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We introduce orbital specific virtuals (OSVs) to represent the truncated pair-specific virtual space in periodic local Møller-Plesset perturbation theory of second order (LMP2). The OSVs are constructed by diagonalization of the LMP2 amplitude matrices which correspond to diagonal Wannier-function (WF) pairs. Only a subset of these OSVs is adopted for the subsequent OSV-LMP2 calculation, namely, those with largest contribution to the diagonal pair correlation energy and with the accumulated value of these contributions reaching a certain accuracy. The virtual space for a general (non diagonal) pair is spanned by the union of the two OSV sets related to the individual WFs of the pair. In the periodic LMP2 method, the diagonal LMP2 amplitude matrices needed for the construction of the OSVs are calculated in the basis of projected atomic orbitals (PAOs), employing very large PAO domains. It turns out that the OSVs are excellent to describe short range correlation, yet less appropriate for long range van der Waals correlation. In order to compensate for this bias towards short range correlation, we augment the virtual space spanned by the OSVs by the most diffuse PAOs of the corresponding minimal PAO domain. The Fock and overlap matrices in OSV basis are constructed in the reciprocal space. The 4-index electron repulsion integrals are calculated by local density fitting and, for distant pairs, via multipole approximation. New procedures for determining the fit-domains and the distant-pair lists, leading to higher efficiency in the 4-index integral evaluation, have been implemented. Generally, and in contrast to our previous PAO based periodic LMP2 method, the OSV-LMP2 method does not require anymore great care in the specification of the individual domains (to get a balanced description when calculating energy differences) and is in that sense a black box procedure. Discontinuities in potential energy surfaces, which may occur for PAO-based calculations if one is not careful, virtually disappear for OSV-LMP2. Moreover, due to much increased compactness of the pair-specific virtual spaces, the OSV-LMP2 calculations are faster and require much less memory than PAO-LMP2 calculations, despite the noticeable overhead of the initial OSV construction procedure. [ABSTRACT FROM AUTHOR]

In order to arrive at linear scaling of the computational cost with molecular size, local coupled cluster methods discriminate pairs of local molecular orbitals according to the spatial separation R of the latter. Only strong pairs are treated at the full coupled cluster level, whereas for weak pairs a lower level of theory (usually Møller-Plesset perturbation theory of second order,MP2) is used. Yet anMP2 treatment of weak pairs is inadequate in certain situations (for example, for describing p-stacking), which calls for an improved but still inexpensive method for dealing with the weak pairs. In a previous contribution, we proposed as a substituent for MP2 the LrCCD3 method, which is based on ring coupled cluster doubles (ring-CCD) and includes all third-order diagrams with energy contributions decaying not quicker than R-6. In the present work, we explore a still more accurate method, which is based on the same principles. It turned out to be essential to abandon the restriction to ring-CCD, i.e., to include further CCD diagrams beyond the ring approximation. The occurring intermediates turn out to be formally very similar to LMP2 density matrices, such that an efficient evaluation of these non-ring CCD diagrams is possible. Furthermore, a computationally cheap a posteriori estimate for the fourth-order singles contribution to the weak pair energy, which also exhibits a decay behavior of R-6, is introduced. The resulting method, denoted as LCCD[S]-R-6, indeed provides a substantial improvement in accuracy over the previous LrCCD3 method at a relatively modest additional computational cost. [ABSTRACT FROM AUTHOR]

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 Mo\ller-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. [ABSTRACT FROM AUTHOR]

We extend the orbital-specific-virtual tensor factorization, introduced for local Mo\ller-Plesset perturbation theory in Ref. [J. Yang, Y. Kurashige, F. R. Manby and G. K. L. Chan, J. Chem. Phys. 134, 044123 (2011)], to local coupled cluster singles and doubles theory (OSV-LCCSD). The method is implemented by modifying an efficient projected-atomic-orbital local coupled cluster program (PAO-LCCSD) described recently, [H.-J. Werner and M. Schütz, J. Chem. Phys. 135, 144116 (2011)]. By comparison of both methods we find that the compact representation of the amplitudes in the OSV approach affords various advantages, including smaller computational time requirements (for comparable accuracy), as well as a more systematic control of the error through a single energy threshold. Overall, the OSV-LCCSD approach together with an MP2 correction yields small domain errors in practical calculations. The applicability of the OSV-LCCSD is demonstrated for molecules with up to 73 atoms and realistic basis sets (up to 2334 basis functions). [ABSTRACT FROM AUTHOR]

