Showing papers on "Møller–Plesset perturbation theory published in 2012"

Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory.

Abstract: Many approximations have been developed to help deal with the O(N4) growth of the electron repulsion integral (ERI) tensor, where N is the number of one-electron basis functions used to represent the electronic wavefunction. Of these, the density fitting (DF) approximation is currently the most widely used despite the fact that it is often incapable of altering the underlying scaling of computational effort with respect to molecular size. We present a method for exploiting sparsity in three-center overlap integrals through tensor decomposition to obtain a low-rank approximation to density fitting (tensor hypercontraction density fitting or THC-DF). This new approximation reduces the 4th-order ERI tensor to a product of five matrices, simultaneously reducing the storage requirement as well as increasing the flexibility to regroup terms and reduce scaling behavior. As an example, we demonstrate such a scaling reduction for second- and third-order perturbation theory (MP2 and MP3), showing that both can be c...

Second-Order Møller-Plesset Perturbation Theory in the Condensed Phase: An Efficient and Massively Parallel Gaussian and Plane Waves Approach.

Abstract: A novel algorithm, based on a hybrid Gaussian and plane waves (GPW) approach, is developed for the canonical second-order Moller-Plesset perturbation energy (MP2) of finite and extended systems. The key aspect of the method is that the electron repulsion integrals (ia|λσ) are computed by direct integration between the products of Gaussian basis functions λσ and the electrostatic potential arising from a given occupied-virtual pair density ia. The electrostatic potential is obtained in a plane waves basis set after solving the Poisson equation in Fourier space. In particular, for condensed phase systems, this scheme is highly efficient. Furthermore, our implementation has low memory requirements and displays excellent parallel scalability up to 100 000 processes. In this way, canonical MP2 calculations for condensed phase systems containing hundreds of atoms or more than 5000 basis functions can be performed within minutes, while systems up to 1000 atoms and 10 000 basis functions remain feasible. Solid LiH has been employed as a benchmark to study basis set and system size convergence. Lattice constants and cohesive energies of various molecular crystals have been studied with MP2 and double-hybrid functionals.

Van der Waals interactions between hydrocarbon molecules and zeolites: periodic calculations at different levels of theory, from density functional theory to the random phase approximation and Møller-Plesset perturbation theory

Abstract: The adsorption of small alkane molecules in purely siliceous and protonated chabazite has been investigated at different levels of theory: (i) density-functional (DFT) calculations with a gradient-corrected exchange-correlation functional; DFT calculations using the Perdew-Burke-Ernzerhof (PBE) functional with corrections for the missing dispersion forces in the form of C(6)∕R(6) pair potentials with (ii) C(6) parameters and vdW radii determined by fitting accurate energies for a large molecular data base (PBE-d) or (iii) derived from "atoms in a solid" calculations; (iv) DFT calculations using a non-local correlation functional constructed such as to account for dispersion forces (vdW-DF); (v) calculations based on the random phase approximation (RPA) combined with the adiabatic-coupling fluctuation-dissipation theorem; and (vi) using Hartree-Fock (HF) calculations together with correlation energies calculated using second-order Moller-Plesset (MP2) perturbation theory. All calculations have been performed for periodic models of the zeolite and using a plane-wave basis and the projector-augmented wave method. The simpler and computationally less demanding approaches (i)-(iv) permit a calculation of the forces acting on the atoms using the Hellmann-Feynman theorem and further a structural optimization of the adsorbate-zeolite complex, while RPA and MP2 calculations can be performed only for a fixed geometry optimized at a lower level of theory. The influence of elevated temperature has been taken into account by averaging the adsorption energies calculated for purely siliceous and protonated chabazite, with weighting factors determined by molecular dynamics calculations with dispersion-corrected forces from DFT. Compared to experiment, the RPA underestimates the adsorption energies by about 5 kJ/mol while MP2 leads to an overestimation by about 6 kJ/Mol (averaged over methane, ethane, and propane). The most accurate results have been found for the "hybrid" RPA-HF method with an average error of less than 2 kJ/mol only, while RPA underestimates the adsorption energies by about 8 kJ/mol on average. MP2 overestimates the adsorption energies slightly, with an average error of 5 kJ/mol. The more approximate and computationally less demanding methods such as the vdW-DF density functional or the C(6)∕R(6) pair potentials with C(6) parameters from "atoms in a solid" calculations overestimate the adsorption energies quite strongly. Relatively good agreement with experiment is achieved with the empirical PBE+d method with an average error of about 5 kJ/mol.

The divide-expand-consolidate family of coupled cluster methods: numerical illustrations using second order Møller-Plesset perturbation theory.

