics, anthropometrics and the YFAS. Participants who volunteered to be recontacted for future research were invited to complete the same survey 18-months later. The YFAS scoring outputs Diagnosis and Symptom scores were tested for agreement and reliability between the two time points. Of the 303 participants who completed the original survey and agreed to be recontacted, 69 participants (22.8% of those recontacted, 94% female, 67% normal weight at baseline) completed the 18-month follow-up survey. At baseline, thirteen participants met the YFAS predefined criteria for Diagnosis, while eleven participants met these criteria at the 18-month follow-up. YFAS Diagnosis was found to have moderate agreement [K = .50, 95% CI (.23, .77)] between the two time points while Symptom scores had good agreement [K = .70, 95% CI (.54, .83)]. Intraclass correlation coefficients were interpreted as moderate over the 18-month period for both the Diagnosis [ICC = .71, 95% CI (.45, .88)] and Symptom scores [ICC = .72, 95% CI (.58, .82)]. YFAS assessed food addiction Diagnosis and Symptom scores were found to be relatively stable over 18-months in a non-clinical population of predominantly female, young adults. Future research is required to determine the impact of behavioural weight loss interventions on YFAS assessed addictive-like eating.
The two faces of static correlation
Publisher: AIP Publishing
Date: 21-03-2011
DOI: 10.1063/1.3570574
Abstract: Restricted Hartree–Fock (RHF) and UHF wavefunctions for beryllium-like ions with nuclear charge 3 ⩽ Z ⩽ 5 are found using a near-complete Slater basis set. The triplet (RHF → UHF) instability and correlation energy are investigated as a function of Z and we find that the instability vanishes for Z & 4.5. We reproduce this surprising behavior using a minimal-basis model and, by comparing with the stretched H2 molecule, conclude that “static” (also known as nondynamical, near-degeneracy, first-order, or strong) correlation comes in two flavors: one that can be captured by UHF and another that cannot. In the former (Type A), there is an “absolute near-degeneracy” in the latter (Type B), there is a “relative near-degeneracy.” This dichotomy clarifies discussions of static correlation effects.
Exact Wave Functions of Two-Electron Quantum Rings
Publisher: American Physical Society (APS)
Date: 23-02-2012
A remarkable identity involving Bessel functions
Publisher: The Royal Society
Date: 18-04-2012
Abstract: We consider a new identity involving integrals and sums of Bessel functions. The identity provides new ways to evaluate integrals of products of two Bessel functions. The identity is remarkably simple and powerful since the summand and the integrand are of exactly the same form and the sum converges to the integral relatively fast for most cases. A proof and numerical ex les of the identity are discussed.
A tale of two electrons: Correlation at high density
Publisher: Elsevier BV
Date: 11-2010
SG‐0: A small standard grid for DFT quadrature on large systems
Publisher: Wiley
Date: 06-03-2006
DOI: 10.1002/JCC.20383
Abstract: We report the development of a new standard quadrature grid for DFT calculations. Standard Grid 0 (SG-0) is designed to be approximately half as large as, and to provide approximately half the accuracy of, the established SG-1 grid. It is based on MultiExp and Lebedev quadrature for radial and angular coordinates, respectively. We find that SG-0 is typically 50% faster than SG-1 for energy, gradient, and hessian calculations for the exchange-correlation energy. This leads to a 35-38% speedup in the total gradient and hessian computations, and we particularly recommend its use for preliminary calculations on moderately large biochemical systems. It has been implemented as the default grid for DFT calculations in the Q-Chem 3.0 package.
Intracule functional models
Publisher: Royal Society of Chemistry (RSC)
Date: 2011
DOI: 10.1039/C1PC90008K
Coulomb energies via Stewart densities
Publisher: Elsevier BV
Date: 04-1998
Performance of Density Functional Theory Procedures for the Calculation of Proton-Exchange Barriers: Unusual Behavior of M06-Type Functionals
Publisher: American Chemical Society (ACS)
Date: 25-07-2014
DOI: 10.1021/CT500506T
Abstract: We have examined the performance of a variety of density functional theory procedures for the calculation of complexation energies and proton-exchange barriers, with a focus on the Minnesota-class of functionals that are generally highly robust and generally show good accuracy. A curious observation is that M05-type and M06-type methods show an atypical decrease in calculated barriers with increasing proportion of Hartree-Fock exchange. To obtain a clearer picture of the performance of the underlying components of M05-type and M06-type functionals, we have investigated the combination of MPW-type and PBE-type exchange and B95-type and PBE-type correlation procedures. We find that, for the extensive E3 test set, the general performance of the various hybrid-DFT procedures improves in the following order: PBE1-B95 → PBE1-PBE → MPW1-PBE → PW6-B95. As M05-type and M06-type procedures are related to PBE1-B95, it would be of interest to formulate and examine the general performance of an alternative Minnesota DFT method related to PW6-B95.
Creating Implicit Measure Stimulus Sets Using a Multi-Step Piloting Method
Publisher: MDPI AG
Date: 03-05-2023
DOI: 10.3390/MPS6030047
Abstract: The effect of arbitrary stimulus selection is a persistent concern when employing implicit measures. The current study tests a data-driven multi-step procedure to create stimulus items using a combination of free-recall and survey data. Six sets of stimulus items were created, representing healthy food and high sugar items in children, adolescents, and adults. Selected items were highly representative of the target concepts, in frequent use, and of near equal length. Tests of the piloted items in two s les showed slightly higher implicit measure–behavior relations compared to a previously used measure, providing preliminary support for the value in empirically based stimulus selection. Further, the items reported as being the most associated with their target concepts differed notably from what one may expect from the guidelines or population consumption patterns, highlighting the importance of informed stimulus selection.
A family of intracules, a conjecture and the electron correlation problem
Publisher: Royal Society of Chemistry (RSC)
Date: 2006
DOI: 10.1039/B511472A
Abstract: We present a radical approach to the calculation of electron correlation energies. Unlike conventional methods based on Hartree-Fock or density functional theory, it is based on the two-electron phase-space information in the Omega intracule, a three-dimensional function derived from the Wigner distribution. Our formula for the correlation energy is isomorphic to the Hartree-Fock energy expression but requires a new type of four-index integral. Preliminary results, obtained using a model that is based on the known correlation energies of small atoms, are encouraging.
