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  • 1
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 115 (2001), S. 9233-9242 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Multiplicative potentials, appropriate for adding to the non-multiplicative fractional orbital exchange term in the Kohn–Sham equations, are determined from correlated ab initio electron densities. The potentials are examined graphically and are used in conjunction with conventional thermochemical data to determine a new hybrid exchange-correlation functional, denoted B97-2. Calculations using B97-2 are compared with those from (a) the B97-1 functional [J. Chem. Phys. 109, 6264 (1998)], which has the same functional form and fraction of orbital exchange, but was fitted to just thermochemical data; and (b) the widely used B3LYP functional [J. Chem. Phys. 98, 5648 (1993)]. B97-2 atomization energies are close to those from B97-1; total electronic energies and ionization potentials are less accurate, but remain an improvement over B3LYP. Molecular structures from all three functionals are comparable. Static isotropic polarizabilities improve from B3LYP to B97-1 to B97-2; the B97-2 functional underestimates experimental values, which is consistent with the neglect of zero-point vibrational corrections. NMR shielding constants—determined as the conventional second derivative of the electronic energy—improve from B3LYP to B97-1 to B97-2. Shieldings determined directly from these DFT electron densities using the recently proposed MKS approach [Chem. Phys. Lett. 337, 341 (2001)] are two to three times more accurate than the conventional shieldings, and exhibit an analogous improvement across the three functionals. Classical reaction barriers for sixteen chemical reactions improve significantly from B3LYP to B97-1 to B97-2. The introduction of multiplicative potentials into semi-empirical hybrid functional development therefore appears beneficial. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 114 (2001), S. 3958-3967 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Exchange-correlation functionals are determined by constraining the potentials of flexible functional forms to be as parallel as possible to asymptotically vanishing ab initio exchange-correlation potentials. No thermochemical or gradient information is explicitly included in the fitting procedure. A range of spatial weightings is considered and the functionals are assessed by comparing with experiment and with the HCTH functional [J. Chem. Phys. 109, 6264 (1998)], which was determined by fitting to both potentials and to thermochemical and gradient data. Optimal thermochemistry, structures, and polarizabilities are simultaneously achieved by emphasizing an intermediate spatial region in the fit; an optimal functional is presented. The thermochemistry of this functional is less accurate than HCTH, although the structures of the fitting molecules are significantly improved. The mean absolute bond length error for 40 of the fitting molecules is 0.006 Å, a factor of 2 improvement over HCTH. The bond lengths of 16 diatomic radicals absent from the fitting data are also improved. For the difficult molecules FOOF, FNO2, O3, FO2, Cr(CO)6, and Ni(CO)4, the results are variable. The new functional improves the polarizabilities of 14 small molecules, compared to HCTH. It also improves electronic excitation energies to Rydberg states of N2, H2CO, and C6H6, although the errors remain significant, reflecting the incorrect asymptotic potential. To obtain optimal nuclear shielding constants, it is necessary to emphasize regions closer to the nuclei; a second functional is presented which gives improved shieldings compared to HCTH. By considering the dominant occupied-virtual excitation contributions to the paramagnetic shieldings in CO and H2O, analogies are drawn between our results and those of a recently proposed method for improving density functional shielding constants. © 2001 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 113 (2000), S. 5185-5192 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The theory is presented for asymptotically correcting the potentials of hybrid exchange-correlation functionals, i.e., those that include a fraction of orbital exchange. The Kohn–Sham equations involve a multiplicative potential due to the continuum part of the hybrid functional and a nonmultiplicative term due to the orbital exchange. In asymptotic regions the multiplicative σ-spin potential is corrected to take the form (CX−1)/r+εHOMO,σ+Iσ, where CX is the fraction of orbital exchange; εHOMO,σ is the σ-spin self-consistent highest occupied Kohn–Sham eigenvalue; and Iσ is an approximate ionization energy. For the hydrogen atom, the asymptotic correction leads to a potential that closely resembles the exact potential; the eigenvalue spectrum is intermediate between the Schrödinger and Hartree–Fock eigenvalues, reflecting the presence of orbital exchange. Kohn–Sham orbitals and eigenvalues determined from this procedure have been used to calculate singlet vertical excitation energies for CO, N2, H2CO, C2H4, and C6H6. The correction significantly improves excitation energies to Rydberg states, with mean absolute errors below 0.2 eV. However, despite including orbital exchange, the results do not represent an improvement over the results obtained by asymptotically correcting a recently developed GGA functional. The asymptotic correction is also shown to reduce static isotropic polarizabilities. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 4
