Minimal basis sets in calculations of intermolecular interaction energies

Several minimal (7, 3/3) Gaussian basis sets have been used to calculate the energies and some other properties of CH₄ and H₂O. Improved basis sets developed for these molecules have been extended to NH₃ and HF and employed to H₂CO and CH₃OH. Interaction energies between XH_n molecules have been calculated using the old and the new minimal basis sets. The results obtained with the new basis sets are comparable in accuracy to those calculated with significantly more extended basis sets involving polarization functions. Binding energies calculated using the counterpoise method are not much different for the new and the old minimal basis sets, and are likely to be more accurate than the results of much more extended calculations.     

Monomer basis-set truncation effects in calculations of interaction energies: A model study

Supermolecular interaction energies are analyzed in terms of the symmetry-adapted perturbation theory and operators defining the inaccuracy of the monomer wave functions. The basis set truncation effects are shown to be of first order in the monomer inaccuracy operators. On the contrary, the usual counterpoise correction schemes are of second order in these operators. Recognition of this difference is used to suggest an approach to corrections for basis-set truncation effects. Also earlier claims--that dimer-centered basis sets may lead to interaction energies free of basis-set superposition effects--are shown to be misleading. According to the present study the basis-set truncation contributions, evaluated by means of the symmetry-adapted perturbation theory with monomer-centered basis sets, provide physically and mathematically justified corrections to supermolecular results for interaction energies.     

The inclusion of electrostatic hydration energies in molecular mechanics calculations

Summary The problem of including solvent effects in molecular mechanics calculations is discussed. It is argued that the neglect of charge-solvent (solvation) interactions can introduce significant errors. The finite difference Poisson-Boltzmann (FDPB) method for calculating electrostatic interactions is summarized and is used as a basis for introducing a new pairwise energy term which accounts for charge-solvent interactions. This term acts between all pairs of atoms usually considered in molecular mechanics calculations and can be easily incorporated into existing force fields. As an example, a parameterization is developed for the CHARMm force field and the results compared to the predictions of the FDPB method. An approach to the realistic incorporation of solvent screening into force fields is also outlined.     

Accurate calculations of intermolecular interaction energies using explicitly correlated wave functions

Explicitly correlated second-order M?ller-Plesset (MP2-F12) calculations of intermolecular interaction energies for the S22 benchmark set of Jurecka, Sponer, Cerny, and Hobza (Chem. Phys. Phys. Chem. 2006, 8, 1985) are presented and compared with standard MP2 results. The MP2 complete basis set limits are estimated using basis set extrapolation and augmented quadruple-zeta and quintuple-zeta basis sets. Already with augmented double-zeta basis sets the MP2-F12 interaction energies are found to be closer to the complete basis set limits than standard MP2 calculations with augmented quintuple-zeta basis sets. Various possible approximations in the MP2-F12 method are systematically tested. Best results are obtained with localized orbitals and the diagonal MP2-F12/C(D) ansatz. Hybrid approximations, in which some contributions of the auxiliary basis set are neglected and which considerably reduce the computational cost, have a negligible effect on the interaction energies. Also the orbital-invariant fixed-amplitude approximation of Ten-no leads to only slightly less accurate results. Preliminary results for the neon and benzene dimers, obtained with the recently proposed CCSD(T)-F12a approximation, indicate that the CCSD(T) basis set limits can also be very closely approached using augmented triple-zeta basis sets.     

Structural properties and interaction energies affecting drug design. An approach combining molecular simulations,statistics, interaction energies and neural networks

In order to elucidate some basic principles for protein–ligand interactions, a subset of 87 structures of human proteins with their ligands was obtained from the PDB databank. After a short molecular dynamics simulation (to ensure structure stability), a variety of interaction energies and structural parameters were extracted. Linear regression was performed to determine which of these parameters have a potentially significant contribution to the protein–ligand interaction. The parameters exhibiting relatively high correlation coefficients were selected. Important factors seem to be the number of ligand atoms, the ratio of N, O and S atoms to total ligand atoms, the hydrophobic/polar aminoacid ratio and the ratio of cavity size to the sum of ligand plus water atoms in the cavity. An important factor also seems to be the immobile water molecules in the cavity. Nine of these parameters were used as known inputs to train a neural network in the prediction of seven other. Eight structures were left out of the training to test the quality of the predictions. After optimization of the neural network, the predictions were fairly accurate given the relatively small number of structures, especially in the prediction of the number of nitrogen and sulfur atoms of the ligand.     