The atomic orbital basis set limit is approached in periodic correlated calculations for solid LiH. The valence correlation energy is evaluated at the level of the local periodic second order Mo\ller-Plesset perturbation theory (MP2), using basis sets of progressively increasing size, and also employing 'bond'-centered basis functions in addition to the standard atom-centered ones. Extended basis sets, which contain linear dependencies, are processed only at the MP2 stage via a dual basis set scheme. The local approximation (domain) error has been consistently eliminated by expanding the orbital excitation domains. As a final result, it is demonstrated that the complete basis set limit can be reached for both HF and local MP2 periodic calculations, and a general scheme is outlined for the definition of high-quality atomic-orbital basis sets for solids. [ABSTRACT FROM AUTHOR]

We have calculated the equilibrium geometry, formation energy, and bulk modulus of two molecular bulk crystals, NH3 and CO2, at the periodic post-Hartree–Fock correlated level. The dependence of the results on the basis set has been analyzed, by employing basis sets up to aug-cc-pVQZ quality. In the calculations, we used the periodic local Mo\ller–Plesset second order perturbation theory (LMP2), implemented in the CRYSCOR program. Multipolar expansion techniques, as well as density fitting, are employed in this code to reduce the number of and to factorize the required electron repulsion integrals; as a consequence of that, the computational cost for the correlation part of the calculations is comparable to that of the Hartree–Fock. Auxiliary calculations performed on molecular dimers are also reported to verify the accuracy of the LMP2 approach and of the basis sets used. Furthermore, the effect of spin-component scaling has been investigated for the two crystals. One intention of the present paper is also to lay out and specify the computational setup, which is generally applicable for accurate CRYSCOR calculations on molecular crystals. [ABSTRACT FROM AUTHOR]