6-311G(MC)(d,p): a second-row analogue of the 6-311G(d,p) basis set: calculated heats of formation for second-row hydrides
Publisher: American Chemical Society (ACS)
Date: 08-1988
DOI: 10.1021/J100328A015
Coulomb-attenuated exchange energy density functionals
Publisher: Informa UK Limited
Date: 07-1996
Mixed Ramp–Gaussian Basis Sets
Publisher: American Chemical Society (ACS)
Date: 02-10-2014
DOI: 10.1021/CT500615M
Abstract: We discuss molecular orbital basis sets that contain both Gaussian and polynomial (r ) functions. We show that, by modeling r -Gaussian products as sums of r s, all of the required one- and two-electron integrals can be computed quickly and accurately. To illustrate our approach, we construct R-31+G, a mixed r -Gaussian basis in which the core basis functions of the 6-31+G basis are replaced by r s. By performing self-consistent Hartree-Fock calculations, we show that the thermochemical predictions of R-31+G and 6-31+G are similar but the former has the potential to be significantly faster.
Basis functions for electronic structure calculations on spheres
Publisher: AIP Publishing
Date: 22-12-2014
DOI: 10.1063/1.4903984
Abstract: We introduce a new basis function (the spherical Gaussian) for electronic structure calculations on spheres of any dimension D. We find general expressions for the one- and two-electron integrals and propose an efficient computational algorithm incorporating the Cauchy-Schwarz bound. Using numerical calculations for the D = 2 case, we show that spherical Gaussians are more efficient than spherical harmonics when the electrons are strongly localized.
Resolutions of the Coulomb operator
Publisher: AIP Publishing
Date: 28-05-2008
DOI: 10.1063/1.2939239
Abstract: We discuss a generalization of the resolution of the identity by considering one-body resolutions of two-body operators, with particular emphasis on the Coulomb operator. We introduce a set of functions that are orthonormal with respect to 1∕r12 and propose that the resulting “resolution of the Coulomb operator,” r12−1=∣ϕi⟩⟨ϕi∣, may be useful for the treatment of large systems due to the separation of two-body interactions. We validate our approach by using it to compute the Coulomb energy of large systems of point charges.
Effects of Coulomb attenuation on chemical properties
Publisher: Elsevier BV
Date: 06-1997
Excitation Number: Characterizing Multiply Excited States
Publisher: American Chemical Society (ACS)
Date: 28-12-2017
Abstract: How many electrons are excited in an electronic transition? In this Letter, we introduce the excitation number η to answer this question when the initial and final states are each modeled by a single-determinant wave function. We show that calculated η values lie close to positive integers, leading to unambiguous assignments of the number of excited electrons. This contrasts with previous definitions of excitation quantities which can lead to mis-assignments. We consider several ex les where η provides improved excited-state characterizations.
Hartree–Fock perturbative corrections for total and reaction energies
Publisher: AIP Publishing
Date: 28-07-2010
DOI: 10.1063/1.3463800
Abstract: We have performed an assessment of the Hartree–Fock perturbative correction (HFPC) on a large and erse set of molecules and reactions. Errors in both absolute and reaction energies with respect to converged secondary basis Hartree–Fock results are reported for a wide spectrum of primary/secondary basis set combinations. These results show that using an adequate primary basis, HFPC can accurately reproduce secondary basis energies at a substantially reduced cost. Comparisons of HFPC with the related dual basis Hartree–Fock (DBHF) scheme are also made for several molecules and target secondary basis sets. Our results indicate that HFPC is faster and more accurate than DBHF for approaching triple-ζ basis sets. For quadruple-ζ secondary basis sets, HFPC is capable of yielding more accurate energies at a marginally increased cost over DBHF.
Why does unrestricted Mo/ller–Plesset perturbation theory converge so slowly for spin-contaminated wave functions?
Publisher: AIP Publishing
Date: 15-12-1988
DOI: 10.1063/1.455312
Abstract: The poor convergence of the unrestricted Mo/ller–Plesset (UMP) series for some systems and the presence of significant spin contamination in the underlying unrestricted Hartree–Fock (UHF) wave functions have both been shown to result from the presence of low-lying, doubly excited determinants. The contributions to the UCI energy from any determinants which mix with the UHF wave function through the problematic doubly excited determinants will be described poorly by UMP theory.
Efficient calculation of short-range Coulomb energies
Publisher: Wiley
Date: 15-07-1999
DOI: 10.1002/(SICI)1096-987X(19990715)20:9<921::AID-JCC3>3.0.CO;2-K
Molecular electronic structure in one-dimensional Coulomb systems
Publisher: Royal Society of Chemistry (RSC)
Date: 2017
DOI: 10.1039/C6CP06801D
Abstract: In this work we explore the nature of chemical bonding in one dimensional molecules.
Computation of Coulomb and exchange radial intracule densities
Publisher: Elsevier BV
Date: 11-1999
Becke–Wigner : a simple but powerful density functional
Publisher: Royal Society of Chemistry (RSC)
Date: 1995
DOI: 10.1039/FT9959104337
Resolutions of the Coulomb operator: II. The Laguerre generator
Publisher: Elsevier BV
Date: 02-2009
Communication: Three-electron coalescence points in two and three dimensions
Publisher: AIP Publishing
Date: 11-11-2015
DOI: 10.1063/1.4935374
Abstract: The form of the wave function at three-electron coalescence points is examined for several spin states using an alternative method to the usual Fock expansion. We find that, in two- and three-dimensional systems, the non-analytical nature of the wave function is characterized by the appearance of logarithmic terms, reminiscent of those that appear as both electrons approach the nucleus of the helium atom. The explicit form of these singularities is given in terms of the interelectronic distances for a doublet and two quartet states of three electrons in a harmonic well.
Leading-order behavior of the correlation energy in the uniform electron gas
Publisher: Wiley
Date: 24-06-2012
DOI: 10.1002/QUA.23155
Computing molecular electrostatic potentials with the PRISM algorithm
Publisher: Elsevier BV
Date: 04-1993
Spin‐unrestricted character of Kohn‐Sham orbitals for open‐shell systems
Publisher: Wiley
Date: 15-11-1995
Self-Consistent Field Calculations of Excited States Using the Maximum Overlap Method (MOM)
Publisher: American Chemical Society (ACS)
Date: 26-08-2008
DOI: 10.1021/JP801738F
Abstract: We present a simple algorithm, which we call the maximum overlap method (MOM), for finding excited-state solutions to self-consistent field (SCF) equations. Instead of using the aufbau principle, the algorithm maximizes the overlap between the occupied orbitals on successive SCF iterations. This prevents variational collapse to the ground state and guides the SCF process toward the nearest, rather than the lowest energy, solution. The resulting excited-state solutions can be treated in the same way as the ground-state solution and, in particular, derivatives of excited-state energies can be computed using ground-state code. We assess the performance of our method by applying it to a variety of excited-state problems including the calculation of excitation energies, charge-transfer states, and excited-state properties.