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 112 (2000), S. 3507-3515 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The asymptotic behavior of the exchange potential is derived from the long-range form of the exchange-only Kohn–Sham equations. This is then used to correct the asymptotic potential of a conventional continuum exchange functional. For atomic systems the influence of the correction on the electronic energy can be rigorously determined using a well-known virial relationship; its effect is to make the continuum exchange more like Hartree–Fock exchange. For molecular systems the model nature of the potential leads to problems with translational non-invariance. Molecular energies are therefore not considered, although optimized molecular structures can still be determined, providing internal coordinates are used. The effect of the asymptotic correction is to slightly shorten the bond lengths, again indicating an increased Hartree–Fock character. Possible implications for functional development are considered. © 2000 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 5
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 10180-10189 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: Conventional continuum exchange-correlation functionals (e.g., local density approximation, generalized gradient approximation) offer a poor description of many response properties, such as static polarizabilities and single photon vertical excitation energies to Rydberg states. These deficiencies are related to errors in the virtual Kohn–Sham orbitals and eigenvalues, which arise due to a fundamental deficiency in the potentials of conventional continuum functionals. Namely, although these potentials approximately average over the exact integer discontinuity in energetically important regions, they fail to do so asymptotically, because they vanish. Our recent functional HCTH [J. Chem. Phys. 109, 6264 (1998)] was designed with this deficiency in mind, although its potential still fails to exhibit the appropriate asymptotic form. In this paper, we present a new procedure that explicitly corrects this asymptotic deficiency for any continuum functional. Self-consistent Kohn–Sham calculations are performed using a corrected potential, which equals the conventional potential δEXC[ρα,ρβ]/δρσ(r) in energetically important regions, but which asymptotically behaves in the required average manner −(1/r)+Iσ+εHOMO,σ. The quantity −(1/r) is determined using a nonlocal expression; Iσ is an approximate σ spin ionization potential; and εHOMO,σ is the highest occupied σ spin eigenvalue. By applying this correction to the HCTH potential, we accurately reproduce the hydrogen atom eigenvalue spectrum, without significantly changing the total energy. We determine corrected orbitals and eigenvalues for a variety of molecules, and use them to compute excitation energies and static polarizabilities. We compare the results with those from a variety of other exchange-correlation functionals. Excitations to Rydberg states are determined as accurately as those to valence states; for CO, N2, H2CO, and C2H4, mean absolute errors are less than 0.35 eV. The static isotropic polarizabilities of 14 small molecules are of MP2 quality. © 1998 American Institute of Physics.
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  • 6
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 109 (1998), S. 6264-6271 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We recently presented a new method for developing generalized gradient approximation (GGA) exchange-correlation energy functionals, using a least-squares procedure involving numerical exchange-correlation potentials and experimental energetics and nuclear gradients. In this paper we use the same method to develop a new GGA functional, denoted HCTH, based on an expansion recently suggested by Becke [J. Chem. Phys. 107, 8554 (1997)]. For our extensive training set, the new functional yields improved energetics compared to both the BLYP and B3LYP functionals [Phys. Rev. A 38, 3098 (1988); Phys. Rev. B 37, 785 (1988); J. Chem. Phys. 98, 5648 (1993); J. Phys. Chem. 98, 11623 (1994)]. The geometries of these systems, together with those of a set of transition metal compounds, are shown to be an improvement over the BLYP functional, while the reaction barriers for six hydrogen abstraction reactions are comparable to those of B3LYP. These improvements are achieved without introducing any fraction of exact orbital exchange into the new functional. We have also re-optimized the functional of Becke—which does involve exact exchange—for use in self-consistent calculations. © 1998 American Institute of Physics.
