Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set

In the past, basis sets for use in correlated molecular calculations have largely been taken from single configuration calculations. Recently, Almlof, Taylor, and co‐workers have found that basis sets of natural orbitals derived from correlated atomic calculations (ANOs) provide an excellent description of molecular correlation effects. We report here a careful study of correlation effects in the oxygen atom, establishing that compact sets of primitive Gaussian functions effectively and efficiently describe correlation effects i f the exponents of the functions are optimized in atomic correlated calculations, although the primitive (s p) functions for describing correlation effects can be taken from atomic Hartree–Fock calculations i f the appropriate primitive set is used. Test calculations on oxygen‐containing molecules indicate that these primitive basis sets describe molecular correlation effects as well as the ANO sets of Almlof and Taylor. Guided by the calculations on oxygen, basis sets for use in correlated atomic and molecular calculations were developed for all of the first row atoms from boron through neon and for hydrogen. As in the oxygen atom calculations, it was found that the incremental energy lowerings due to the addition of correlating functions fall into distinct groups. This leads to the concept of c o r r e l a t i o n c o n s i s t e n t b a s i s s e t s, i.e., sets which include all functions in a given group as well as all functions in any higher groups. Correlation consistent sets are given for all of the atoms considered. The most accurate sets determined in this way, [5s4p3d2f1g], consistently yield 99% of the correlation energy obtained with the corresponding ANO sets, even though the latter contains 50% more primitive functions and twice as many primitive polarization functions. It is estimated that this set yields 94%–97% of the total (HF+1+2) correlation energy for the atoms neon through boron.

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen

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.

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The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

A description of the ab initio quantum chemistry package GAMESS is presented. Chemical systems containing atoms through radon can be treated with wave functions ranging from the simplest closed-shell case up to a general MCSCF case, permitting calculations at the necessary level of sophistication. Emphasis is given to novel features of the program. The parallelization strategy used in the RHF, ROHF, UHF, and GVB sections of the program is described, and detailed speecup results are given. Parallel calculations can be run on ordinary workstations as well as dedicated parallel machines. © John Wiley & Sons, Inc.

General atomic and molecular electronic structure system

The generation and trapping of the high-temperature oxosilyliumyl cation radicals (28SiO+ and 29SiO+) in neon matrixes at 4 K; an ESR and ab initio CI theoretical investigation