Auxiliary basis expansions for large-scale electronic structure calculations
Publisher: Proceedings of the National Academy of Sciences
Date: 21-04-2005
Abstract: One way to reduce the computational cost of electronic structure calculations is to use auxiliary basis expansions to approximate four-center integrals in terms of two- and three-center integrals, usually by using the variationally optimum Coulomb metric to determine the expansion coefficients. However, the long-range decay behavior of the auxiliary basis expansion coefficients has not been characterized. We find that this decay can be surprisingly slow. Numerical experiments on linear alkanes and a toy model both show that the decay can be as slow as 1/ r in the distance between the auxiliary function and the fitted charge distribution. The Coulomb metric fitting equations also involve ergent matrix elements for extended systems treated with periodic boundary conditions. An attenuated Coulomb metric that is short-range can eliminate these oddities without substantially degrading calculated relative energies. The sparsity of the fit coefficients is assessed on simple hydrocarbon molecules and shows quite early onset of linear growth in the number of significant coefficients with system size using the attenuated Coulomb metric. Hence it is possible to design linear scaling auxiliary basis methods without additional approximations to treat large systems.
Computation and interpretation of molecular Omega intracules
Publisher: AIP Publishing
Date: 02-07-2007
DOI: 10.1063/1.2746028
Abstract: The Omega intracule is a three-dimensional function that describes the relative positions, momenta, and directions of motion of pairs of electrons in a system. In this paper, we describe the computation of the Omega intracule for a molecular system whose electronic wave function is expanded in a Gaussian basis set. This is followed by implementation details and numerical tests. Finally, we use the Omega intracules of a number of small systems to illustrate the power of this function to extract simple physical insights from complicated wave functions.
The role of vibrational doorway states in positron annihilation with large molecules
Publisher: Elsevier BV
Date: 07-2004
Tribute to Leo Radom
Publisher: American Chemical Society (ACS)
Date: 05-12-2019
How well can RMP4 theory treat homolytic fragmentations?
Publisher: Elsevier BV
Date: 12-2017
A point-charge model for electrostatic potentials based on a local projection of multipole moments
Publisher: Informa UK Limited
Date: 20-12-2006
Self-consistent-field calculations of core excited states
Publisher: AIP Publishing
Date: 25-03-2009
DOI: 10.1063/1.3092928
Abstract: The accuracy of core excitation energies and core electron binding energies computed within a Δself-consistent-field framework is assessed. The variational collapse of the core excited state is prevented by maintaining a singly occupied core orbital using an overlap criterion called the maximum overlap method. When applied to a wide range of small organic molecules, the resulting core excitation energies are not systematically underestimated as observed in time-dependent density functional theory and agree well with experiment. The accuracy of this approach for core excited states is illustrated by the calculation of the pre-edge features in x-ray absorption spectra of plastocyanin, which shows that accurate results can be achieved with Δself-consistent-field calculations when used in conjunction with uncontracted basis functions.
Parallelization of SCF calculations within Q-Chem
Publisher: Elsevier BV
Date: 06-2000
Stereoselective Association of Binuclear Metallacycles in Coordination Polymers
Publisher: American Chemical Society (ACS)
Date: 10-05-2003
DOI: 10.1021/JA029048Y
Abstract: A series of structurally related binuclear metallacycles [Cd(NO(3))(2)L](2), where L is an angular exo-bidentate ligand, have been synthesized. Each metallacycle contains two coordinatively unsaturated, chiral metal centers within a single molecule, and the assembly of these metallacycles into polymeric framework structures has been studied systematically for the first time. Stereoselective homochiral association of [Cd(NO(3))(2)L](2) leads to the formation of helical coordination polymers, whereas meso type association results in nonhelical chain structures. The type of stereoselective aggregation depends on the conditions of self-assembly as well as on ligand functionality. Both helical and nonhelical polymeric complexes have been isolated for the metallacycle [Cd(NO(3))(2)(2,4'-pyacph)](2) (2,4'-pyacph = 2,4'-(4-ethynylphenyl)bipyridyl). Homochiral association results in the formation of helical [Cd(NO(3))]( infinity ) chains which link the binuclear [Cd(NO(3))(2)(2,4'-pyacph)](2) metallacycles into racemic two-dimensional sheets which contain both P and M [Cd(NO(3))]( infinity ) helices. In contrast, meso-association leads to the formation of nonhelical one-dimensional chains. It is shown that the product of homochiral association is predominately formed at room temperature and that of meso-association is generated at elevated temperatures. Thus, it may be concluded that the homochiral association appears to be energetically less favorable than the meso-association, a conclusion that has been confirmed by theoretical calculations of the crystal lattice energy. Several high-yield syntheses of bipyridyl-type ligands used for metallacyclic assembly are also reported.
Efficient Method for Calculating Effective Core Potential Integrals
Publisher: American Chemical Society (ACS)
Date: 21-02-2018
Abstract: Effective core potential (ECP) integrals are among the most difficult one-electron integrals to calculate due to the projection operators. The radial part of these operators may include r
Communication: A new approach to dual-basis second-order Møller–Plesset calculations
Publisher: AIP Publishing
Date: 28-02-2011
DOI: 10.1063/1.3556705
Abstract: We describe a hierarchy of approximations (MP2[x]) that allow one to estimate second-order Møller–Plesset (MP2) energies in a large basis set from small-basis calculations. The most cost-effective approximation, MP2[K], is significantly cheaper than full MP2 but numerical tests on small atoms and molecules indicate that it is nonetheless accurate. We conclude that MP2[K] is an attractive level of theory for large systems.
Diagnostics of molecular orbital quality
Publisher: Canadian Science Publishing
Date: 08-2010
DOI: 10.1139/V10-039
Abstract: We discuss several measures of the quality of a molecular orbital. Each requires only that the orbital be associated with a well-defined Fock operator and is thus applicable to both Hartree–Fock and density functional orbitals. One of the measures, the γ diagnostic, ranges from γ = 0 (perfect) to γ = π/2 (poor) and is conceptually simple. We illustrate its usefulness by applying it to a number of small atoms and ions.
Simple models for describing the fragmentation behavior of multiply charged cations
Publisher: Wiley
Date: 12-03-1988
Exact and approximate solutions to the one‐center McMurchie–Davidson tree‐search problem
Publisher: Wiley
Date: 12-1991
Excited states of spherium
Publisher: Informa UK Limited
Date: 02-09-2010
Ground state of two electrons on a sphere
Publisher: American Physical Society (APS)
Date: 30-06-2009
The hemibonded dimer radical cation of thiirane
Publisher: American Chemical Society (ACS)
Date: 04-1989
DOI: 10.1021/JA00190A007
Remembrance: John A. Pople (1925–2004)
Publisher: AIP Publishing
Date: 06-05-2004
DOI: 10.1063/1.1757682
Advances in methodologies for linear-scaling density functional calculations
Publisher: Elsevier
Date: 1996
Deceptive convergence in møller-plesset perturbation energies
Publisher: Elsevier BV
Date: 11-1986
Can correlation bring electrons closer together?