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  • 7
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 107 (1997), S. 1536-1543 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We compute molecular Hartree-Fock-Kohn-Sham correlation potentials from ab initio coupled-cluster densities via a modified Zhao, Morrison and Parr [Phys. Rev. A, 50, (1994) 2138] scheme involving exact exchange. We examine the potential for several small systems, and observe complex structure. By fitting a functional expansion to our potentials we obtain a closed-shell functional which is an improvement over other pure correlation functionals in Hartree-Fock-Kohn-Sham calculations. The leading term in our functional is dependent on the number of electrons. Our results lead us to question the utility of correlation defined within the Hartree-Fock-Kohn-Sham scheme, and to consider alternative partitionings of the exchange-correlation energy.© 1997 American Institute of Physics.
    Type of Medium: Electronic Resource
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  • 8
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 105 (1996), S. 9200-9213 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: We describe our implementation of the Zhao, Morrison, and Parr method [Phys. Rev. A 50, 2138 (1994)] for the calculation of molecular exchange-correlation potentials from high-level ab initio densities. The use of conventional Gaussian basis sets demands careful consideration of the value of the Lagrange multiplier associated with the constraint that reproduces the input density. Although formally infinite, we demonstrate that a finite value should be used in finite basis set calculations. The potential has been determined for Ne, HF, N2, H2O, and N2(1.5re), and compared with popular analytic potentials. We have then examined how well the Zhao, Morrison, Parr potential can be represented using a computational neural network. Assuming vxc=vxc(ρ), we incorporate the neural network into a regular Kohn–Sham procedure [Phys. Rev. A 140, 1133 (1965)] with encouraging results. The extension of this method to include density derivatives is briefly outlined. © 1996 American Institute of Physics.
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  • 9
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 108 (1998), S. 2545-2555 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: A procedure is presented for the possible systematic development of exchange-correlation functionals using ab initio electron densities and accurate total energies. For a training set of first row open- and closed-shell systems, densities are computed and are used to determine asymptotically vanishing exchange-correlation potentials. The new functional is then written as an expansion in products of the density and its gradient, and optimum expansion parameters are determined through a least squares fit involving both these potentials and accurate exchange-correlation energies. Unlike conventional functionals, the potential of the fitted functional approaches a non-zero value asymptotically, and this is achieved by introducing a self-consistently computed system-dependent shift into the fitting procedure. This shift represents the influence of the integer derivative discontinuity in the exact energy. The method has been used to determine a 21 term spin-polarized exchange-correlation functional using Brueckner Doubles or MP2 densities of 20 small systems. For those with open-shells the computed shifts are close to the hardness of the system, while for closed-shells they are considerably smaller than the hardness. These observations are consistent with theoretical requirements. A comparison of the new potential with conventional potentials highlights important differences in the inter-shell and asymptotic regions, while the values of the shifts and highest occupied self-consistent eigenvalues suggest improved asymptotic densities. The mean absolute errors in self-consistent total energies and optimized bond-lengths of systems in the training set are 0.003Eh and 0.01 Å, respectively. Comparable values are obtained for 12 first-row closed-shell systems outside the training set. Compared to conventional functionals, the new functional predicts a significantly improved classical barrier height for the hydrogen abstraction reaction H+H2→H2+H. © 1998 American Institute of Physics.
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  • 10
    Electronic Resource
    Electronic Resource
    College Park, Md. : American Institute of Physics (AIP)
    The Journal of Chemical Physics 104 (1996), S. 5555-5557 
    ISSN: 1089-7690
    Source: AIP Digital Archive
    Topics: Physics , Chemistry and Pharmacology
    Notes: The potential energy surface of the (H2O)5 water cluster is examined using Kohn–Sham density functional theory, Hartree–Fock theory and second-order Møller–Plesset theory. Two distinct minima on the energy surface may be interconverted through the transfer of two hydrogen atoms, representing a possible mechanism for ionic dissociation in water clusters. Our calculations suggest a concerted mechanism where the two hydrogen atoms move simultaneously through a late transition state. © 1996 American Institute of Physics.
    Type of Medium: Electronic Resource
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