An alternative approach for the calculation of correlation energy in periodic systems: a hybrid MP2(B3LYP) study of the He-MgO(100) interaction

A practical and efficient method for exploiting second order Rayleigh-Schr?dinger perturbation theory to approximate the correlation energy contribution to the London dispersion interaction is presented. The correlation energy is estimated as the M?ller-Plesset contribution computed using single particle orbitals from hybrid exchange density functional theory as the reference state.     

Analysis of self-consistency effects in range-separated density-functional theory with Møller-Plesset perturbation theory

Range-separated density-functional theory combines wave function theory for the long-range part of the two-electron interaction with density-functional theory for the short-range part. When describing the long-range interaction with non-variational methods, such as perturbation or coupled-cluster theories, self-consistency effects are introduced in the density functional part, which for an exact solution requires iterations. They are generally assumed to be small but no detailed study has been performed so far. Here, the authors analyze self-consistency when using M?ller-Plesset-type (MP) perturbation theory for the long range interaction. The lowest-order self-consistency corrections to the wave function and the energy, that enter the perturbation expansions at the second and fourth order, respectively, are both expressed in terms of the one-electron reduced density matrix. The computational implementation of the latter is based on a Neumann series which, interestingly, even though the effect is small, usually diverges. A convergence technique, which perhaps can be applied in other uses of Neumann series in perturbation theory, is proposed. The numerical results thus obtained show that, in weakly bound systems, self-consistency can be neglected since the long-range correlation does not affect the density significantly. Although MP is not adequate for multireference systems, it can still be used as a reliable analysis tool. Though the density change is not negligible anymore in such cases, self-consistency effects are found to be much smaller than long-range correlation effects (less than 10% for the systems considered). For that reason, a sensible approximation might be to update the short-range energy functional term while freezing its functional derivative, namely, the short-range local potential, in the wave function optimization. The accuracy of such an approximation still needs to be assessed.     

Third-order corrections to random-phase approximation correlation energies

Several random-phase approximation (RPA) correlation methods were compared in third order of perturbation theory. While all of the considered approaches are exact in second order of perturbation theory, it is found that their corresponding third-order correlation energy contributions strongly differ from the exact third-order correlation energy contribution due to missing interactions of the particle-particle-hole-hole type. Thus a simple correction method is derived which makes the different RPA methods also exact to third-order of perturbation theory. By studying the reaction energies of 16 chemical reactions for 21 small organic molecules and intermolecular interaction energies of 23 intermolecular complexes comprising weakly bound and hydrogen-bridged systems, it is found that the third-order correlation energy correction considerably improves the accuracy of RPA methods if compared to coupled-cluster singles doubles with perturbative triples as a reference.     

Investigation of intermolecular interactions based on the atomic statistical model

Possibilities of improving individual contributions to the statistical interaction energy (kinetic and exchange) are examined. A new method of calculating statistical interaction energies is proposed. The exchange term is calculated using a suitably modified second-order gradient correction. For the kinetic contribution the accurate formula corresponding to the first-order perturbation theory is applied. The calculations have been carried out for several pairs of noble gas atoms.     

Perturbation calculation of the interaction energy using orthogonalized orbitals

The diagrammatic Rayleigh-Schr?dinger perturbation theory for the interaction of two closed-shell systems is developed up to the third order of pertur-bation using orthogonalized orbitals. The interaction energy is expressed by the Rayleigh-Schr?dinger perturbation expansion. A simple approach for the estimation of basis set superposition error is introduced. The preliminary calculations of the intermolecular interactions for the He dimer within the augmented cc-pVTZ basis set are compared with the supermolecular approach, perturbation calculation in biorthogonal basis sets and symmetry adapted perturbation theory results. Received: 17 December 1996 / Accepted: 5 November 1997     

Anharmonic Force Fields and Perturbation Theory in the Interpretation of Vibrational Spectra of Polyatomic Molecules

The problem of describing real vibrational spectra of large molecules in terms of perturbation theory is considered. Equations necessary for presenting theoretical anharmonic force fields in various coordinate systems (Cartesian, normal, and internal curvilinear) are discussed. A review of second-order perturbation theory equations necessary for calculating certain spectroscopic values (anharmonicity constants, rotational-vibrational interaction, etc.) is given. A scheme for including resonances based on the construction of the interaction matrix between vibrational transitions of various types is described. This scheme can be used as a basis for anharmonic calculations of vibrations of medium-sized molecules.     

A Simple Approximate Perturbation Approach to Quasi-degenerate Systems

In this paper a simple approximate approach for the study of quasi-degenerate systems is presented in the frame of multireference perturbation theory. The formulation can be considered as an approximation of the quasi-degenerate perturbation theory (QDPT) with the simplification that only the state specific (diagonal) perturbation corrections to the energy have to be computed. The new approach is discussed and compared with previous QDPT formulations using the weakly avoided crossing model (for which new properties are here presented) and applied to the case of the neutral/ionic energy crossing in the LiF molecule.     