Publisher: Informa UK Limited
Date: 20-04-2009
Uniform electron gases
Publisher: Springer Science and Business Media LLC
Date: 13-12-2012
BFW: A Density Functional for Transition Metal Clusters
Publisher: American Chemical Society (ACS)
Date: 14-03-2007
DOI: 10.1021/JP067752L
Abstract: Ionization potentials (IPs) or electron affinities (EAs) for transition metal clusters are an important property that can be used to identify and differentiate between clusters. Accurate calculation of these values is therefore vital. Previous attempts using a variety of DFT models have correctly predicted trends, but have relied on the use of scaling factors to compare to experimental IPs. In this paper, we introduce a new density functional (BFW) that is explicitly designed to yield accurate, absolute IPs for transition metal clusters. This paper presents the numerical results for a selection of transition metal clusters and their carbides, nitrides, and oxides for which experimental IPs are known. When tested on transition metal clusters, the BFW functional is found to be significantly more accurate than B3LYP and B3PW91.
Kohn—Sham density-functional theory within a finite basis set
Publisher: Elsevier BV
Date: 11-1992
An Examination of the Relationship Between Transition State Geometry in Hydron Transfer Reactions and the Temperature Dependence of the Primary Kinetic Isotope Effect
Publisher: Wiley
Date: 1985
A density functional study of the simplest hydrogen abstraction reaction. Effect of self-interaction correction
Publisher: Elsevier BV
Date: 04-1994
Extraction of Stewart Atoms from Electron Densities
Publisher: American Chemical Society (ACS)
Date: 1996
DOI: 10.1021/JP961524H
Harmonically trapped jellium
Publisher: Informa UK Limited
Date: 27-04-2012
Efficient calculation ofp-values in linear-statistic permutation significance tests
Publisher: Informa UK Limited
Date: 2007
Uniform electron gases. III. Low-density gases on three-dimensional spheres
Publisher: AIP Publishing
Date: 25-08-2015
DOI: 10.1063/1.4929353
Abstract: By combining variational Monte Carlo (VMC) and complete-basis-set limit Hartree-Fock (HF) calculations, we have obtained near-exact correlation energies for low-density same-spin electrons on a three-dimensional sphere (3-sphere), i.e., the surface of a four-dimensional ball. In the VMC calculations, we compare the efficacies of two types of one-electron basis functions for these strongly correlated systems and analyze the energy convergence with respect to the quality of the Jastrow factor. The HF calculations employ spherical Gaussian functions (SGFs) which are the curved-space analogs of Cartesian Gaussian functions. At low densities, the electrons become relatively localized into Wigner crystals, and the natural SGF centers are found by solving the Thomson problem (i.e., the minimum-energy arrangement of n point charges) on the 3-sphere for various values of n. We have found 11 special values of n whose Thomson sites are equivalent. Three of these are the vertices of four-dimensional Platonic solids — the hyper-tetrahedron (n = 5), the hyper-octahedron (n = 8), and the 24-cell (n = 24) — and a fourth is a highly symmetric structure (n = 13) which has not previously been reported. By calculating the harmonic frequencies of the electrons around their equilibrium positions, we also find the first-order vibrational corrections to the Thomson energy.
A rationalization of unusually late transition structures for dication fragmentations
Publisher: Elsevier BV
Date: 05-1987
The potential energy surface for the [C2H2O]+˙ system: The ketene radical cation [CH2CO]+˙ and its isomers
Publisher: Wiley
Date: 12-1984
Decomposition of exchange-correlation energies
Publisher: Elsevier BV
Date: 10-1999
Calculating molecular vibrational spectra beyond the harmonic approximation
Publisher: Springer Science and Business Media LLC
Date: 27-04-2007
Atomic and molecular intracules for excited states
Publisher: AIP Publishing
Date: 05-04-2004
DOI: 10.1063/1.1690233
Abstract: Intracules in position space, momentum space and phase space have been calculated for low-lying excited states of the He atom, Be atom, formaldehyde and butadiene. The phase-space intracules (Wigner intracules) provide significantly more information than the position- and momentum-space intracules, particularly for the Be atom. Exchange effects are investigated through the differences between corresponding singlet and triplet states.
DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science
Publisher: Royal Society of Chemistry (RSC)
Date: 2022
DOI: 10.1039/D2CP02827A
Abstract: In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method developers and practitioners.
Q-Chem 2.0: a high-performanceab initio electronic structure program package
Publisher: Wiley
Date: 2000
DOI: 10.1002/1096-987X(200012)21:16<1532::AID-JCC10>3.0.CO;2-W
Chemistry in one dimension
Publisher: Royal Society of Chemistry (RSC)
Date: 2015
DOI: 10.1039/C4CP03571B
Abstract: Orbital basis functions in a one-dimensional triatomic molecule ABC.
Intracule functional models. V. Recurrence relations for two-electron integrals in position and momentum space
Publisher: Royal Society of Chemistry (RSC)
Date: 2011
DOI: 10.1039/C0CP02154G
Abstract: The approach used by Ahlrichs [Phys. Chem. Chem. Phys., 2006, 8, 3072] to derive the Obara-Saika recurrence relation (RR) for two-electron integrals over Gaussian basis functions, is used to derive an 18-term RR for six-dimensional integrals in phase space and 8-term RRs for three-dimensional integrals in position or momentum space. The 18-term RR reduces to a 5-term RR in the special cases of Dot and Posmom intracule integrals in Fourier space. We use these RRs to show explicitly how to construct Position, Momentum, Omega, Dot and Posmom intracule integrals recursively.
Density Functional Partitions
Publisher: American Chemical Society (ACS)
Date: 1996
DOI: 10.1021/JP963467Y
Correlation energy of two electrons in the high-density limit
Publisher: AIP Publishing
Date: 22-12-2009
DOI: 10.1063/1.3275519
Abstract: We consider the high-density-limit correlation energy Ec in D≥2 dimensions for the S1 ground states of three two-electron systems: helium (in which the electrons move in a Coulombic field), spherium (in which they move on the surface of a sphere), and hookium (in which they move in a quadratic potential). We find that the Ec values are strikingly similar, depending strongly on D but only weakly on the external potential. We conjecture that for large D, the limiting correlation energy Ec∼−δ2/8 in any confining external potential, where δ=1/(D−1).