An efficient method to compute analytical energy derivatives for local second-order Møller–Plesset perturbation energy is presented. Density fitting approximations are employed for all 4-index integrals and their derivatives. Using local fitting approximations, quadratic scaling with molecular size and cubic scaling with basis set size for a given molecule is achieved. The density fitting approximations have a negligible effect on the accuracy of optimized equilibrium structures or computed energy differences. The method can be applied to much larger molecules and basis sets than any previous second-order Møller–Plesset gradient program. The efficiency and accuracy of the method is demonstrated for a number of organic molecules as well as for molecular clusters. Examples of geometry optimizations for molecules with 100 atoms and over 2000 basis functions without symmetry are presented. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The ground- and first excited state of s-tetrazine arising from a π*←n excitation (1Ag,1B3u) have been studied using the complete active space (CASSCF) and the second order multiconfiguration perturbation theory (CASPT2) ab initio methods. The focus of this study is on the effect of the electronic excitation on the molecular structure and on those electronic properties which are important to model the solvatochromatic behavior of the molecule in polymer matrices as used in permanent hole burning experiments. Since the accurate computation of excited state molecular properties represents a major challenge for today’s numerical quantum chemistry, some technical aspects are also considered. The present study shows that the change in geometry upon electronic excitation is small. This is in partial contradiction with the experimental studies which however disagree among themselves [see K. K. Innes, I. G. Ross, and W. R. Moomaw, J. Mol. Spectrosc. 132, 492 (1988), and R. E. Smalley, L. Wharton, and D. H. Levi, ibid. 66, 375 (1977)]. This study also confirms that the first excited state equilibrium structure is of D2h symmetry. In an earlier theoretical study it was found that the D2h symmetry structure may represent a saddle point rather than a minimum on the excited state potential surface [see A. C. Scheiner and H. F. Schaefer III, J. Chem. Phys. 87, 3539 (1987)]. In the first excited state, we observe an increase of the mean polarizability of s-tetrazine along with an enhanced anisotropy. The change in the polarizability is almost exclusively in the ‘‘in-plane’’ components of the tensor; the polarizability in the vertical direction is nearly unchanged. This observation questions recent experimental results reported for this molecule [see S. Heitz, D. Weidnauer, and A. Hese, J. Chem. Phys. 95, 7952 (1991)]. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A torsional potential energy surface for the cyclic water trimer was calculated at the level of second-order Mo\ller–Plesset perturbation theory. For the construction of this ab initio surface, the first-order wave function was expanded in a many-electron basis which linearly depends on the interelectronic coordinates r12. The one-electron basis of Gaussian orbitals was calibrated on the water monomer and dimer to ensure that the ab initio surface computed represents the (near- ) basis set limit for the level of theory applied. The positions of the free O—H bonds are described by three torsional angles. The respective three-dimensional torsional space was investigated by 70 counterpoise corrected single-point calculations for various values of these angles, providing a grid to fit an analytical representation of the potential energy surface. The four symmetry unique stationary points previously found at the Hartree–Fock and conventional Mo\ller–Plesset levels [Schütz et al., J. Chem. Phys. 99, 5228 (1993)] were studied in detail: Relative energies of the structures were calculated by applying second-order Mo\ller–Plesset and coupled cluster methods; harmonic vibrational frequencies were calculated at the second-order Mo\ller–Plesset level with a 6-311++G(d,p) basis set at these stationary points. It is expected that the present torsional potential energy surface for the water trimer will play an important role in the understanding of the vibrational transitions observed by far-infrared vibration–rotation–tunneling spectroscopy in terms of a nearly free pseudorotational interconversion on a cyclic vibrational–tunneling path. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The recently proposed minimax quadrature for Laplace-transformed energy denominators in second order Mo\ller–Plesset perturbation theory is compared to the conventionally used least-squares quadrature. Our test calculations show that the quality of the least-squares quadrature is not inferior compared to minimax. Its computational overhead (required to determine points and weights of the quadrature) is clearly insignificant relative to the subsequent MP2 calculation. For high accuracy and all-electron calculations (correlated core) good starting guesses for the roots are essential. [ABSTRACT FROM AUTHOR]

We present an accurate first-principles method for calculating the energy of physisorption, based on a fully periodic local M0ller-Plesset second order perturbation theory (LMP2) treatment. The LMP2 inter-surface-adsorbate interaction energy is scaled with a factor, obtained by comparing the method error of LMP2 versus coupled cluster singles doubles theory with perturbative triples at the basis set limit in small clusters mimicking the system under study. This method is applied to the investigation of geometrical frustration in argon monolayers adsorbed on the MgO (100) surface. It is found that several arrangements of the argon monolayer, i.e., 3x2, 4x2, optimal hexagonal, and Ç x 2 ID noncommensurate have very similar adsorption energies, which agrees with the experimental observations. Moreover, this study provides further insight in to the Ar-MgO adsorption process and sheds light on a controversy among different experiments. The calculated adsorption energy of 2.3 kcal/mol is in a very good agreement with the experimental values, which range from 2.0 to 2.3 kcal/mol, and provides a new benchmark for this system. [ABSTRACT FROM AUTHOR]

Periodic local Møller-Plesset second-order perturbation theory (MP2) is applied to investigate the structural and energetic properties of the cubic and hexagonal polymorphs of boron nitride. While the Hartree-Fock (HF) solution significantly underbinds both systems and energetically favors h-BN, the post-HF correlation treatment recovers the lacking amount of the interaction energy and reverts the sign of the relative stability between the two compounds. It provides the physically correct picture and predicts cohesive energies, lattice constants, bulk moduli, and the relative stability in good agreement with experiment. Density-functional theory (DFT) results, on the other hand, are inconclusive and exhibit a strong dependence on the chosen functional. The results of MP2 as well as DFT with an empirical dispersion correction indicate that the dispersion contribution to binding is essential not only for the layered polymorph, but also (and even more so) for the cubic one. [ABSTRACT FROM AUTHOR]