Ab initio calculation of the MgO(100) interaction with He and Ne: a HF + MP2 and HF + MP2(B3LYP) comparison

Second order Rayleigh Schr?dinger perturbation theory is applied to calculate the correlation energy contribution to the London dispersion interaction to approximate the interaction of the He and Ne with the MgO(100) surface; single particle orbitals using either Hartree-Fock theory or hybrid-exchange density functional theory are used as the reference state.     

Intermolecular interaction energy of CH4 trimer by symmetry-adapted perturbation theory

The interaction energy for the cyclic CH₄ trimer is studied in terms of symmetry-adapted perturbation theory. The interaction energy around the van der Waals minimum is dominated by attractive dispersion energy, and the repulsive contribution at the smaller angle region is due to the first-order exchange energy. The total interaction energy is approximated by additive two-body components, because of a mutual cancellation between nonadditive three-body ones.     

Interaction energies for the water dimer by supermolecular methods and symmetry-adapted perturbation theory: the role of bond functions and convergence of basis subsets

 Using a systematic series of basis sets in supermolecular and symmetry-adapted intermolecular perturbation theory calculations it is examined how interaction energies of various water dimer structures change upon addition and shifting of bond functions. Their addition to augmented double- and triple-zeta basis sets brings the sum of the electron correlation contributions to the second-order interaction energy nearly to convergence, while accurate first-order electrostatic and exchange contributions require better than augmented quadruple-zeta quality. A scheme which combines the different perturbation energy contributions as computed in different basis subsets performs uniformly well for the various dimer structures. It yields a symmetry-adapted perturbation theory value of −21.08 kJ/mol for the energy of interaction of two vibrationally averaged water molecules compared to −21.29 kJ/mol when the full augmented triple-zeta basis set is used throughout. Received: 4 November 1999 / Accepted: 8 February 2000 / Published online: 12 May 2000     

Description of noncovalent interactions involving π-system with high precision: An assessment of RPA,MP2, and DFT-D methods

Efficient approaches with high precision are essential for understanding the formation and stability of noncovalent interaction complexes. Here, 21 noncovalent interaction complexes involving π-system are selected and grouped in three subsets according to ETS–NOCV method: dispersion-dominated, electrostatic-dominated, and mixed. We mainly focus on examining the performance of random-phase approximation (RPA) on these π systems. The tested RPA-based method includes standard RPA and its variants including the related single excitations (SEs), renormalized single excitations (rSEs), second-order screened exchange (SOSEX), and the renormalized second-order perturbation theory (rPT2). The routine second-order Møller–Plesset perturbation theory (MP2) and three popular DFT-D functionals (M06-2X-D3, ωB97XD, and PBE-D3(BJ)) are also assessed for comparison. In this work, besides the calculation of interaction energies at Dunning-type aug-cc-pVDZ and aug-cc-pVTZ basis set, we also present a larger database of interaction energies calculated using MP2 and RPA methods with Dunning-type aug-cc-pVQZ basis set. An accurate CCSD(T)/CBS scheme is used to provide benchmark database. In addition to the high-level results, we also provide potential energy surfaces (PES) of different interaction type. Among all the tested methods, MP2 has a satisfactory performance on electrostatic-dominated and mixed-type systems, except for dispersion-dominated systems. DFT-D functionals, especially ωB97XD functional, has a balanced performance across all the tested systems. Importantly, for RPA-based methods, the calculation accuracy can be dramatically improved by taking into account SE or exchange effects, especially in the mixed complexes. We conclude that rPT2 among all the test RPA-based methods gives an overall satisfactory performance across different interaction types. © 2019 Wiley Periodicals, Inc.     

Symmetry-adapted perturbation theory analysis of the N...HX hydrogen bonds

The main aim of the study was the detailed investigation of the interaction energy decomposition in dimers and trimers containing N...HX bonds of different types. The study of angular dependence of interaction energy terms partitioned according to the symmetry-adapted perturbation theory (SAPT) was performed for the dimers containing N...HX bonds as mentioned above: ammonia-HX (X = F, Cl, Br) and pyridine-HF complexes. It was found that the electrostatic and induction terms exhibit strong angular dependence, while the exchange contributions are less affected. The dispersion terms are virtually nondirectional. In addition, the three-body SAPT interaction energy analysis for the mixed acid-base NH3...(HF)2 and (NH3)2...HF trimers revealed strong differences between interactions of similar strength but different types (i.e., hydrogen bond and general electrostatic interaction). The importance of the induction terms for the nonadditivity of the interaction energy in strongly polar systems was confirmed.     

The perturbation calculation of van der Waals potentials

Summary The unsymmetrized perturbation theory for interaction potentials is reformulated in such a way that the overlap and exchange effects can be taken into account in a satisfactory and conceptually simple way. This formulation, known as the generalized Heitler-London theory, its shown to be valid regardless of the ultimate limit to which the polarization approximation converges. Within the framework of this theory, the van der Waals potential of the triplet H₂(³ _u ) state is calculated and shown to be in excellent agreement with the exactab initio results. Both the exchange energy and the polarization energy are obtained from a perturbation calculation.     

