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In this paper, we report reimplementation of the core algorithms of relativistic coupled cluster theory aimed at modern heterogeneous high-performance computational infrastructures. The code is designed for parallel execution on many compute nodes with optional GPU coprocessing, accomplished via the new ExaTENSOR back end. The resulting ExaCorr module is primarily intended for calculations of molecules with one or more heavy elements, as relativistic effects on the electronic structure are included from the outset. In the current work, we thereby focus on exact two-component methods and demonstrate the accuracy and performance of the software. The module can be used as a stand-alone program requiring a set of molecular orbital coefficients as the starting point, but it is also interfaced to the DIRAC program that can be used to generate these. We therefore also briefly discuss an improvement of the parallel computing aspects of the relativistic self-consistent field algorithm of the DIRAC program.
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The implementation and evaluation of a multilayer extension of the divide-expand-consolidate (DEC) scheme within the LSDalton program is presented. The DEC scheme is a linear-scaling, fragmentation-based local coupled-cluster (CC) method that provides a means of overcoming the scaling wall associated with canonical CC electronic structure calculations on large molecular systems. Taking advantage of the local nature of correlation effects, the correlation energy for the full molecule is calculated from a set of independent fragments using localized molecular orbitals. However, when only a small subsystem of a larger system is of interest, for example, adsorption sites or catalytically active sites, the majority of the computational time may be spent evaluating the correlation energy of fragments which have little effect on the properties in the area of interest (AOI). The multilayer DEC (ML-DEC) scheme addresses this by taking advantage of the independent nature of the fragments in order to evaluate the correlation energy of various regions of the system at different levels of theory. Regions far from the AOI are evaluated at lower (cheaper) levels of theory such as Hartree-Fock (HF) or Møller-Plesset second-order perturbation theory (MP2), while the area immediately surrounding the AOI is treated with a higher level CC model. Through the ML-DEC scheme, the computational cost of CC calculations on these types of systems can be significantly reduced while maintaining the accuracy of higher-level calculations. Results from HF/RI-MP2 and RI-MP2/CCSD ML-DEC calculations of the binding energy of a fatty acid dimer are presented. We find that the ML-DEC scheme is capable of reproducing DEC energy differences at a target level of theory, provided that the region treated at the target level of theory is chosen to be sufficiently large. Time-to-solution is found to be significantly reduced, particularly in the RI-MP2/CCSD calculations. Finally, the ML-DEC scheme is applied to the calculation of CO2 adsorption in a Mg-MOF-74 channel.
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The earlier proposed multi-reference state-specific coupled-cluster theory with the complete active space reference [CASCC; Lyakh et al., J. Chem. Phys. 122, 024108 (2005)] suffered from a problem of energy discontinuities when the formal reference state was changing in the calculation of the potential energy curve (PEC). A simple remedy to the discontinuity problem is found and is presented in this work. It involves using natural complete active space self-consistent field active orbitals in the complete active space coupled-cluster calculations. The approach gives smooth PECs for different types of dissociation problems, as illustrated in the calculations of the dissociation of the single bond in the hydrogen fluorine molecule and of the symmetric double-bond dissociation in the water molecule.
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The recently developed method [M. Musial, J. Chem. Phys. 136, 134111 (2012)] to study double electron attached states has been applied to the description of the ground and excited state potential energy curves of the alkali metal dimers. The method is based on the multireference coupled cluster scheme formulated within the Fock space formalism for the (2,0) sector. Due to the use of the efficient intermediate Hamiltonian formulation, the approach is free from the intruder states problem. The description of the neutral alkali metal dimers is accomplished via attaching two electrons to the corresponding doubly ionized system. This way is particularly advantageous when a closed shell molecule dissociates into open shell subunits while its doubly positive cation generates the closed shell fragments. In the current work, we generate the potential energy curves for the ground and multiple excited states of the Li2 and Na2 molecules. In all cases the potential energy curves are smooth for the entire range of interatomic distances (from the equilibrium point to the dissociation limit). Based on the calculated potential energy curves, we are able to compute spectroscopic parameters of the systems studied.