Abstract: Previously, we have introduced the linear scaling coupled cluster (CC) divide-expand-consolidate (DEC) method, using an occupied space partitioning of the standard correlation energy. In this article, we show that the correlation energy may alternatively be expressed using a virtual space partitioning, and that the Lagrangian correlation energy may be partitioned using elements from both the occupied and virtual partitioning schemes. The partitionings of the correlation energy leads to atomic site and pair interaction energies which are term-wise invariant with respect to an orthogonal transformation among the occupied or the virtual orbitals. Evaluating the atomic site and pair interaction energies using local orbitals leads to a linear scaling algorithm and a distinction between Coulomb hole and dispersion energy contributions to the correlation energy. Further, a detailed error analysis is performed illustrating the error control imposed on all components of the energy by the chosen energy threshold. This error control is ultimately used to show how to reduce the computational cost for evaluating dispersion energy contributions in DEC.

Optimization of orbital-specific virtuals in local Møller-Plesset perturbation theory

Abstract: We present an orbital-optimized version of our orbital-specific-virtuals second-order Moller-Plesset perturbation theory (OSV-MP2). The OSV model is a local correlation ansatz with a small basis of virtual functions for each occupied orbital. It is related to the Pulay–Saebo approach, in which domains of virtual orbitals are drawn from a single set of projected atomic orbitals; but here the virtual functions associated with a particular occupied orbital are specifically tailored to the correlation effects in which that orbital participates. In this study, the shapes of the OSVs are optimized simultaneously with the OSV-MP2 amplitudes by minimizing the Hylleraas functional or approximations to it. It is found that optimized OSVs are considerably more accurate than the OSVs obtained through singular value decomposition of diagonal blocks of MP2 amplitudes, as used in our earlier work. Orbital-optimized OSV-MP2 recovers smooth potential energy surfaces regardless of the number of virtuals. Full optimization is still computationally demanding, but orbital optimization in a diagonal or Kapuy-type MP2 approximation provides an attractive scheme for determining accurate OSVs.

Analytic gradient for second order Møller-Plesset perturbation theory with the polarizable continuum model based on the fragment molecular orbital method

Abstract: A new energy expression is proposed for the fragment molecular orbital method interfaced with the polarizable continuum model (FMO/PCM). The solvation free energy is shown to be more accurate on a set of representative polypeptides with neutral and charged residues, in comparison to the original formulation at the same level of the many-body expansion of the electrostatic potential determining the apparent surface charges. The analytic first derivative of the energy with respect to nuclear coordinates is formulated at the second-order Moller-Plesset (MP2) perturbation theory level combined with PCM, for which we derived coupled perturbed Hartree-Fock equations. The accuracy of the analytic gradient is demonstrated on test calculations in comparison to numeric gradient. Geometry optimization of the small Trp-cage protein (PDB: 1L2Y) is performed with FMO/PCM/6-31(+)G(d) at the MP2 and restricted Hartree-Fock with empirical dispersion (RHF/D). The root mean square deviations between the FMO optimized and NMR experimental structure are found to be 0.414 and 0.426 A for RHF/D and MP2, respectively. The details of the hydrogen bond network in the Trp-cage protein are revealed.

Molecular gradient for second-order Møller-Plesset perturbation theory using the divide-expand-consolidate (DEC) scheme

Abstract: We demonstrate that the divide-expand-consolidate (DEC) scheme – which has previously been used to determine the second-order Moller–Plesset (MP2) correlation energy – can be applied to evaluate the MP2 molecular gradient in a linear-scaling and embarrassingly parallel manner using a set of local Hartree–Fock orbitals. All manipulations of four-index quantities (describing electron correlation effects) are carried out using small local orbital fragment spaces, whereas two-index quantities are treated for the full molecular system. The sizes of the orbital fragment spaces are determined in a black-box manner to ensure that the error in the DEC-MP2 correlation energy compared to a standard MP2 calculation is proportional to a single input threshold denoted the fragment optimization threshold (FOT). The FOT also implicitly controls the error in the DEC-MP2 molecular gradient as substantiated by a theoretical analysis and numerical results. The development of the DEC-MP2 molecular gradient is the initial step towards calculating higher order energy derivatives for large molecular systems using the DEC framework, both at the MP2 level of theory and for more accurate coupled-cluster methods.

Coupled Cluster and Møller-Plesset Perturbation Theory Calculations of Noncovalent Intermolecular Interactions using Density Fitting with Auxiliary Basis Sets from Cholesky Decompositions.

