The MRCC program system: Accurate quantum chemistry from water to proteins.

MRCC is a package of ab initio and density functional quantum chemistry programs for accurate electronic structure calculations. The suite has efficient implementations of both low- and high-level correlation methods, such as second-order Møller-Plesset (MP2), random-phase approximation (RPA), second-order algebraic-diagrammatic construction [ADC(2)], coupled-cluster (CC), configuration interaction (CI), and related techniques. It has a state-of-the-art CC singles and doubles with perturbative triples [CCSD(T)] code, and its specialties, the arbitrary-order iterative and perturbative CC methods developed by automated programming tools, enable achieving convergence with regard to the level of correlation. The package also offers a collection of multi-reference CC and CI approaches. Efficient implementations of density functional theory (DFT) and more advanced combined DFT-wave function approaches are also available. Its other special features, the highly competitive linear-scaling local correlation schemes, allow for MP2, RPA, ADC(2), CCSD(T), and higher-order CC calculations for extended systems. Local correlation calculations can be considerably accelerated by multi-level approximations and DFT-embedding techniques, and an interface to molecular dynamics software is provided for quantum mechanics/molecular mechanics calculations. All components of MRCC support shared-memory parallelism, and multi-node parallelization is also available for various methods. For academic purposes, the package is available free of charge.

Novel strategy to implement active-space coupled-cluster methods.

A new approach is presented for the efficient implementation of coupled-cluster (CC) methods including higher excitations based on a molecular orbital space partitioned into active and inactive orbitals. In the new framework, the string representation of amplitudes and intermediates is used as long as it is beneficial, but the contractions are evaluated as matrix products. Using a new diagrammatic technique, the CC equations are represented in a compact form due to the string notations we introduced. As an application of these ideas, a new automated implementation of the single-reference-based multi-reference CC equations is presented for arbitrary excitation levels. The new program can be considered as an improvement over the previous implementations in many respects; e.g., diagram contributions are evaluated by efficient vectorized subroutines. Timings for test calculations for various complete active-space problems are presented. As an application of the new code, the weak interactions in the Be dimer were studied.

A quasiparticle-based multi-reference coupled-cluster method.

The purpose of this paper is to introduce a quasiparticle-based multi-reference coupled-cluster (MRCC) approach. The quasiparticles are introduced via a unitary transformation which allows us to represent a complete active space reference function and other elements of an orthonormal multi-reference (MR) basis in a determinant-like form. The quasiparticle creation and annihilation operators satisfy the fermion anti-commutation relations. On the basis of these quasiparticles, a generalization of the normal-ordered operator products for the MR case can be introduced as an alternative to the approach of Mukherjee and Kutzelnigg [Recent Prog. Many-Body Theor. 4, 127 (1995); Mukherjee and Kutzelnigg, J. Chem. Phys. 107, 432 (1997)]. Based on the new normal ordering any quasiparticle-based theory can be formulated using the well-known diagram techniques. Beyond the general quasiparticle framework we also present a possible realization of the unitary transformation. The suggested transformation has an exponential form where the parameters, holding exclusively active indices, are defined in a form similar to the wave operator of the unitary coupled-cluster approach. The definition of our quasiparticle-based MRCC approach strictly follows the form of the single-reference coupled-cluster method and retains several of its beneficial properties. Test results for small systems are presented using a pilot implementation of the new approach and compared to those obtained by other MR methods.

An efficient linear-scaling CCSD(T) method based on local natural orbitals.

An improved version of our general-order local coupled-cluster (CC) approach [Z. Rolik and M. Kállay, J. Chem. Phys. 135, 104111 (2011)] and its efficient implementation at the CC singles and doubles with perturbative triples [CCSD(T)] level is presented. The method combines the cluster-in-molecule approach of Li and co-workers [J. Chem. Phys. 131, 114109 (2009)] with frozen natural orbital (NO) techniques. To break down the unfavorable fifth-power scaling of our original approach a two-level domain construction algorithm has been developed. First, an extended domain of localized molecular orbitals (LMOs) is assembled based on the spatial distance of the orbitals. The necessary integrals are evaluated and transformed in these domains invoking the density fitting approximation. In the second step, for each occupied LMO of the extended domain a local subspace of occupied and virtual orbitals is constructed including approximate second-order Mo̸ller-Plesset NOs. The CC equations are solved and the perturbative corrections are calculated in the local subspace for each occupied LMO using a highly-efficient CCSD(T) code, which was optimized for the typical sizes of the local subspaces. The total correlation energy is evaluated as the sum of the individual contributions. The computation time of our approach scales linearly with the system size, while its memory and disk space requirements are independent thereof. Test calculations demonstrate that currently our method is one of the most efficient local CCSD(T) approaches and can be routinely applied to molecules of up to 100 atoms with reasonable basis sets.