The performance of the Becke—Lee—Yang—Parr (B—LYP) density functional theory with various basis sets
Publisher: Elsevier BV
Date: 09-1992
Transformation of α-Tocopherol (Vitamin E) and Related Chromanol Model Compounds into Their Phenoxonium Ions by Chemical Oxidation with the Nitrosonium Cation
Publisher: American Chemical Society (ACS)
Date: 16-11-2005
DOI: 10.1021/JO0517951
Abstract: [reaction: see text] Alpha-tocopherol (alpha-TOH), the main oil component making up vitamin E, and its nonnatural solid 6-hydroxy-2,2,5,7,8-pentamethylchroman and 6-hydroxy-2,5,7,8-tetramethylchroman-2-carboxylic acid structurally related analogues were oxidized quantitatively with 2 mol equiv of NO+ SbF6(-) in CH3CN at 233 K to form phenoxonium cations (alpha-TO+ SbF6(-)) in a chemically reversible two-electron/one-proton process. Solution-phase infrared spectroscopy, 1H and 13C NMR spectroscopy, and corresponding theoretical calculations of the spectroscopic data using density-based and wave-function-based models support the identity of the remarkably stable phenoxonium cations. The presence of an oxygen atom in the para position to the hydroxyl group and the chromanol ring structure appear to be important factors in stabilization of the phenoxonium ions, which raises the interesting possibility that the cations play a crucial role in the mode of action of vitamin E in biological systems. Although the phenoxonium cations are reactive toward nucleophiles such as water, they may be moderately stable in the hydrophobic (lipophilic) environment where vitamin E is known to occur naturally.
Efficient computation of two-electron - repulsion integrals and their nth-order derivatives using contracted Gaussian basis sets
Publisher: American Chemical Society (ACS)
Date: 07-1990
DOI: 10.1021/J100377A031
Two‐electron repulsion integrals over Gaussian s functions
Publisher: Wiley
Date: 12-1991
The prism algorithm for two‐electron integrals
Publisher: Wiley
Date: 12-1991
The role of exchange in systematic DFT errors for some organic reactions
Publisher: Royal Society of Chemistry (RSC)
Date: 2009
DOI: 10.1039/B818412G
Abstract: Serious (up to 87 kJ mol(-1)) systematic DFT errors in a series of isodesmic reactions are found to be due to the DFT exchange component, and can be largely corrected by substitution of the DFT exchange energy with the Fock exchange energy.
Communication: Hartree-Fock description of excited states of H2
Publisher: AIP Publishing
Date: 19-09-2014
DOI: 10.1063/1.4896182
Abstract: Hartree-Fock (HF) theory is most often applied to study the electronic ground states of molecular systems. However, with the advent of numerical techniques for locating higher solutions of the self-consistent field equations, it is now possible to examine the extent to which such mean-field solutions are useful approximations to electronic excited states. In this Communication, we use the maximum overlap method to locate 11 low-energy solutions of the HF equation for the H2 molecule and we find that, with only one exception, these yield surprisingly accurate models for the low-lying excited states of this molecule. This finding suggests that the HF solutions could be useful first-order approximations for correlated excited state wavefunctions.
Avoiding Negligible Shell Pairs and Quartets in Electronic Structure Calculations
Publisher: American Chemical Society (ACS)
Date: 17-01-2023
Interfacing Q‐Chem and CHARMM to perform QM/MM reaction path calculations
Publisher: Wiley
Date: 02-03-2007
DOI: 10.1002/JCC.20587
Abstract: A hybrid quantum mechanical/molecular mechanical (QM/MM) potential energy function with Hartree-Fock, density functional theory (DFT), and post-HF (RIMP2, MP2, CCSD) capability has been implemented in the CHARMM and Q-Chem software packages. In addition, we have modified CHARMM and Q-Chem to take advantage of the newly introduced replica path and the nudged elastic band methods, which are powerful techniques for studying reaction pathways in a highly parallel (i.e., parallel arallel) fashion, with each pathway point being distributed to a different node of a large cluster. To test our implementation, a series of systems were studied and comparisons were made to both full QM calculations and previous QM/MM studies and experiments. For instance, the differences between HF, DFT, MP2, and CCSD QM/MM calculations of H2O...H2O, H2O...Na+, and H2O...Cl- complexes have been explored. Furthermore, the recently implemented polarizable Drude water model was used to make comparisons to the popular TIP3P and TIP4P water models for doing QM/MM calculations. We have also computed the energetic profile of the chorismate mutase catalyzed Claisen rearrangement at various QM/MM levels of theory and have compared the results with previous studies. Our best estimate for the activation energy is 8.20 kcal/mol and for the reaction energy is -23.1 kcal/mol, both calculated at the MP2/6-31+G(d)//MP2/6-31+G(d)/C22 level of theory.
Long-Lived Radical Cations as Model Compounds for the Reactive One-Electron Oxidation Product of Vitamin E
Publisher: American Chemical Society (ACS)
Date: 29-07-2008
DOI: 10.1021/JP804135E
Abstract: Heterocyclic compounds with structures similar to vitamin E, but without the hydroxyl hydrogen atom, were synthesized and their electrochemical behavior examined in acetonitrile solutions and as solids in aqueous solutions of varying pH by attaching the compounds to the surface of a glassy carbon electrode. Compound 1, containing a fully methylated aromatic ring was found to be the most long-lived following one-electron oxidation, with its radical cation (1+*) surviving in acidic aqueous solutions and able to be isolated as a salt, 1+*(SbF6-), when reacted with NOSbF6 in CH3CN. Electrochemical, UV-vis and FTIR experiments on 1+*, in addition to the results from theoretical calculations, indicated that the electrochemical, electronic and structural properties of 1+* are very similar to those of the radical cation of vitamin E.
Preliminary results on the performance of a family of density functional methods
Publisher: AIP Publishing
Date: 15-11-1992
DOI: 10.1063/1.463975
Abstract: The performance of six density functional methods is examined for a set of 32 small neutral molecular systems. The Kohn–Sham orbitals were obtained using the 6-31G* basis set, without employing any auxiliary fitting procedures. Atomization energies were calculated by each density functional method, as well as by Hartree–Fock, MP2, and QCISD using the same basis. Comparisons with experimental results are summarized for each method. Two of the density functional methods give excellent agreement with experiment, while none of the other density functional or ab initio methods give acceptable results.
A standard grid for density functional calculations
Publisher: Elsevier BV
Date: 07-1993
The efficient transformation of (m0|n0) to (ab|cd) two-electron repulsion integrals
Publisher: Elsevier BV
Date: 04-1993
Picosecond time-resolved infrared study of 2-aminopurine ionisation in solution
Publisher: Springer Science and Business Media LLC
Date: 09-2007
DOI: 10.1039/B705801B
Abstract: Two photon ionisation of 2-aminopurine (2AP) has been monitored following 267 nm irradiation in neutral and acidic aqueous solutions using picosecond time-resolved infrared spectroscopy (ps-TRIR). The transient infrared spectra obtained in neutral and acidic conditions show significant differences that are consistent with the formation of different species, namely the 2AP radical cation, 2AP+*, in acidic conditions and the uncharged radical, 2AP*(-H+), in neutral conditions. The ps-TRIR data indicate that deprotonation of 2AP+* in neutral solution takes place within <2 ps following photoionisation. DFT calculations (EDF1/6-31+G*) were used to support the assignment of the intermediates observed in these spectroscopic experiments.