Exchange processes in nmr

The exchange of particles and the (noncorporeal) exchange of magnetization in systems are considered where nuclei exist in various regions which differ in their magnetic resonance properties. We start with the stochastic theory of nuclear magnetic resonance and relaxation in such systems. Two-region systems are treated in some detail; here, also, the modified Bloch equations are introduced. Experimental examples concerning adsorbent-adsorbate systems are given. Finally, the influence of cross-relaxation on the relaxation of molecules adsorbed on interfaces is taken into account, the corresponding theory being treated. NMR methods which allow to distinguish between particle and spin exchange are discussed.     

MBPT studies of van der Waals molecules. III. The reliability of apparently accurate calculations for the magnesium dimer

The interaction potential for the magnesium dimer is calculated by using the diagrammatic many-body perturbation theory within the framework of the supermolecule approach. Different approximations for the perturbation treatment of the electron correlation effects are analysed with particular emphasis on the results of the complete fourth-order many-body perturbation theory. The influence of the composition of the basis set on the calculated interaction potentials and the basis set superposition effects are investigated. It is concluded that the interaction potentials for van der Waals systems calculated by the supermolecule technique might be highly uncertain because of the basis set superposition effects at the correlated level. The advantages and disadvantages of different methods for the calculation of the energy of weakly interacting systems are discussed in the light of their ability to cope with both the electron correlation problem and the basis set superposition effect.     

Interaction energy contributions of H-bonded and stacked structures of the AT and GC DNA base pairs from the combined density functional theory and intermolecular perturbation theory approach

Stacked and Watson-Crick structures of DNA base pairs are investigated with the DFT-SAPT variant of intermolecular perturbation theory, yielding a rigorous decomposition of the interaction energy into electrostatic, induction, dispersion, and exchange contributions. Their interplay in the various structures is analyzed. Total interaction energies extrapolated to the complete basis set limit are compared with corresponding second-order M?ller-Plesset and estimated coupled-cluster theory results.     

Proton transfer in small model systems: A density functional study

The structures, interaction energies, and proton-transfer features of some representative intermolecular complexes are determined by using a density functional which incorporates gradient corrections and, as recently suggested by Becke, some Hartree–Fock exchange. The results are compared with those obtained by high-order many-body perturbation theory and by a number of more conventional density functionals. Hydrogen-bond strengths and interatomic distances between heavy atoms are well reproduced by several density functionals. However, inclusion of some Hartree–Fock exchange is mandatory to improve XH bond lengths, and, especially, energy barriers governing proton transfer. Use of the new functional significantly improves the agreement with experimental and post-Hartree–Fock results. This paves the route for a detailed theoretical study of proton-transfer processes in large, biologically significant systems. © 1995 John Wiley & Sons, Inc.     

Power series expansion of the random phase approximation correlation energy: The role of the third- and higher-order contributions

We derive a power expansion of the correlation energy of weakly bound systems within the random phase approximation (RPA), in terms of the Coulomb interaction operator, and we show that the asymptotic limit of the second- and third-order terms yields the van der Waals (vdW) dispersion energy terms derived by Zaremba-Kohn and Axilrod-Teller within perturbation theory. We then show that the use of the second-order expansion of the RPA correlation energy results in rather inaccurate binding energy curves for weakly bonded systems, and discuss the implications of our findings for the development of approximate vdW density functionals. We also assess the accuracy of different exchange energy functionals used in the derivation of vdW density functionals.     

A model study of the intermolecular interactions of amino acids in aqueous solution: The glycine-water system

We have performed calculations of the glycine zwitterion surrounded by water molecules with the help of the mutually consistent field (MCF) method and perturbation theoretical expressions. Two different models for the hydration shell have been chosen, the glycine·6H₂O and glycine·12H₂O complexes, representing the most probable first and second solvation shell, respectively. To calculate the exchange and charge transfer energy contributions we have applied approximative expressions derived from perturbation theory for weakly overlapping subunits. For the sake of comparison we also calculated the interaction energy in the supermolecule approach for the smaller of the two solvation complexes. Furthermore, we have investigated the part of the potential energy surface which is determined by varying the lengths of the hydrogen bonds between glycine and water in the complex glycine·12H₂O using the electrostatic approach. The exchange energy contribution to the interaction energy for different points on the surface was approximated with the help of an analytical expression fitted to three directly calculated points. For the charge transfer energy a polynomial expansion of second order was established on the basis of five values, computed with the aid of the perturbation theoretical expression. To get a more detailed insight in the relatively strong hydrogen bonds between the water molecules and the ionic hydrophilic parts of glycineab initio model studies on NH ₄ ⁺ ·3H₂O and HCOO⁻·3H₂O systems are reported.