Abstract: We compute noncovalent intermolecular interaction energies for the S22 test set [Phys. Chem. Chem. Phys. 2006, 8, 1985-1993] of molecules at the Moller-Plesset and coupled cluster levels of supermolecular theory using density fitting (DF) to approximate all two-electron integrals. The error due to the DF approximation is analyzed for a range of auxiliary basis sets derived from Cholesky decomposition (CD) in conjunction with correlation consistent and atomic natural orbital valence basis sets. A Cholesky decomposition threshold of 10(-4)E(h) for full molecular CD and its one-center approximation (1C-CD) generally yields errors below 0.03 kcal/mol, whereas 10(-3)E(h) is sufficient to obtain the same level of accuracy or better with the atomic CD (aCD) and atomic compact CD (acCD) auxiliary basis sets. Comparing to commonly used predefined auxiliary basis sets, we find that while the aCD and acCD sets are larger by a factor of 2-4 with triple-zeta AO basis sets, they provide results 1-2 orders of magnitude more accurate.

NMR shielding tensors for density fitted local second-order Møller-Plesset perturbation theory using gauge including atomic orbitals.

Abstract: An efficient method for the calculation of nuclear magnetic resonance (NMR) shielding tensors is presented, which treats electron correlation at the level of second-order Moller-Plesset perturbation theory. It uses spatially localized functions to span occupied and virtual molecular orbital spaces, respectively, which are expanded in a basis of gauge including atomic orbitals (GIAOs or London atomic orbitals). Doubly excited determinants are restricted to local subsets of the virtual space and pair energies with an interorbital distance beyond a certain threshold are omitted. Furthermore, density fitting is employed to factorize the electron repulsion integrals. Ordinary Gaussians are employed as fitting functions. It is shown that the errors in the resulting NMR shielding constant, introduced (i) by the local approximation and (ii) by density fitting, are very small or even negligible. The capabilities of the new program are demonstrated by calculations on some extended molecular systems, such as the cyclobutane pyrimidine dimer photolesion with adjacent nucleobases in the native intrahelical DNA double strand (ATTA sequence). Systems of that size were not accessible to correlated ab initio calculations of NMR spectra before. The presented method thus opens the door to new and interesting applications in this area.

Theoretical study of the aqueous solvation of HgCl2: Monte Carlo simulations using second-order Moller-Plesset-derived flexible polarizable interaction potentials.

Abstract: A study of the solvation of HgCl2 including ab initio aggregates of up to 24 water molecules and the results of extensive Monte Carlo simulations for the liquid phase using MP2-derived interaction potentials is presented. The interaction potentials are flexible, polarizable, and include non-additive effects. We conclude that a cluster description of the solvation mechanism is limited when compared to the condensed phase. The molecular image derived from the MC simulations is peculiar. It resembles that of a hydrophobic solute, which explains the rather easy passage of this neutral molecule through the cell membrane; however, it also shows an intermittent binding of one, two, or three water molecules to HgCl2 in the fashion of a hydrophilic solute.

The Liouville-Lanczos Approach to Time-Dependent Density-Functional (Perturbation) Theory

Abstract: Most current implementations of time-dependent density-functional theory are designed to deal with the lowest-lying portion of the spectrum (often just a few of the very first discrete lines) of systems consisting of up to a few tens of atoms. We introduce a method that allows for the simulation of extended portions of the spectrum of systems virtually of the same size as possibly treatable with state-of-art ground-state DFT techniques.

Communication: Explicitly correlated four-component relativistic second-order Møller-Plesset perturbation theory.

Abstract: We propose explicitly correlated Ansatz for four-component relativistic methods within the framework of the no-pair approximation. Kinetically balanced geminal basis is derived to satisfy the cusp conditions in the non-relativistic limit based on the Levy-Leblend-like equation. Relativistic variants of strong-orthogonality projection operator (Ansatze 2α and 2β) suitable for practical calculations are introduced by exploiting the orthogonal complement of the large-component basis. A pilot implementation is performed for the second order Moller-Plesset perturbation theory.

Cluster Perturbation Theory

Abstract: Cluster perturbation theory (CPT) is a simple approximation scheme that applies to lattice models with local interactions, like the Hubbard model, or models where the local interaction is predominant. It proceeds by tiling the lattice into identical, finite-size clusters, solving these clusters exactly and treating the inter-cluster hopping terms at first order in strong-coupling perturbation theory. This review will focus on the kinematical aspects of CPT, in particular the periodization procedure, and on the practical implementation of CPT using an exact diagonalization solver for the cluster. Applications of CPT will be briefly reviewed.