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The initial implementation of the triple electron attachment (TEA) equation-of-motion (EOM) coupled cluster (CC) method is presented, aiming at the description of electronic states with three open shell electrons outside a suitably chosen closed shell vacuum. In particular, such an approach can be used for describing dissociation of chemical bonds predominantly formed by three valence electrons, for example, in LiC and NaC molecules. Both ground and excited states are considered while rigorously maintaining the correct spin value. The preliminary results show a correct asymptotic behavior of the dissociation curves. At the same time, we emphasize that a chemically accurate description will require an extension of the minimal TEA-EOM-CC model introduced here, analogous to those already used in the double ionization potential and double electron attachment methods.
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A formulation of an adaptive coupled-cluster theory is presented. The method automatically "adjusts" to any state of an electronic system and converges to the full CI limit, thus being capable of describing both single- and multireference phenomena. Adaptivity is accomplished through a guided selection of a compact set of cluster amplitudes as required for a proper description of the electronic system under consideration. The approach suggested is of "black-box" type. A special importance-selection function (discriminatory function) is explicitly introduced for the guided selection of variables involved in the theoretical model. The method is tested on molecules which exhibit strong multireference character in the region of chemical bond elongation. An unambiguous comparison with formally exact full CI solutions shows that the method is capable of providing mHartee accuracy using a rather compact set of cluster amplitudes.
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This work reviews the state-specific multireference coupled-cluster (CC) approaches which have been developed as approximate methods for performing high-level quantum mechanical calculations on quasidegenerate ground and excited states of atomic and molecular systems. The term "quasidegenerate" refers to a state that cannot be described even in the first approximation by a single-determinant wavefunction (a Slater determinant), but requires two or more determinants for this purpose. The main challenge with applying the coupled-cluster theory to such states is in describing the electron correlation effects in the wavefunctions representing these states in a manner that is size-extensive, yet accurate and simple enough so the method can be routinely applied to small and medium-size molecular systems. We are describing how this can be accomplished within a theory that focuses on only one state of the system in a single CC calculation (the state-specific theory).
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The complete-active-space coupled-cluster approach with single and double excitations (CASCCSD) based on the ansatz of Oliphant and Adamowicz [J. Chem. Phys. 94, 1229 (1991); 96, 3739 (1992)] is used to derive an approach termed XCASCCSD for calculating potential energy surfaces of ground and excited electronic states with different multiplicities and symmetries. The XCASCCSD approach explicitly includes a procedure for spin and spatial orbital-momentum symmetry adaptation of the wave function that has allowed us to consider states with degenerate formal references. The XCASCCSD method is applied to calculate potential energy surfaces of the ground and some lowest singlet and triplet excited states of the FH and C(2) molecules. Some states of C(2) are known to have a very strong "multireference" character making their description difficult with single-reference methods. The problem of the change of the formal reference determinant along the potential energy surface is discussed. Also, vertical excitation energies of formaldehyde calculated with the XCASCCSD approach are presented.
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The recently proposed multireference state-specific coupled-cluster theory with the complete active space reference has been used to study electronically excited states with different spatial and spin symmetries. The algorithm for the method has been obtained using the computerized approach for automatic generation of coupled-cluster diagrams with an arbitrary level of the electronic excitation from a formal reference determinant. The formal reference is also used to generate the genuine reference state in the form of a linear combination of determinants contracted to a configuration with the spin and spatial symmetries of the target state. The natural-orbital expansions of the one-electron configuration inferaction density matrix allowed us to obtain the most compact orbital space for the expansion of the reference function. We applied our approach in the calculations of singlet and triplet states of different spatial symmetries of the water molecule. The comparisons of the results with values obtained using other many-particle methods and with the full configuration interaction results demonstrate good ability of the approach to deal with electronic excited states.
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An algorithm for generation of the spin-orbital diagrammatic representation, the corresponding algebraical formulas, and the computer code of the coupled-cluster (CC) method with an arbitrary level of the electronic excitations has been developed. The method was implemented in the general case as well as for specific application in the state-specific multireference coupled-cluster theory (SSMRCC) based on the concept of a "formal reference state." The algorithm was tested in SSMRCC calculations describing dissociation of a single bond and in calculations describing simultaneous dissociation of two single bonds--the problem requiring up to six-particle excitations in the CC operator.