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

A new time-independent perturbation theory is developed for the multireference problem. In the derivation, neither perturbed wave function nor intermediate normalization condition is required. In the single-reference case, the present approach gives the same perturbation expressions as Rayleigh-Schrodinger perturbation theory. In the multireference case, the perturbation expressions are derived with two kinds of partitions and can be applied to those cases with or without the definition of the zeroth Hamiltonian H 0 . As the size of the reference space is decreased to 1, one multireference expansion returns to the single-reference one with Epstein-Nesbet partition, while another is reduced to a new expansion. These two multireference perturbation expansions are further expressed with the eigenvectors of the Hamiltonian within the reference space for an efficient implementation. The correspondences between the single-reference and multireference perturbation expansion are discussed.

New time‐independent perturbation theory for the multireference problem

Conceptual errors in Kalamboukis' recent paper (1980) are pointed out. A correct outline of the Davidson algorithm (1975) is given.

Comments on the Kalamboukis tests of the Davidson algorithm

Calculations using an extended basis set and the Becke 3-parameter exchange functional and Perdew 86 correlation functional are used to predict the geometry and isotropic hyperfine coupling constants for Mgn+ clusters (n⩽6). The Mg3+ results agree with our previous MRSDCI results and disagree with another recent DFT calculation. For n=4 and 5, our results agree with previous work. For n=6, we obtain a trapezoid-based bipyramid that was not considered in any previous papers. Based on these calculations, we are able to rationalize the experimental hyperfine couplings.

Density functional calculations for Mgn+ clusters

Diagonal linear inequalities are derived for three- and four-body reduced density matrices. These give a different insight into the previous derivations of linear inequalities for the two-body reduced density matrix. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2003

Linear inequalities for density matrices: III

The mapping between the local one-body potential and the ground state density is discussed. The role of degenerate ground states, which form a set of measure zero in potential space, is shown to be amplified by the unitary transformation between degenerate densities, forming a space filling set in density space. A numerical experiment demonstrating these features is carried out. No indication of non-V representable densities is encountered.

Ernest R. Davidson

Papers

New time‐independent perturbation theory for the multireference problem

Comments on the Kalamboukis tests of the Davidson algorithm

Density functional calculations for Mgn+ clusters

Linear inequalities for density matrices: III

Mapping between local potentials and ground state densities