Generalized Møller–Plesset Multiconfiguration Perturbation Theory Applied to an Open-Shell Antisymmetric Product of Strongly Orthogonal Geminals Reference Wave Function

Abstract: The antisymmetric product of strongly orthogonal geminals (APSG) method is a wave function theory that can effectively treat the static electron correlation. Recently, we proposed the open-shell APSG method using one-electron orbitals for open-shell parts. In this paper, we have extended the perturbation correction to the open-shell APSG calculations through Moller-Plesset-type multiconfiguration perturbation theory (MP-MCPT). Numerical applications demonstrate that the present open-shell MP-MCPT can reasonably reproduce the dissociation energies or equilibrium distances for open-shell systems.

When does the non-variational nature of second-order Møller-Plesset energies manifest itself? All-electron correlation energies for open-shell atoms from K to Br

Abstract: All-electron correlation energies E(c) are not very well known for open-shell atoms with more than 18 electrons. The complete basis-set (CBS) limits of second-order Moller-Plesset (MP2) perturbation theory energies are obtained for open-shell atoms by computations in large basis sets combined with a knowledge of the MP2/CBS limit for the next larger closed-shell atom with the same valence shell structure. Then higher-order correlation corrections are found by coupled-cluster calculations using basis sets that are not quite as large. The method is validated for the open-shell atoms from Al to Cl for which E(c) is reasonably well established. Then, the method is used to obtain non-relativistic E(c) values, probably accurate to 3%, for the open-shell atoms of the fourth period: K, Sc-Cu, and Ga-Br. These energies are compared with the predictions of 19 density functionals and may be useful for the parameterization of new ones. The results show that MP2 overestimates |E(c)| for atoms heavier than Fe.

Embedded cluster density functional and second-order Møller-Plesset perturbation theory study on the adsorption of N2 on the rutile (110) surface.

Abstract: The adsorption of N2 on the rutile TiO2 (110) surface in the limit of low coverage has been studied as a prototype example for the adsorption of non-polar molecules on strongly ionic oxide surfaces. We employed for this study an embedded cluster ansatz in combination with density functional theory and wavefunction methods. Both, clusters saturated with hydrogen atoms and electrostatically embedded clusters have been applied and methods and basis sets have been varied to test their reliability and accuracy for describing the electrostatic potential on the surface and its interaction with the non-polar N2 molecule. Quantum clusters consisting of up to 342 atoms have been used to converge the results with respect to the cluster size. For electrostatically embedded clusters, the convergence can considerably be enhanced by optimizing the charges for the point charge embedding. On the rutile (110) surface an accurate account of the long ranging interaction of the adsorbate with the bridging oxygen atoms is important for quantitative adsorption energies of weakly bound molecules. In addition the geometric relaxation of the surface has a marked influence on the results, whereas the basis set–dependence is small. Of all methods investigated (HF, DFT/PBE, DFT/B3LYP, MP2), only MP2 and DFT/B3LYP were able to describe the adsorption of N2 on the rutile surface properly. After including the zeropoint vibrational energy, the calculated adsorption energy is close to experimental results. The approach is thus promising for future investigations on adsorption energies and structures of non-polar molecules on ionic oxide surfaces.

State-specific complete active space multireference Møller–Plesset perturbation approach for multireference situations: illustrating the bond breaking in hydrogen halides

Abstract: Assessment of the complete active space-based state-specific multireference Moller–Plesset perturbation theory, SS-MRMPPT, has been performed on the ground states of HX (X = F, Cl, and Br) systems through the computation of potential energy surface (PES) and spectroscopic constants (such as equilibrium bond lengths, rotational constants, centrifugal distortion constants, vibrational frequencies, anharmonicity constants, and dissociation energies that are closely related to the shape and accuracy of the energy surfaces) extracted from the computed PES. The SS-MRMPPT (involves multiple amplitude sets to parametrize the exact wavefunction) approach isolates one of the several states provided by an effective Hamiltonian in an attempt to avert intruder states in size-extensive manner and hence it forms the basis of a robust approach to the electron correlation problem in cases where a multireference formalism is required. The absence of intruder problem makes SS-MRMPPT an interesting choice for the calculation of the dissociation energy surface(s). The performance of the method has been judged by comparing the results with calculations provided by current generation ab initio methods (multireference or single-reference methods) and we found, in general, a very good accordance between them which clearly demonstrates the usefulness of the SS-MRMPPT method.