Accurate pair interaction energies for helium from supermolecular Gaussian geminal calculations

Nonrelativistic clamped-nuclei pair interaction energy for ground-state helium atoms has been computed for 12 interatomic separations ranging from 3.0 to 9.0 bohr. The calculations applied the supermolecular approach. The major part of the interaction energy was obtained using the Gaussian geminal implementation of the coupled-cluster theory with double excitations (CCD). Relatively small contributions from single, triple, and quadruple excitations were subsequently included employing the conventional orbital coupled-cluster method with single, double, and noniterative triple excitations [CCSD(T)] and the full configuration interaction (FCI) method. For three distances, the single-excitation contribution was taken from literature Gaussian-geminal calculations at the CCSD level. The orbital CCSD(T) and FCI calculations used very large basis sets, up to doubly augmented septuple- and sextuple-zeta size, respectively, and were followed by extrapolations to the complete basis set limits. The accuracy of the total interaction energies has been estimated to be about 3 mK or 0.03% at the minimum of the potential well. For the attractive part of the well, the relative errors remain consistently smaller than 0.03%. In the repulsive part, the accuracy is even better, except, of course, for the region where the potential goes through zero. For interatomic separations smaller than 4.0 bohr, the relative errors do not exceed 0.01%. Such uncertainties are significantly smaller than the expected values of the relativistic and diagonal Born-Oppenheimer contributions to the potential.     

Accurate lattice energies of organic molecular crystals from periodic turbomole calculations

Accurate lattice energies of organic crystals are important i.e. for the pharmaceutical industry. Periodic DFT calculations with atom‐centered Gaussian basis functions with the Turbomole program are used to calculate lattice energies for several non‐covalently bound organic molecular crystals. The accuracy and convergence of results with basis set size and k‐space sampling from periodic calculations is evaluated for the two reference molecules benzoic acid and naphthalene. For the X23 benchmark set of small molecular crystals accurate lattice energies are obtained using the PBE‐D3 functional. In particular for hydrogen‐bonded systems, a sufficiently large basis set is required. The calculated lattice energy differences between enantiopure and racemic crystal forms for a prototype set of chiral molecules are in good agreement with experimental results and allow the rationalization and computer‐aided design of chiral separation processes. © 2018 Wiley Periodicals, Inc.     

Configuration interaction calculations of the valence ionization energies of the water dimer

The eight vertical valence ionization energies of the water dimer are calculated by the ΔCI method. Excellent agreement with measurements of the first and second ionization energies is found. Calculations of the remaining six ionization energies is found. Calculations of the remaining six ionization energies are sufficiently accurate to be of value in the identification and assignment of the dimer photoelectron spectrum.     

Non-empirical calculations of HF oligomers

The Gibbs free energies of oligomers of hydrogen fluoride are calculated using the ab-initio molecular orbital method and by statistical mechanics. The equilibrium of gaseous hydrogen fluoride is discussed.     

Accuracy of basis-set extrapolation schemes for DFT-RPA correlation energies in molecular calculations

We construct a reference benchmark set for atomic and molecular random phase approximation (RPA) correlation energies in a density functional theory framework at the complete basis-set limit. This set is used to evaluate the accuracy of some popular extrapolation schemes for RPA all-electron molecular calculations. The results indicate that for absolute energies, accurate results, clearly outperforming raw data, are achievable with two-point extrapolation schemes based on quintuple- and sextuple-zeta basis sets. Moreover, we show that results in good agreement with the benchmark can also be obtained by using a semiempirical extrapolation procedure based on quadruple- and quintuple-zeta basis sets. Finally, we analyze the performance of different extrapolation schemes for atomization energies.     

Quantitative calculations of antibody--antigen binding: steroid--DB3 binding energies by the linear interaction energy method

Linear interaction energy/molecular dynamics calculations have been used to compute steroid/antibody binding energies. The absolute binding affinities of 10 steroids to antibody DB3 and of a hapten to catalytic antibody 1E9 are computed and compared to experiment. A detailed analysis of the molecular origins of the observed binding patterns is provided. The binding energy of an untested steroid is predicted.     