Upon pyrolysis, vinylcyclopropane undergoes a rearrangement to cyclopentene1a which has been characterized as a firstorder reaction in the gas phase. Frey determined that log k (s-1) ) (13.5 49 600)/2.303RT for loss of vinylcyclopropane,1b and Wellington reported log k (s-1) ) (13.6 49 700)/2.303RT for formation of cyclopentene.1c Numerous studies reveal that geometric isomerization of starting material occurs 5-40 times faster than allylic rearrangement.2 In the simplest case, the Arrhenius parameters for the interconversion of cisand trans2-deuteriovinylcyclopropane are log k (s-1) ) (14.02 47 100/ 2.3RT.2b The mechanism of the geometric isomerization has been generally attributed to reversible formation of a biradical in which rotation around non-allylic bonds occurs faster than ring closure back to starting material. Because of the orbital overlap in the allylic moiety it is generally expected that both transoid and cisoid species are possible. These biradicals, however, would not be expected to interconvert, since allyl radical resonance energy of 10-15 kcal/mol would be lost. This constitutes a barrier which would be expected to be substantially larger than the barrier to ring closure. Therefore, the only fate of the transoid species would be reclosure to the geometric isomers of starting material. The cisoid biradical species, however, might be responsible for both geometric isomerization and allylic rearrangement (Scheme 1). Alternatively, a concerted 1,3-sigmatropic shift might be responsible for the ringexpanding rearrangement so that the geometric isomerization could therefore occur Via biradicals or some process separate from the 1,3-shift. In principle, four stereochemical outcomes can be envisioned for the rearrangement of the parent compound as a result of breaking either the C1-C2 bond (or the C1-C3 bond), since the methylene (CH2) carbon can migrate with retention or inversion and the allylic unit can be used either suprafacially or antarafacially. Baldwin and Andrews found that the 1,3shift proceeded via all four possible pathways in the pyrolysis of optically active trans-2-methyl-1-(trans-1′-propenyl)cyclopropane, but the Woodward-Hoffmann “allowed” suprafacial inversion pathway constituted 65% of the total reaction.3 Concern that the methyl group at the migration terminus might influence the direction of rotation provoked studies on materials having a deuterium label on C2′,4 and these indicated dominant (ca. 55-70%) suprafacial inversion stereochemistry in the 1,3-sigmatropic shift. Concern that the alkyl substitution at the migrating carbon might have an effect led to the study in our laboratory of 2,3,2′-trideuterio-1′-tert-butylvinylcyclopropane, which rearranged with at least 70% suprafacial inversion stereochemistry, and a more detailed examination suggested at least 90% stereospecificity in an si sense after correction for the geometric isomerization of starting material.5 However, with the parent system involving deuterium labeling at C2, C3, and C2′, Baldwin et al. found that the ratio of si, ar, sr, and ai products is 40:13:23:24, respectively, when isotope effects are ignored.6 Theoretical work on the vinylcyclopropane rearrangement using density functional theory and unrestricted Hartree-Fock calculations has been reported by the Houk group,7 but we felt it was appropriate to use a complete active space self-consistent field (CASSCF) method (4-orbital/4-electron) with a 6-31G* basis set since biradical-like species were most likely involved.8 Exploration of the vinylcyclopropane energy surface focused only on those structures whose allyl moiety has a geometry that can give rise to cyclopentene; the only exception was the global minimum for vinylcyclopropane, namely, the anti form. No symmetry restrictions were imposed on the calculations, and the vibrational frequencies of all species were calculated in order to exclude those with more than one imaginary frequency. Contrary to the mechanistic hypothesis of Scheme 1, CASSCF calculations reveal the presence of only four minima on the energy surface for the vinylcyclopropane to cyclopentene thermal rearrangement in the all-protio case. These are three conformations of vinylcyclopropane (the two enantiomers of a gauche conformation, VCP-g, and the anti conformation, VCPa) and cyclopentene, CP. No biradical intermediates could be found. However, four transition states were located. These are a transition state for geometric isomerization by single rotation about the C2-C3 bond, TSG; a Cs transition state for single rotation about the C1-C3 bond, TS-ca (cisoid allyl with anti substitution), a transition state for the 1,3-shift, TS13; and a Cs transition state for enantiomerization of the suprafacial inversion transition state, TS-cs (cisoid allyl with syn substitution). The minima (except for VCP-a) and saddle points are depicted on an energy surface starting with 2′,2-dideuteriovinylcyclopropane (Scheme 2) in which the C2-C3-C1-C1′ dihedral angle is plotted against the trans-C2D-D-C3-C2-C1 dihedral angle. The use of two deuteriums provides a minimally labeled (1) (a) Overberger, C. G.; Borchert, A. E. J. Am. Chem. Soc. 1960, 82, 4896. Neureiter, N. P. J. Org. Chem. 1959, 24, 2044 (first observed the rearrangement with geminal dichloro substituion on the cyclopropane ring). (b) Flowers, M. C.; Frey, H. M. J. Chem. Soc. 1961, 3547. (c) Wellington, C. A. J. Phys. Chem. 1962, 66, 1671. (2) (a) For studies of 2-methylvinylcyclopropane, see: Ellis, R. J.; Frey, H. M. J. Chem. Soc. 1964, 5578. Roth, W. R.; Konig, J. Justus Liebigs Ann. Chem. 1965, 688, 28. (b) Willcott, M. R., III; Cargle, V. H. J. Am. Chem. Soc. 1967, 89, 273. Willcott, M. R., III; Cargle, V. H. Unpublished work cited in Willcott, M. R., III; Cargill, R. L.; Sears, A. B. Prog. Phys. Org. Chem. 1972, 9, 25. (c) Willcott, M. R., III; Cargle, V. H. J. Am. Chem. Soc. 1969, 91, 4310. (3) Andrews, G. D.; Baldwin, J. E. J. Am. Chem. Soc. 1976, 98, 6705. (4) (a) Gajewski, J. J.; Squicciarini, M. P. J. Am. Chem. Soc. 1989, 111, 6717. (b) Baldwin, J. E.; Gahtlia, N. D. J. Am. Chem. Soc. 1991, 113, 6273. (5) Gajewski, J. J.; Olson, L. P. J. Am. Chem. Soc. 1991, 113, 7432. Gajewski, J. J.; Olson, L. P., Willcott, M. R., III J. Am. Chem. Soc. 1996, 118, 299. (6) Baldwin, J. E.; Villarica, K. A.; Freedberg, D. I.; Anet, F. A. L. J. Am. Chem. Soc. 1994, 116, 10845. (7) Wiest, O.; Storer, J.; Fennen, J.; Nendel, M.; Houk, K. N. Book of Abstracts, 210th National Meeting of the American Chemical Society, Chicago, IL, Fall 1995; American Chemical Society: Washington, DC, 1995; ORGN 33. (8) See Davidson, E. R.; Gajewski, J. J.; Shook, C. A.; Cohen, T. J. Am. Chem. Soc. 1995, 117, 8495. Scheme 1. Observed Thermally Induced Isomerizations of 2-Deuteriovinylcyclopropane via Hypothetical Cisoid and Transoid Biradical Intermediates 10543 J. Am. Chem. Soc. 1997, 119, 10543-10544