Simple Models for Difficult Electronic Excitations
Publisher: American Chemical Society (ACS)
Date: 14-02-2018
Abstract: We present a single-determinant approach to three challenging topics in the chemistry of excited states: double excitations, charge-transfer states, and conical intersections. The results are obtained by using the Initial Maximum Overlap Method (IMOM) which is a modified version of the Maximum Overlap Method (MOM). The new algorithm converges better than the original, especially for these difficult problems. By considering several case studies, we show that a single-determinant framework provides a simple and accurate alternative for modeling excited states in cases where other low-cost methods, such as CIS and TD-DFT, either perform poorly or fail completely.
How does a dication lose a proton?
Publisher: American Chemical Society (ACS)
Date: 08-1988
DOI: 10.1021/JA00224A012
Q‐Chem: an engine for innovation
Publisher: Wiley
Date: 12-11-2012
DOI: 10.1002/WCMS.1122
Benchmark correlation energies for small molecules
Publisher: Informa UK Limited
Date: 20-03-2005
The ACDCP model for estimating the kinetic energy release and transition structure bond length in the fragmentation of a diatomic dication
Publisher: Elsevier BV
Date: 06-1988
Two-Electron Integrals over Gaussian Geminals
Publisher: American Chemical Society (ACS)
Date: 26-09-2016
Abstract: The evaluation of contracted two-electron integrals over a Gaussian geminal operator is pivotal to erse quantum chemistry methods. In this article, using the unique factorization properties and the sparsity of these integrals, a novel, near-optimal computation algorithm is presented. Our method employs a combination of recently developed upper bounds, recurrence relations in the spirit of the Head-Gordon-Pople approach, and late- and early-contraction paths in the PRISM style. A detailed study of the FLOP (floating-point operations) cost reveals that the new algorithm is computationally much cheaper than any other previous scheme.
Approaching the Hartree–Fock limit by perturbative methods
Publisher: AIP Publishing
Date: 15-06-2009
DOI: 10.1063/1.3152864
Abstract: We describe perturbative methods for improving finite-basis Hartree–Fock calculations toward the complete-basis limit. The best method appears to offer quadratic error reduction and preliminary numerical applications demonstrate that remarkably accurate Hartree–Fock energies can be obtained.
Uniform electron gases. II. The generalized local density approximation in one dimension
Publisher: AIP Publishing
Date: 17-03-2014
DOI: 10.1063/1.4867910
Abstract: We introduce a generalization (gLDA) of the traditional Local Density Approximation (LDA) within density functional theory. The gLDA uses both the one-electron Seitz radius rs and a two-electron hole curvature parameter η at each point in space. The gLDA reduces to the LDA when applied to the infinite homogeneous electron gas but, unlike the LDA, it is also exact for finite uniform electron gases on spheres. We present an explicit gLDA functional for the correlation energy of electrons that are confined to a one-dimensional space and compare its accuracy with LDA, second- and third-order Møller-Plesset perturbation energies, and exact calculations for a variety of inhomogeneous systems.
Intracule Functional Theory
Publisher: IMPERIAL COLLEGE PRESS
Date: 08-2011
Exact wave functions for concentric two-electron systems
Publisher: Elsevier BV
Date: 2014
MP2[V] – A Simple Approximation to Second-Order Møller–Plesset Perturbation Theory
Publisher: American Chemical Society (ACS)
Date: 27-03-2015
Abstract: We propose a simplified variant of the dual-basis MP2[K] scheme [ J. Chem. Phys. 2011, 134, 081103] that bootstraps a small-basis MP2 result to a large-basis one. This simplified method, which we call MP2[V], assumes the occupied orbitals are adequately described by the smaller basis, and, therefore, only the relaxation of the virtual orbitals is considered when shifting to the larger basis. Numerical tests on several organic reactions and noncovalent interactions show that MP2[V] yields absolute and relative energies that are in excellent agreement with the conventional large-basis MP2 calculations but in a small fraction of the time.
Many-Electron Integrals over Gaussian Basis Functions. I. Recurrence Relations for Three-Electron Integrals
Publisher: American Chemical Society (ACS)
Date: 30-03-2016
Abstract: Explicitly correlated F12 methods are becoming the first choice for high-accuracy molecular orbital calculations and can often achieve chemical accuracy with relatively small Gaussian basis sets. In most calculations, the many three- and four-electron integrals that formally appear in the theory are avoided through judicious use of resolutions of the identity (RI). However, for the intrinsic accuracy of the F12 wave function to not be jeopardized, the associated RI auxiliary basis set must be large. Here, inspired by the Head-Gordon-Pople and PRISM algorithms for two-electron integrals, we present an algorithm to directly compute three-electron integrals over Gaussian basis functions and a very general class of three-electron operators without invoking RI approximations. A general methodology to derive vertical, transfer, and horizontal recurrence relations is also presented.
Intracule functional models. II. Analytically integrable kernels
Publisher: AIP Publishing
Date: 10-10-2007
DOI: 10.1063/1.2795694
Abstract: We present, within the framework of intracule functional theory (IFT), a class of kernels whose correlation integrals can be found in closed form. This approach affords three major advantages over other kernels that we have considered previously ease of implementation, computational efficiency, and numerical stability. We show that even the simplest member of the class yields reasonable estimates of the correlation energies of 18 atomic and 56 molecular systems and we conclude that this kernel class will prove useful in the development of future IFT models.
A new gradient-corrected exchange functional
Publisher: Informa UK Limited
Date: 10-1996
Electron correlation in Hooke’s law atom in the high-density limit
Publisher: AIP Publishing
Date: 03-2005
DOI: 10.1063/1.1862237
Abstract: Closed-form expressions for the first three terms in the perturbation expansion of the exact energy and Hartree–Fock energy of the lowest singlet and triplet states of the Hooke’s law atom are found. These yield elementary formulas for the exact correlation energies (−49.7028 and −5.80765mEh) of the two states in the high-density limit and lead to a pair of necessary conditions on the exact correlation kernel G(w) in Hartree–Fock–Wigner theory.
Two Electrons on a Hypersphere: A Quasiexactly Solvable Model
Publisher: American Physical Society (APS)
Date: 18-09-2009
Modeling the potential of a charge distribution
Publisher: AIP Publishing
Date: 05-1992
DOI: 10.1063/1.462530
Abstract: We describe a numerically straightforward method for obtaining a model distribution whose potential is as close as possible, in a least-squares sense, to that of a known charge distribution.