State specific multireference Møller–Plesset perturbation theory: A few applications to ground, excited and ionized states

Abstract: We provide further tests and illustrations of the complete active space based state specific multireference Moller–Plesset perturbation theory (SS-MRMPPT) which opens the way for the treatment of dynamic correlations in situations containing significant static correlations also in an accurate, size- extensive and intruder free manner enjoying at the same time a very favorable computational cost. We have investigated various interesting and computationally challenging systems [H 2 O, H 2 O + , BeC, MgC, CO + , Be 3 , benzene, trimethylenemethane and 1,2,3-tridehydrobenzene] in either their ground, or excited/ionized states. It is found that SS-MRMPPT calculations provide very encouraging results which can be meaningfully compared with other state-of-the-art theoretical estimates. Present results convincingly indicate that the SS-MRMPPT method is not only successful in portraying situations that warrant MR description but also performs acceptably good in cases where a naive single-reference method is enough which reinforces the claim that the SS-MRMPPT is a very useful and flexible ab initio method.

Coupled-cluster, Möller Plesset (MP2), density fitted local MP2, and density functional theory examination of the energetic and structural features of hydrophobic solvation: water and pentane.

Abstract: The interaction potentials between immiscible polar and non-polar solvents are a major driving force behind the formation of liquid:liquid interfaces. In this work, the interaction energy of water–pentane dimer has been determined using coupled-cluster theory with single double (triple) excitations [CCSD(T)], 2nd order Moller Plesset perturbation theory (MP2), density fitted local MP2 (DF-LMP2), as well as density functional theory using a wide variety of density functionals and several different basis sets. The M05-2X exchange correlation functionals exhibit excellent agreement with CCSD(T) and DF-LMP2 after taking into account basis set superposition error. The gas phase water–pentane interaction energy is found to be quite sensitive to the specific pentane isomer (2,2-dimethylpropane vs. n-pentane) and relative orientation of the monomeric constituents. Subsequent solution phase cluster calculations of 2,2-dimethylpropane and n-pentane solvated by water indicate a positive free energy of solvation that...

Molecular Structure, Experimental and Theoretical Spectroscopic Studies and Quantum Chemical Calculation of Phenoxyacetic Acid and its p-chloro Derivative

Abstract: The Fourier Transform Infrared spectra of crystallized phenoxyacetic acid and p-chloro derivative have been recorded in the region 4000-400 cm -1 . The geometry was calculated by Hartree-Fock (HF), Density Functional Theory (B3LYP) and Moller Plesset(MP2) Perturbation theory invoking 6-311++g(d,p) basis set. The harmonic vibrational frequency and, infrared intensities have been investigated with the help of B3LYP methods. The scaled theoretical wavenumbers showed very good agreement with the experimental values. The thermodynamic functions of the title compounds were also performed at B3LYP/6-311++g(d,p) level of theory. A detailed interpretation of the infrared spectra of Phenoxyacetic acid and p-chloro derivative of Phenoxy acetic acid have been reported.

Second-order Brillouin-Wigner perturbation theory: size-extensivity correction

Abstract: Size-extensivity correction to second-order Brillouin-Wigner perturbation theory is derived and implemented For the size-extensivity correction, renormalization term is obtained by modifying the non-physical term in the denominator of the second-order Brillouin-Wigner formulae We have achieved improved results The method is illustrated in a series calculations on H2O, BH, HOF, Be and Ne using three different basis sets, and the results are then compared with corresponding coupled cluster double and second-order MOller–Plesset perturbation theory

Application of Local Second-Order Møller-Plesset Perturbation Theory to the Study of Structures in Solution.

Abstract: In this work, we discuss the use of local second order Moller-Plesset perturbation theory (LMP2) in combination with the COSMO continuum solvation model for obtaining optimized geometries of molecules in solution. Density-fitting approximations, which reduce the computational cost relative to the basis set size, are also applied. We present results for small molecular systems, which show the same pattern observed in gas phase calculations. LMP2 results are found to be in excellent agreement with the canonical method. The only difference noticed is a slight increase in the average bond lengths, which is linked to the implicit reduction of basis set superposition effects (BSSE). Applications in the geometry optimization of an arginine model interacting with anions in solution as well as to the conformers of oligo-β-peptides are discussed.

Explicitly correlated second-order Møller-Plesset perturbation theory employing pseudospectral numerical quadratures.

Abstract: We implemented explicitly correlated second-order Moller-Plesset perturbation theory with numerical quadratures using pseudospectral construction of grids. Introduction of pseudospectral approach for the calculation of many-electron integrals gives a possibility to use coarse grids without significant loss of precision in correlation energies, while the number of points in the grid is reduced about nine times. The use of complementary auxiliary basis sets as the sets of dealiasing functions is justified at both theoretical and computational levels. Benchmark calculations for a set of 16 molecules have shown the possibility to keep an error of second-order correlation energies within 1 milihartree (mH) with respect to MP2-F12 method with dense grids. Numerical tests for a set of 13 isogyric reactions are also performed.