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 x‐ray form factors for a bonded hydrogen in the hydrogen molecule have been calculated for a spherical approximation to the bonded atom. These factors may be better suited for the least‐squares refinement of x‐ray diffraction data from organic molecular crystals than those for the isolated hydrogen atom. It has been shown that within the spherical approximation for the bonded hydrogens in H2, a least‐squares refinement of the atomic positions will result in a bond length (Re value) short of neutron diffraction or spectroscopic values. The spherical atoms are optimally positioned 0.07 A off each proton into the bond. A nonspherical density for the bonded hydrogen atom in the hydrogen molecule has also been defined and the corresponding complex scattering factors have been calculated. The electronic density for the hydrogen molecule in these calculations was based on a modified form of the Kolos—Roothaan wavefunction for H2. Scattering calculations were made tractable by expansion of a plane wave in spheroidal wavefunctions.

Coherent X‐Ray Scattering for the Hydrogen Atom in the Hydrogen Molecule

A contracted Gaussian basis set capable of describing about 63% of the correlation energy of N2 has been used in a detailed configuration-interaction calculation. Second-order perturbation theory overestimated the correlation energy by 23–50% depending on how H0 was chosen. Pair-pair interaction affects the correlation energy by about 20% while quadruple excitations have an 8% effect.

Configuration interaction calculations on the nitrogen molecule

The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices

Ligand spin polarization and antiferromagnetic coupling in transition metal dimers

The quantum chemistry literature containa references to a plethora of basis seta, currently numbering almost 100. While professional quantum chemists might become familiar with several dozen of these in a lifetime of calculations, the OCeasionaJ user of ab initio programs probably wishes to ignore all but the two or three sets which, through habitual use, have become personal favorites. Unfortunately, this attitude has its drawbacks. Intelligent reading of the literature requires a t least a cursory knowledge of the limitations of other basis sets. Information conceming the likely aceuracy of a specific basis for a particular property is essential in order to judge the adequacy of the computational method and, hence, the soundness of the results. Occasionally, for reasons of economy or computational feasibility, a basii set is selected for which the computed results are nearly without significance. In light of the large number of publications reporting new basis sets or detailing the performance of existing sets the task of remaining informed has become very diffteult for experts and nonexperts alike. The existence of such a vast multitude of basis sets is attributable, a t least in part, to the difficulty of finding a single set of functions which is flexible enough to produce 'good" results over a wide range of molecular geometries and is still small enough to leave the problem computationally tractible and economically within reason. The driving force behind much of the research effort in small basis sets is the fact that the computer time required for some parts of an ab initio calculation is very strongly dependent on the number of basis functions. For example, the integral evaluation goes as the fourth power of the number of Gaussian primitives. Fortunately this is the only step which explicitly depends on the number of primitives. All subsequent steps depend on the number of contracted functions formed from the primitives. The concept of primitive and contracted functions will be discussed later. Consider a collection of K identical atoms, each with n doubly occupied orbitals and N unoccupied (or virtual) orbitals. The SCF step increases as (n + N'K', while the full transformation of the integrals over the original basis functions to integrals over molecular orbitals goes as (n + N5P. Methods to account for correlation effects vary greatly. Only a few of the popular ones will be considered here. Second order Moller-Plesset (MP2) perturbation theory goes as n2NX4 but still requires an nN4F integral transformation. MP3 goes as n2N4P, while a Hartree-Fock singles and doubles CI will have n2WK4 configurations, (n2NW')' hamiltonian matrix elements of which n2N4P will be nonzero. Pople and co-workers' have proposed

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Ernest R. Davidson

Papers

Coherent X‐Ray Scattering for the Hydrogen Atom in the Hydrogen Molecule

Configuration interaction calculations on the nitrogen molecule

The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices

Ligand spin polarization and antiferromagnetic coupling in transition metal dimers

Basis Set Selection for Molecular Calculations