A general-order local coupled-cluster method based on the cluster-in-molecule approach.

A general-order local coupled-cluster (CC) method is presented which has the potential to provide accurate correlation energies for extended systems. Our method combines the cluster-in-molecule approach of Li and co-workers [J. Chem. Phys. 131, 114109 (2009)] with the frozen natural orbital (NO) techniques widely used for the cost reduction of correlation methods. The occupied molecular orbitals (MOs) are localized, and for each occupied MO a local subspace of occupied and virtual orbitals is constructed using approximate Møller-Plesset NOs. The CC equations are solved and the correlation energies are calculated in the local subspace for each occupied MO, while the total correlation energy is evaluated as the sum of the individual contributions. The size of the local subspaces and the accuracy of the results can be controlled by varying only one parameter, the threshold for the occupation number of NOs which are included in the subspaces. Though our local CC method in its present form scales as the fifth power of the system size, our benchmark calculations show that it is still competitive for the CC singles and doubles (CCSD) and the CCSD with perturbative triples [CCSD(T)] approaches. For higher order CC methods, the reduction in computation time is more pronounced, and the new method enables calculations for considerably bigger molecules than before with a reasonable loss in accuracy. We also demonstrate that the independent calculation of the correlation contributions allows for a higher order description of the chemically more important segments of the molecule and a lower level treatment of the rest delivering further significant savings in computer time.

High-accuracy theoretical thermochemistry of atmospherically important sulfur-containing molecules.

In this study, several sulfur-containing molecules with atmospherical importance were investigated by means of high-accuracy quantum chemical calculations including: HSO, HOS, HOSO2, HSNO, SH, CH2SO, CH2SH, S2COH, and SCSOH. After identifying the stable conformers of the molecules, a coupled-cluster-based composite model chemistry, which includes contributions up to quadruple excitations as well as corrections beyond the nonrelativistic and Born­Oppenheimer approximations, was applied to calculate the corresponding heat of formation (Δ(f)H(0)° and Δ(f)H(298)°) and entropy (S(298)°) values. In most of the cases, this study delivers more reliable estimates for the investigated thermodynamic properties than those reported in previous investigations. Our data also suggest that the experimental heats of formation associated with the HSO molecule are very likely to belong to its structural isomer, HOS. It is also confirmed by the calculated thermodynamic properties including standard reaction entropies, enthalpies, and equilibrium constants that, in the reaction CS2 + OH CS2OH, the SCSOH structural isomer is produced. It is also noted that the currently accepted Δ(f)H(0)°(S(gas)) = 274.73 ± 0.3 kJ/mol value is in need of revision, and based on a recent measurement, which is also confirmed by our computations, it is advised to update it to Δ(f)H(0)°(S(gas)) = 277.25 ± 0.3 kJ/mol.

Cost reduction of high-order coupled-cluster methods via active-space and orbital transformation techniques.

We discuss several techniques which have the potential to decrease the computational expenses of high-order coupled-cluster (CC) methods with a reasonable loss in accuracy. In particular, the CC singles, doubles, and triples (CCSDT) as well as the CC singles, doubles, triples, and perturbative quadruples [CCSDT(Q)] methods are considered, which are frequently used in high-precision model chemistries for the calculation of iterative triples and quadruples corrections. First, we study the possibilities for using active spaces to decrease the computational costs. In this case, an active space is defined and some indices of cluster amplitudes are restricted to be in the space. Second, the application of transformed virtual orbitals is investigated. In this framework, to reduce the computation time the dimension of the properly transformed virtual one-particle space is truncated. We have found that the orbital transformation techniques outperform the active-space approaches. Using the transformation techniques, the computational time can be reduced in average by an order of magnitude without significant loss in accuracy. It is demonstrated that high-order CC calculations are possible for considerably larger systems than before using the implemented techniques.

High-accuracy thermochemistry of atmospherically important fluorinated and chlorinated methane derivatives.

