The method of dispersion correction as an add-on to standard Kohn-Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination numbers (CN). They are used to interpolate between dispersion coefficients of atoms in different chemical environments. The method only requires adjustment of two global parameters for each density functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of atomic forces. Three-body nonadditivity terms are considered. The method has been assessed on standard benchmark sets for inter- and intramolecular noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean absolute deviations for the S22 benchmark set of noncovalent interactions for 11 standard density functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C(6) coefficients also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.

http://dns2.asia.edu.tw/~ysho/YSHO-English/1000%20WC/PDF/J%20Che%20Phy132,%20154104.pdf

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu

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.

Semiempirical GGA-type density functional constructed with a long-range dispersion correction.

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.

/pdf/the-m06-suite-of-density-functionals-for-main-group-1748swzp1l.pdf

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

It is shown by an extensive benchmark on molecular energy data that the mathematical form of the damping function in DFT-D methods has only a minor impact on the quality of the results. For 12 different functionals, a standard "zero-damping" formula and rational damping to finite values for small interatomic distances according to Becke and Johnson (BJ-damping) has been tested. The same (DFT-D3) scheme for the computation of the dispersion coefficients is used. The BJ-damping requires one fit parameter more for each functional (three instead of two) but has the advantage of avoiding repulsive interatomic forces at shorter distances. With BJ-damping better results for nonbonded distances and more clear effects of intramolecular dispersion in four representative molecular structures are found. For the noncovalently-bonded structures in the S22 set, both schemes lead to very similar intermolecular distances. For noncovalent interaction energies BJ-damping performs slightly better but both variants can be recommended in general. The exception to this is Hartree-Fock that can be recommended only in the BJ-variant and which is then close to the accuracy of corrected GGAs for non-covalent interactions. According to the thermodynamic benchmarks BJ-damping is more accurate especially for medium-range electron correlation problems and only small and practically insignificant double-counting effects are observed. It seems to provide a physically correct short-range behavior of correlation/dispersion even with unmodified standard functionals. In any case, the differences between the two methods are much smaller than the overall dispersion effect and often also smaller than the influence of the underlying density functional.

Effect of the damping function in dispersion corrected density functional theory

The cylic formamide dimer was used as a model system for the investigation of proton-transfer phenomena in DNA base pairs. The section of the potential energy surface (PES) in the coordinates of transferring protons was studied using a wide set of computational methods, from semiempirical (PM3,MNDO-M) to the ab initio MP2/DZ+2P level of theory. Three qualitatively different patterns of stationary points were obtained, depending on the computational method used. The MP2/DZ+2P calculation resulted in two minima on the PES, corresponding to the amino-keto and imino-enol tautomeric forms, separated by a low-lying transition state. The amino-keto tautomer was found to be more stable than the imino-enol one by 15.6 kcal/mol

Double Proton Transfer: From the Formamide Dimer to the Adenine.cntdot..cntdot..cntdot.Thymine Base Pair

Thermodynamic characteristics for the formation of H-bonded DNA base pairs

The title calculations were performed with the aim of providing data for the critical examination of the utility of the basis set superposition error (BSSE) correction. The main results obtained are as follows. The SCF interaction energies corrected for the BSSE and evaluated with the basis sets of split-valence and DZ origin are similar. With the stabilization energy, both the basis set superposition error and the intersystem correlation energy are important. MP2 stabilization energies are only slightly dependent on basis set for basis sets of DZ + P or better quality. The basis set superposition error at both the SCF and MP2 levels remains almost unchanged when passing from the 6–31G* to the 6–311G(2d, 2p) basis set. At the SCF level sufficiently accurate geometries were obtained with the standard 6–31G* basis set. Optimization at the MP2 level with this and larger basis sets brings about only small changes with respect to optimum SCF geometries.

The superposition error problem: the (HF)2 and (H2O)2 complexes at the SCF and MP2 levels

An accurate description of the interactions between DNA bases is of fundamental importance in the theoretical analysis of DNA structure, flexibility and dynamics. These base-base interactions are significantly influenced by the properties of the DNA base amino groups. In the present paper we show that, in constrast to the empirical force fields, ab initio calculations predict non-planar geometries for the DNA base amino groups. We compare the amino group non-planarity of cytosine, adenine, guanine, the guanine amino tautomer, 2-aminoadenine, 5-methylcytosine and the guanine formamidine hydrogen bonded complex, at the HF/6–31G(NH 2 ∗ ) level of theory. In addition, the geometry of cytosine is optimized at the MP2/6–31G ∗ , MP2/6–31G(NH ∗ 2 ), HF/6–31G ∗ , HF/4–21G(NH ∗ 2 ) and HF/6–31G levels of theory to estimate the role of electron correlation and polarization functions in the amino group geometry. It is shown that the gradient geometry optimization with inclusion of electron correlation significantly increases the non-planarity of the cytosine amino group compared to the HF level of calculations. The influence of non-planar DNA base amino groups on the conformational variability of DNA is briefly discussed.

Pavel Hobza

Papers

Double Proton Transfer: From the Formamide Dimer to the Adenine.cntdot..cntdot..cntdot.Thymine Base Pair

Thermodynamic characteristics for the formation of H-bonded DNA base pairs

The superposition error problem: the (HF)2 and (H2O)2 complexes at the SCF and MP2 levels

Sequence dependent intrinsic deformability of the DNA base amino groups. An ab initio quantum chemical analysis

Weak intermolecular interaction: III.Ab initio SCF calculation of interaction energy and its components near the van der waals minimum