Invariance of the Correlation Energy at High Density and Large Dimension in Two-Electron Systems
Publisher: American Physical Society (APS)
Date: 07-09-2010
KWIK: Coulomb Energies in O(N) Work
Publisher: American Chemical Society (ACS)
Date: 1996
DOI: 10.1021/JP952841B
Two-electron distribution functions and intracules
Publisher: Springer Science and Business Media LLC
Date: 06-2003
Decay behavior of least-squares coefficients in auxiliary basis expansions
Publisher: AIP Publishing
Date: 08-08-2005
DOI: 10.1063/1.2000867
Abstract: Many quantum chemical methods, both wave function and density based, rely on an expansion of elements of the electron density in an auxiliary basis. However, little is known about the analytical behavior of the expansion coefficients and, in particular, about their rate of decay with distance. We discuss an exactly solvable model system and characterize the expansion coefficients for various fitting metrics and various dimensionalities of the auxiliary basis. In the case of Coulomb fitting, we find that the decay rate depends critically on the effective dimensionality D of the auxiliary basis, varying from O(r−1) to O(r−3) to O(e−ζr) for D=1, 2, or 3.
Economical Models for Electron Densities
Publisher: American Chemical Society (ACS)
Date: 31-10-2023
An algorithm for the location of branching points on reaction paths
Publisher: Wiley
Date: 07-1988
Isomers of C20. Dramatic effect of gradient corrections in density functional theory
Publisher: Elsevier BV
Date: 11-1993
Resolutions of the Coulomb Operator: IV. The Spherical Bessel Quasi-Resolution
Publisher: American Chemical Society (ACS)
Date: 16-03-2011
DOI: 10.1021/CT200115T
Methods for constructing Stewart atoms
Publisher: Elsevier BV
Date: 04-2000
A tensor approach to two-electron matrix elements
Publisher: AIP Publishing
Date: 07-1997
DOI: 10.1063/1.474359
Abstract: We present a new algorithm, the COLD PRISM, for computing matrix elements in molecular orbital calculations. Whereas traditional approaches form these from two-electron repulsion integrals (ERIs) which, in turn, are formed from shell-pair data, we introduce several alternative paths that do not involve ERIs as intermediates. Tensor multiplication can be used as the basic arithmetic operation on all of the new PRISM paths and the associativity of tensor multiplication plays a key role. We have implemented our approach in the Q-Chem program.
A new expansion of the Coulomb interaction
Publisher: Elsevier BV
Date: 05-1997
The continuous fast multipole method
Publisher: Elsevier BV
Date: 11-1994
Chemistry without Coulomb tails
Publisher: Elsevier BV
Date: 05-1996
Variable Scan Rate Cyclic Voltammetry and Theoretical Studies on Tocopherol (Vitamin E) Model Compounds
Publisher: American Chemical Society (ACS)
Date: 08-05-2008
DOI: 10.1021/JP710995N
Abstract: Variable scan rate (0.1-500 V s(-1)) cyclic voltammetry experiments were performed on a series of model tocopherol (vitamin E) compounds with differing degrees of methyl substitution around the aromatic (phenolic) ring. alpha-Tocopherol, with a fully methylated aromatic ring, produced stable phenoxonium cations upon oxidation in CH3CN, and was modeled via an ECE mechanism (where "E" represents an electron transfer and "C" a chemical step). Compounds with less methyl substitution around the aromatic ring were more reactive following oxidation, and formed additional oxidation products (hemiketals and p-quinones), and were modeled according to a more complicated ECECC mechanism. The equilibrium and rate constants associated with the chemical steps were estimated by digital simulations of the variable scan rate data over a range of temperatures ( T = 253-313 K) in acetonitrile containing 0.5 M Bu4NPF6 as the supporting electrolyte. The relative lifetimes of the phenoxonium cations of tocol and the tocopherols were compared with theoretical results obtained from molecular orbital calculations.
Correlation energy of two electrons in a ball
Publisher: AIP Publishing
Date: 17-06-2010
DOI: 10.1063/1.3455706
Abstract: We study the ground-state correlation energy Ec of two electrons of opposite spin confined within a D-dimensional ball (D≥2) of radius R. In the high-density regime, we report accurate results for the exact and restricted Hartree–Fock energy, using a Hylleraas-type expansion for the former and a simple polynomial basis set for the latter. By investigating the exact limiting correlation energy Ec(0)=limR→0Ec for various values of D, we test our recent conjecture [P.-F. Loos and P. M. W. Gill, J. Chem. Phys. 131, 241101 (2009)] that in the large-D limit, Ec(0)∼−δ2/8 for any spherically symmetric confining external potential, where δ=1/(D−1).
Wigner intracule for the Kellner helium‐like ions
Publisher: Wiley
Date: 2004
DOI: 10.1002/QUA.20125
Thinking outside the box: The uniform electron gas on a hypersphere
Publisher: AIP Publishing
Date: 07-12-2011
DOI: 10.1063/1.3665393
Abstract: We discuss alternative homogeneous electron gas systems in which a finite number n of electrons are confined to a D-dimensional sphere. We derive the first few terms of the high-density (rs → 0, where rs is the Seitz radius) energy expansions for these systems and show that, in the thermodynamic limit (n → ∞), these terms become identical to those of D-dimensional jellium.
Resolutions of the Coulomb Operator: V. The Long-Range Ewald Operator
Publisher: American Chemical Society (ACS)
Date: 28-06-2011
DOI: 10.1021/CT200305N
Abstract: We show that the long-range Ewald operator can be resolved as erf(ωr12)/r12 = ∑k ϕk*(r1) ϕk(r2), where ϕk is proportional to the product of a spherical Bessel function and a spherical harmonic. We demonstrate the use of this new resolution by calculating the long-range Coulomb energy of the nanodiamond crystallite C84H64 and the long-range exchange energy of the graphene C96H24. The resolution appears particularly effective for long-range exchange calculations.
Intracule functional models. IV. Basis set effects
Publisher: AIP Publishing
Date: 24-04-2009
DOI: 10.1063/1.3122422
Abstract: We have calculated position and dot intracules for a series of atomic and molecular systems, starting from an unrestricted Hartree–Fock wave function, expanded using the STO-3G, 6–31G, 6–311G, 6-311++G, 6-311++G(d,p), 6-311++G(3d,3p), and 6-311++G(3df,3pd) basis sets as well as the nonpolarized part of Dunning’s cc-pV5Z basis. We find that the basis set effects on the intracules are small and that correlation energies from the dot intracule ansatz are remarkably insensitive to the basis set quality. Mean absolute errors in correlation energies across the G1 data set agree to within 2 mEh for all basis sets tested.