High-precision quantum chemical calculations have been performed for atmospherically important halomethane derivatives including CF, CF(3), CHF(2), CH(2)F, CF(2), CF(4), CHF, CHF(3), CH(3)F, CH(2)F(2), CCl, CCl(3), CHCl(2), CH(2)Cl, CCl(2), CCl(4), CHCl, CHCl(3), CH(3)Cl, CH(2)Cl(2), CHFCl, CF(2)Cl, CFCl(2), CFCl, CFCl(3), CF(2)Cl(2), CF(3)Cl, CHFCl(2), CHF(2)Cl, and CH(2)FCl. Theoretical estimates for the standard enthalpy of formation at 0 and 298.15 K as well as for the entropy at 298.15 K are presented. The determined values are mostly within the experimental uncertainty where accurate experimental results are available, while for the majority of the considered heat of formation and entropy values the present results represent the best available estimates.

Comparative study of multireference perturbative theories for ground and excited states.

Three recently developed multireference perturbation theories (PTs)-generalized Van Vleck PT (GVVPT), state-specific multireference PT (SS-MRPT), and multiconfiguration PT (MCPT)-are briefly reviewed and compared numerically on representative examples, at the second order of approximations. We compute the dissociation potential curve of the LiH molecule and the BeH(2) system at various geometries, both in the ground and in the first excited singlet state. Furthermore, the ethylene twisting process is studied. Both Møller-Plesset (MP) and Epstein-Nesbet partition are used for MCPT and SS-MRPT, while GVVPT uses MP partitioning. An important thrust in our comparative study is to ascertain the degree of interplay of dynamical and nondynamical correlation for both ground and excited states. The same basis set and the same set of orbitals are used in all calculations to keep artifactual differences away when comparing the results. Nonparallelity error is used as a measure of the performance of the respective theories. Significant differences among the three methods appear when an intruder state is present. Additionally, difficulties arise (a) in MCPT when the choice of a pivot determinant becomes problematic, and (b) in SS-MRPT when there are small coefficients of the model function and there is implicit division by these coefficients, which generates a potential instability of the solutions. Ways to alleviate these latter shortcomings are suggested.

A sparse matrix based full-configuration interaction algorithm.

We present an algorithm related to the full-configuration interaction (FCI) method that makes complete use of the sparse nature of the coefficient vector representing the many-electron wave function in a determinantal basis. Main achievements of the presented sparse FCI (SFCI) algorithm are (i) development of an iteration procedure that avoids the storage of FCI size vectors; (ii) development of an efficient algorithm to evaluate the effect of the Hamiltonian when both the initial and the product vectors are sparse. As a result of point (i) large disk operations can be skipped which otherwise may be a bottleneck of the procedure. At point (ii) we progress by adopting the implementation of the linear transformation by Olsen et al. [J. Chem Phys. 89, 2185 (1988)] for the sparse case, getting the algorithm applicable to larger systems and faster at the same time. The error of a SFCI calculation depends only on the dropout thresholds for the sparse vectors, and can be tuned by controlling the amount of system memory passed to the procedure. The algorithm permits to perform FCI calculations on single node workstations for systems previously accessible only by supercomputers.

Multiconfiguration perturbation theory: size consistency at second order.

A modified version of a previously elaborated multiconfiguration perturbation theory (MCPT) [Rolik et al. J. Chem. Phys. 119, 1922 (2003)] is presented. In the modified formulation size consistency is ensured at second order in energy, by omitting projectors from the zero order Hamiltonian operator. This MCPT formulation is abbreviated as SC2-MCPT (size consistent at second order). To ensure proper separability, we also require that energy denominators are constructed as differences of some one-particle energies. A similar choice for energy denominators also renders the well-known multireference Moller-Plesset (MRMP) energy size consistent at second order. The same thing applies to the related multireference perturbation theory by Witek, Nakano, and Hirao.

Comparison of low-order multireference many-body perturbation theories.

Tests have been made to benchmark and assess the relative accuracies of low-order multireference perturbation theories as compared to coupled cluster (CC) and full configuration interaction (FCI) methods. Test calculations include the ground and some excited states of the Be, H(2), BeH(2), CH(2), and SiH(2) systems. Comparisons with FCI and CC calculations show that in most cases the effective valence shell Hamiltonian (H(v)) method is more accurate than other low-order multireference perturbation theories, although none of the perturbative methods is as accurate as the CC approximations. We also briefly discuss some of the basic differences among the multireference perturbation theories considered in this work.