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

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

The calculation of accurate electron affinities (EAs) of atomic or molecular species is one of the most challenging tasks in quantum chemistry. We describe a reliable procedure for calculating the electron affinity of an atom and present results for hydrogen, boron, carbon, oxygen, and fluorine (hydrogen is included for completeness). This procedure involves the use of the recently proposed correlation‐consistent basis sets augmented with functions to describe the more diffuse character of the atomic anion coupled with a straightforward, uniform expansion of the reference space for multireference singles and doubles configuration‐interaction (MRSD‐CI) calculations. Comparison with previous results and with corresponding full CI calculations are given. The most accurate EAs obtained from the MRSD‐CI calculations are (with experimental values in parentheses) hydrogen 0.740 eV (0.754), boron 0.258 (0.277), carbon 1.245 (1.263), oxygen 1.384 (1.461), and fluorine 3.337 (3.401). The EAs obtained from the MR‐SD...

/pdf/electron-affinities-of-the-first-row-atoms-revisited-5bxyhjrawl.pdf

Electron affinities of the first-row atoms revisited. Systematic basis sets and wave functions

A new hybrid exchange–correlation functional using the Coulomb-attenuating method (CAM-B3LYP)

A role for electronic structure databases in assisting users of quantum chemistry applications select better model parameters is discussed in light of experiences gained from a software prototype known as the Computational Chemistry Input Assistant (CCIA). It is argued that the ready availability of information pertaining to the applications and theoretical models can substantially increase the likelihood of novice users obtaining the desired accuracy from their calculations while simultaneously making better use of computer resources. Expert users, who find themselves contemplating studies in new areas of research, may also benefit from the proposed tools. For maximum impact, this assistance should be provided while users are actively engaged in preparing calculations. © 1996 by John Wiley & Sons, Inc.

The role of databases in support of computational chemistry calculations

A systematic series of calculations encompassing a wide range of basis sets and correlated methods has been used to estimate the complete basis set, full CI hydrogen bond strength in the water dimer system. The largest basis set included up through h polarization functions on oxygen and g functions on hydrogen. The complete basis set limit for the self‐consistent‐field (SCF) interaction energy is estimated to be −3.55 kcal/mol with an accompanying correlation contribution of ∼−1.5 kcal/mol. This leads to an interaction energy of −5.1 kcal/mol, exclusive of vibrational zero‐point considerations, and is in good agreement with experimental measurements of −5.4±0.7 kcal/mol. Inclusion of an approximate adjustment for the basis set superposition error via the Boys/Bernardi counterpoise correction was found to substantially improve agreement with ΔE∞, our estimate of the complete basis set interaction energy, at the both the SCF and correlated levels for basis sets that were lacking in sufficient near‐valence d...

Application of systematic sequences of wave functions to the water dimer

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

/pdf/basis-set-selection-for-molecular-calculations-3xye1nz5d2.pdf

Basis Set Selection for Molecular Calculations

An assortment of 1‐ and 2‐electron water properties were extracted from a systematic sequence of wave functions. The regularity inherent in this sequence permitted simple exponential fits of the resulting energies and, in many cases, the properties. To the extent the exponential fit accurately reflects the asymptotic convergence of a specific property, it provides an estimate of the complete basis set, full configuration interaction (CI) limiting value at a reduced computational expense. As a consequence of the vast reduction in the number of configurations that must be treated variationally, the proposed scheme may make possible improved estimates of the complete basis set, full CI limit beyond what could be obtained from explicit computations. In order to judge the accuracy of the procedure, we have carried out the highest level ab initio calculations to date on water, recovering in excess of 96% of the estimated valence correlation energy.

/pdf/the-use-of-systematic-sequences-of-wave-functions-for-15xmogi68m.pdf

The use of systematic sequences of wave functions for estimating the complete basis set, full configuration interaction limit in water

Large scale ab initio molecular orbital calculations on the binding energy of the water dimer have been performed. These calculations extend the previous correlation consistent basis set work to include larger basis sets (up to 574 functions), and core/valence correlation effects have now been included. The present work confirms the earlier estimate of −4.9 kcal/mol as the MP2(FC) basis set limit. Core/valence correlation effects are found to increase the binding energy by ∼0.05 kcal/mol. The best estimate of the electronic binding energy of the water dimer is −5.0 ± 0.1 kcal/mol. Correcting this value for zero-point and temperature effects yields the value ΔH(375) = −3.2 ± 0.1 kcal/mol. This value is within the error limits of the best experimental estimate of −3.6 ± 0.5 kcal/mol with the calculations favoring the lower end of the experimental energy range. It should be useful to adopt the present estimate in empirical and semiempirical model potentials.

David Feller

Papers

The role of databases in support of computational chemistry calculations

Application of systematic sequences of wave functions to the water dimer

Basis Set Selection for Molecular Calculations

The use of systematic sequences of wave functions for estimating the complete basis set, full configuration interaction limit in water

Hydrogen bond energy of the water dimer