惰性气体原子与HF分子相互作用的分子形貌动态研究

研究了惰性气体原子(Rg=He,Ne,Ar和Kr)分别向HF分子两端原子接近过程中分子形貌的动态变化,使用MELD精密从头算方法中的CISD/6-311++G(2d,2p)方法,计算了FH-Rg和HF-Rg2个二聚体的单电子作用势、分子平面的边界轮廓以及相应界面上的电子密度.研究表明,惰性气体原子Rg分别向HF的两端接近时,双方的外形在接近的方向上均有伸手欢迎的表示,分子的前沿电子密度也相应的发生变化,对惰性键提供了一种新的认识.     

Power transformations improve interpolation of grids for molecular mechanics interaction energies

A common strategy for speeding up molecular docking calculations is to precompute nonbonded interaction energies between a receptor molecule and a set of three‐dimensional grids. The grids are then interpolated to compute energies for ligand atoms in many different binding poses. Here, I evaluate a smoothing strategy of taking a power transformation of grid point energies and inverse transformation of the result from trilinear interpolation. For molecular docking poses from 85 protein‐ligand complexes, this smoothing procedure leads to significant accuracy improvements, including an approximately twofold reduction in the root mean square error at a grid spacing of 0.4 Å and retaining the ability to rank docking poses even at a grid spacing of 0.7 Å. © 2018 Wiley Periodicals, Inc.     

Electrostatic energy calculations by a Finite-difference method: Rapid calculation of charge–solvent interaction energies

Finite-difference Poisson–Boltzmann (FDPB) methods allow a fast and accurate calculations of the reaction field (charge–solvent) energies for molecular systems. Unfortunately, the energy in the FDPB calculations includes the self-energies and the finite-difference approximation to the Coulombic energies as well as the reaction field energy. A second finite-difference calculation, in a uniform dielectric, is therefore necesssary to eliminate these contributions. In this article we describe a rapid and accurate method to calculate the self energy and finite-difference Coulombic energies in a uniform dielectric thus eliminating the need for a second finite-difference calculation. The computational savings for this method range from a factor of 4 for a typical protein to a factor of 10³ for small molecules. © 1992 by John Wiley & Sons, Inc.     

Comparison of the numerical stability of methods for anharmonic calculations of vibrational molecular energies

On model examples, we compare the performance of the vibrational self-consistent field, variational, and four perturbational schemes used for computations of vibrational energies of semi-rigid molecules, with emphasis on the numerical stability. Although the accuracy of the energies is primarily dependent on the quality of the potential energy surface, approximate approaches to the anharmonic vibrational problem often do not converge to the same results due to the approximations involved. For furan, the sensitivity to variations of the anharmonic potential was systematically investigated by adding random noise to the cubic and quartic constants. The self-consistent field methods proved to be the most resistant to the potential variations. The second order perturbational techniques are sensitive to random degeneracies and provided the least stable results. However, their stability could be significantly improved by a simple generalization of the perturbational formula. The variational configuration interaction is practically limited by the size of the matrix that can be diagonalized for larger molecules; however, relatively fewer states need to be involved than for smaller ones, in favor of the computing.     

DFT and MO calculations of atomic and molecular chemisorption energies on surface cluster models

Summary Density functional theory (DFT) (including gradient corrections) and MCPF calculations have been performed for atomic (H, C, N, O) and molecular CH _x (x = 1–3) chemisorption on cluster models of different sites of the Cu(100) surface. The DFT and MCPF results are in good agreement once the important effects of core-valence correlation have been accounted for in the MCPF calculations by including contributions from a core polarization potential (CPP); in the DFT approach the core-valence correlation is obtained directly from the total density using the functional. Very large effects on the four-fold hollow site binding energy from core-valence correlation are found for C, N and CH. Several different DFT functionals were employed and compared in the calculations.     

Harmonic force fields from molecular energy calculations : Tests of a method using indo and MINDO/2 semiempirical molecular energies

A numerically stable method for simultaneous calculation of force constants and coupling constants from energy data has been designed and tested. It has been used to obtain harmonic force fields for a set of small molecules from INDO and MINDO/2 calculations.