Application of semiempirical molecular orbital theory to cationic intermediates involved in the solvolysis of 1-halobicyclo[n.1.1]alkanes
Publisher: American Chemical Society (ACS)
Date: 09-1988
DOI: 10.1021/JO00253A030
Exact exchange functional for the hydrogen atom
Publisher: American Physical Society (APS)
Date: 03-1993
Rapid evaluation of two-center two-electron integrals
Publisher: Wiley
Date: 2000
DOI: 10.1002/1096-987X(200012)21:16<1505::AID-JCC7>3.0.CO;2-4
A rotationally invariant procedure for density functional calculations
Publisher: Elsevier BV
Date: 08-1994
Explicit-r12 correlation methods and local correlation methods
Publisher: Royal Society of Chemistry (RSC)
Date: 2008
DOI: 10.1039/B808067B
Reply to Comment on “Computing molecular electrostatic potentials with the PRISM algorithm”
Publisher: Elsevier BV
Date: 02-1994
Intracule functional models: I. Angle-corrected correlation kernels
Publisher: Royal Society of Chemistry (RSC)
Date: 2007
DOI: 10.1039/B709513A
Abstract: We explore the merits of applying a simple angle-dependent correction to the correlation kernel within the framework of Hartree-Fock-Wigner theory. Based on numerical results for the first eighteen atoms, we conclude that such a correction offers a significant improvement over the action kernel that we and others have explored previously.
Resolutions of the Coulomb operator : Part III. Reduced-rank Schrödinger equations
Publisher: Royal Society of Chemistry (RSC)
Date: 2009
DOI: 10.1039/B910613H
Abstract: We consider a modified Schrödinger equation wherein the electron-electron repulsion terms r(ij)(-1) are approximated by truncated one-particle resolutions. Numerical results for the He atom and H2 molecule at the Hartree-Fock, second-order Møller-Plesset, and configuration interaction levels show that the solutions of the resulting reduced-rank Schrödinger equations converge rapidly, and that even low-rank approximations can yield energies with chemical accuracy.
Intracule functional models : Part III. The dot intracule and its Fourier transform
Publisher: Royal Society of Chemistry (RSC)
Date: 2008
DOI: 10.1039/B803919D
Abstract: The dot intracule D(x) of a system gives the Wigner quasi-probability of finding two of its electrons with u.v = x, where u and v are the interelectronic distance vectors in position and momentum space, respectively. In this paper, we discuss D(x) and show that its Fourier transform d(k) can be obtained in closed form for any system whose wavefunction is expanded in a Gaussian basis set. We then invoke Parseval's theorem to transform our intracule-based correlation energy method into a d(k)-based model that requires, at most, a one-dimensional quadrature.
EDF2: A Density Functional for Predicting Molecular Vibrational Frequencies
Publisher: CSIRO Publishing
Date: 2004
DOI: 10.1071/CH03263
Abstract: The majority of calculations of molecular vibrational spectra are based on the harmonic approximation but are compared (usually after empirical scaling) with experimental anharmonic frequencies. Any agreement that is observed in such cases must be attributable to fortuitous cancellation of errors and it would certainly be preferable to develop a more rigorous computational approach. In this paper, we introduce a new density functional model (EDF2) that is explicitly designed to yield accurate harmonic frequencies, and we present numerical results for a wide variety of molecules whose experimental harmonic frequencies are known. The EDF2 model is found to be significantly more accurate than other DFT models and competitive with the computationally expensive CCSD(T) method.
An improved criterion for evaluating the efficiency of two-electron integral algorithms
Publisher: Elsevier BV
Date: 04-1993
Distribution of r·p in Atomic Systems
Publisher: American Chemical Society (ACS)
Date: 14-10-2010
DOI: 10.1021/JP107658A
Abstract: We present formulas for computing the probability distribution of the posmom s = r · p in atoms, when the electronic wave function is expanded in a single particle Gaussian basis. We study the posmom density, S(s), for the electrons in the ground states of 36 lightest atoms (H-Kr) and construct an empirical model for the contribution of each atomic orbital to the total S(s). The posmom density provides unique insight into types of trajectories electrons may follow, complementing existing spectroscopic techniques that provide information about where electrons are (X-ray crystallography) or where they go (Compton spectroscopy). These, a priori, predictions of the quantum mechanically observable posmom density provide an challenging target for future experimental work.
Distributions of r1·r2 and p1·p2 in Atoms
Publisher: American Chemical Society (ACS)
Date: 19-04-2012
DOI: 10.1021/CT300218C
Abstract: We consider the two-electron position and momentum dot products, α = r1·r2 and β = p1·p2, and present a method for extracting their distributions, A(α) and B(β), from molecular wave functions built on Gaussian basis functions. The characteristics of the Hartree-Fock AHF(α) and BHF(β) for He and the first-row atoms are investigated, with particular attention to the effects of Pauli exchange. The effects of electron correlation are studied via the holes, ΔA(α) ≡ A(α) - AHF(α) and ΔB(β) ≡ B(β) - BHF(β), and the hole structures are rationalized in terms of radial and angular correlation effects. Correlation effects are also examined through an analysis of the first moments of A(α), AHF(α), B(β), and BHF(β).
Chem1D: a software package for electronic structure calculations on one-dimensional systems
Publisher: Informa UK Limited
Date: 10-03-2015
Assessment of DFT Methods for Transition Metals with the TMC151 Compilation of Data Sets and Comparison with Accuracies for Main-Group Chemistry
Publisher: American Chemical Society (ACS)
Date: 31-05-2019
Abstract: In the present study, we have gathered a collection (that we term TMC151) of accurate reference data for transition-metal reactions for the assessment of quantum chemistry methods. It comprises diatomic dissociation energies and reaction energies and barriers for prototypical transition-metal reactions. Our assessment of a erse range of different types of DFT methods shows that the most accurate functionals include ωB97M-V, ωB97X-V, MN15, and B97M-rV. Notably, they have also been previously validated to be highly robust for main-group chemistry. Nevertheless, even these methods show substantially worse accuracies for transition metals than for main-group chemistry. For less accurate methods, there is not a good correlation between their accuracies for main-group and transition-metal chemistries. Thus, in the development of new DFT, it is important to assess the accuracies for both types of data. In this regard, we have formulated the TMC34 model for efficient assessment of the performance for transition metals, which complements our previously developed MG8 model for main-group chemistry. Together, they provide a cost-effective means for initial assessment of new methodologies.
Related Organisations
Related Funding Activities
Discovery Projects - Grant ID: DP0771978
Start Date: 2007
End Date: 12-2010
Amount: $503,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP0984806
Start Date: 2009
End Date: 12-2011
Amount: $280,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP140104071
Start Date: 2014
End Date: 12-2017
Amount: $330,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP1094170
Start Date: 2010
End Date: 12-2012
Amount: $440,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP160100246
Start Date: 2016
End Date: 12-2021
Amount: $717,400.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP0664466
Start Date: 2006
End Date: 08-2009
Amount: $238,000.00
Funder: Australian Research Council
View Funded ActivityDiscovery Projects - Grant ID: DP120104740
Start Date: 2012
End Date: 06-2016
Amount: $325,000.00
Funder: Australian Research Council
View Funded Activity