Author

# Samuel Francis Boys

Other affiliations: University of London

Bio: Samuel Francis Boys is an academic researcher from University of Cambridge. The author has contributed to research in topics: Wave function & Antisymmetric relation. The author has an hindex of 20, co-authored 33 publications receiving 22825 citations. Previous affiliations of Samuel Francis Boys include University of London.

##### Papers

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TL;DR: In this paper, a direct difference method for the computation of molecular interactions has been based on a bivariational transcorrelated treatment, together with special methods for the balancing of other errors.

Abstract: A new direct difference method for the computation of molecular interactions has been based on a bivariational transcorrelated treatment, together with special methods for the balancing of other errors. It appears that these new features can give a strong reduction in the error of the interaction energy, and they seem to be particularly suitable for computations in the important region near the minimum energy. It has been generally accepted that this problem is dominated by unresolved difficulties and the relation of the new methods to these apparent difficulties is analysed here.

19,483 citations

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1,180 citations

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1,060 citations

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TL;DR: In this paper, it was shown that the only obstacle to the evaluation of wave functions of any required degree of accuracy is the labour of computation, and that all necessary integrals can be explicitly evaluated.

Abstract: This communication deals with the general theory of obtaining numerical electronic wave functions for the stationary states of atoms and molecules. It is shown that by taking Gaussian functions, and functions derived from these by differentiation with respect to the parameters, complete systems of functions can be constructed appropriate to any molecular problem, and that all the necessary integrals can be explicitly evaluated. These can be used in connexion with the molecular orbital method, or localized bond method, or the general method of treating linear combinations of many Slater determinants by the variational procedure. This general method of obtaining a sequence of solutions converging to the accurate solution is examined. It is shown that the only obstacle to the evaluation of wave functions of any required degree of accuracy is the labour of computation. A modification of the general method applicable to atoms is discussed and considered to be extremely practicable.

1,036 citations

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TL;DR: In this article, it was shown that if any factors of the form exp(c ij ) are included in the expansion functions there are explicit formulas for all the necessary many-dimensional integrals.

Abstract: Some years ago the author proved that explicit formulae could be obtained for all the many-dimensional integrals occurring in variational solutions of Schrodinger’s many-electron equation for molecules if the expansion functions are constructed from factors of polynomials and radial Gaussian functions about any centres. These have been applied both directly and indirectly in calculations on molecular structure. An extension to this analysis is now reported and it is shown that if any factors of the form exp (– cr ij ) are included in the expansion functions there are explicit formulas for all the necessary many-dimensional integrals. This will make possible both direct and indirect calculations with a more powerful class of expansion functions which appear as if they may give faster convergence for the hitherto very troublesome electronic correlation aspects of many-dimensional wave functions.

254 citations

##### Cited by

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TL;DR: A new density functional of the generalized gradient approximation (GGA) type for general chemistry applications termed B97‐D is proposed, based on Becke's power‐series ansatz from 1997, and is explicitly parameterized by including damped atom‐pairwise dispersion corrections of the form C6 · R−6.

Abstract: A new density functional (DF) of the generalized gradient approximation (GGA) type for general chemistry applications termed B97-D is proposed. It is based on Becke's power-series ansatz from 1997 and is explicitly parameterized by including damped atom-pairwise dispersion corrections of the form C(6) x R(-6). A general computational scheme for the parameters used in this correction has been established and parameters for elements up to xenon and a scaling factor for the dispersion part for several common density functionals (BLYP, PBE, TPSS, B3LYP) are reported. The new functional is tested in comparison with other GGAs and the B3LYP hybrid functional on standard thermochemical benchmark sets, for 40 noncovalently bound complexes, including large stacked aromatic molecules and group II element clusters, and for the computation of molecular geometries. Further cross-validation tests were performed for organometallic reactions and other difficult problems for standard functionals. In summary, it is found that B97-D belongs to one of the most accurate general purpose GGAs, reaching, for example for the G97/2 set of heat of formations, a mean absolute deviation of only 3.8 kcal mol(-1). The performance for noncovalently bound systems including many pure van der Waals complexes is exceptionally good, reaching on the average CCSD(T) accuracy. The basic strategy in the development to restrict the density functional description to shorter electron correlation lengths scales and to describe situations with medium to large interatomic distances by damped C(6) x R(-6) terms seems to be very successful, as demonstrated for some notoriously difficult reactions. As an example, for the isomerization of larger branched to linear alkanes, B97-D is the only DF available that yields the right sign for the energy difference. From a practical point of view, the new functional seems to be quite robust and it is thus suggested as an efficient and accurate quantum chemical method for large systems where dispersion forces are of general importance.

23,058 citations

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TL;DR: The M06-2X meta-exchange correlation function is proposed in this paper, which is parametrized including both transition metals and nonmetals, and is a high-non-locality functional with double the amount of nonlocal exchange.

Abstract: We present two new hybrid meta exchange- correlation functionals, called M06 and M06-2X. The M06 functional is parametrized including both transition metals and nonmetals, whereas the M06-2X functional is a high-nonlocality functional with double the amount of nonlocal exchange (2X), and it is parametrized only for nonmetals.The functionals, along with the previously published M06-L local functional and the M06-HF full-Hartree–Fock functionals, constitute the M06 suite of complementary functionals. We assess these four functionals by comparing their performance to that of 12 other functionals and Hartree–Fock theory for 403 energetic data in 29 diverse databases, including ten databases for thermochemistry, four databases for kinetics, eight databases for noncovalent interactions, three databases for transition metal bonding, one database for metal atom excitation energies, and three databases for molecular excitation energies. We also illustrate the performance of these 17 methods for three databases containing 40 bond lengths and for databases containing 38 vibrational frequencies and 15 vibrational zero point energies. We recommend the M06-2X functional for applications involving main-group thermochemistry, kinetics, noncovalent interactions, and electronic excitation energies to valence and Rydberg states. We recommend the M06 functional for application in organometallic and inorganometallic chemistry and for noncovalent interactions.

22,326 citations

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TL;DR: In this paper, a direct difference method for the computation of molecular interactions has been based on a bivariational transcorrelated treatment, together with special methods for the balancing of other errors.

Abstract: A new direct difference method for the computation of molecular interactions has been based on a bivariational transcorrelated treatment, together with special methods for the balancing of other errors. It appears that these new features can give a strong reduction in the error of the interaction energy, and they seem to be particularly suitable for computations in the important region near the minimum energy. It has been generally accepted that this problem is dominated by unresolved difficulties and the relation of the new methods to these apparent difficulties is analysed here.

19,483 citations

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TL;DR: In this paper, an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so-called PBE generalized gradient functional with a predefined amount of exact exchange is presented.

Abstract: We present an analysis of the performances of a parameter free density functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amount of exact exchange. The results obtained for structural, thermodynamic, kinetic and spectroscopic (magnetic, infrared and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chemistry and condensed matter physics.

13,411 citations

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TL;DR: The re-optimization of a recently proposed long-range corrected hybrid density functional, omegaB97X-D, to include empirical atom-atom dispersion corrections yields satisfactory accuracy for thermochemistry, kinetics, and non-covalent interactions.

Abstract: We report re-optimization of a recently proposed long-range corrected (LC) hybrid density functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom–atom dispersion corrections. The resulting functional, ωB97X-D yields satisfactory accuracy for thermochemistry, kinetics, and non-covalent interactions. Tests show that for non-covalent systems, ωB97X-D shows slight improvement over other empirical dispersion-corrected density functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as ωB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.

9,184 citations