Calculational Evidence for Lack of Intermediates in the Thermal Unimolecular Vinylcyclopropane to Cyclopentene 1,3-Sigmatropic Shift

The recently derived local spin operator 〈SA2〉 directly determines the spin state of an atom or molecular fragment A, whereas the 〈SA·SB〉 operator represents the Heisenberg Hamiltonian spin coupling between A and B Although one typically associates such spin properties with open-shell molecules, in the single-determinant molecular orbital approximation, these operators may be related to chemically relevant quantities such as bond order regardless of whether the system has unpaired electrons Here we demonstrate the usefulness of these operators as molecular properties that can be applied to wave functions for which many properties are not defined, namely, multideterminant wave functions Analysis of the wave functions of o-, m-, and p-benzyne indicates that these spin operators are able to detect subtle differences in electronic structure within a series of isomers with unpaired electrons Hydrogen atom addition and abstraction processes are then used to illustrate that the operators are able to track ch

Local Spin III: Wave Function Analysis along a Reaction Coordinate, H Atom Abstraction, and Addition Processes of Benzyne

Algorithms are presented for SCF calculations on several types of excited states. The one-Hamiltonian method can be formulated so that it applies to either particle- or hole-type doublet states or to particle-hole triplet states. The one-Hamiltonian method works for particle-hole singlet states only if they are of different symmetry from the ground state. The sequential orthogonalization method is more restricted since it does not work for hole states. The sequential orthogonalization method, however, does apply to excited singlet states, provided the excitation is from the highest filled orbital.

Ernest R. Davidson

Papers

The generation and trapping of the high-temperature oxosilyliumyl cation radicals (28SiO+ and 29SiO+) in neon matrixes at 4 K; an ESR and ab initio CI theoretical investigation

Calculational Evidence for Lack of Intermediates in the Thermal Unimolecular Vinylcyclopropane to Cyclopentene 1,3-Sigmatropic Shift

Local Spin III: Wave Function Analysis along a Reaction Coordinate, H Atom Abstraction, and Addition Processes of Benzyne

SCF methods for excited states

Dependence of the singlet-triplet splitting in heterosubstituted carbenes on the heteroatom electronegativity and conformation