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Sherrill, C. David

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Author: Bochevarov, Arteum D. ×

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    Hybrid correlation models based on active-space partitioning: Seeking accurate O(N ⁵) ab initio methods for bond breaking
    (Georgia Institute of Technology, 2006-08) Bochevarov, Arteum D. ; Temelso, Berhane ; Sherrill, C. David
    Møller-Plesset second-order (MP2) perturbation theory remains the least expensive standard ab initio method that includes electron correlation, scaling as O(N ⁵) with the number of molecular orbitals N. Unfortunately, when restricted Hartree-Fock orbitals are employed, the potential energy curves calculated with this method are of little use at large interatomic separations because of the divergent behavior of MP2 in these regions. In our previous study [J. Chem. Phys. 122, 234110 (2005)] we combined the MP2 method with the singles and doubles coupled cluster (CCSD) method to produce a hybrid method that retains the computational scaling of MP2 and improves dramatically the shape of the MP2 curves. In this work we expand the hybrid methodology to several other schemes. We investigate a new, improved MP2-CCSD method as well as a few other O(N ⁵) methods related to the Epstein-Nesbet pair correlation theory. Nonparallelity errors across the dissociation curve as well as several spectroscopic constants are computed for BH, HF, H₂O, CH+, CH₄, and Li₂ molecules with the 6-31G* basis set and compared with the corresponding full configuration interaction results. We show that among the O(N ⁵) methods considered, our new hybrid MP2-CCSD method is the most accurate and significantly outperforms MP2 not only at large interatomic separations, but also near equilibrium geometries.
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    Hybrid correlation models based on active-space partitioning: Correcting second-order Møller-Plesset perturbation theory for bond-breaking reactions
    (Georgia Institute of Technology, 2005-06) Bochevarov, Arteum D. ; Sherrill, C. David
    Møller–Plesset second-order (MP2) perturbation theory breaks down at molecular geometries which are far away from equilibrium. We decompose the MP2 energy into contributions from different orbital subspaces and show that the divergent behavior of the MP2 energy comes from the excitations located within a small (or sometimes even the minimal) active space. The divergent behavior of the MP2 energy at large interfragment distances may be corrected by replacing a small number of terms by their more robust counterparts from coupled-cluster (CCSD) theory. We investigated several schemes of such a substitution, and we find that a coupling between the active-space CCSD and the remaining MP2 amplitudes is necessary to obtain the best results. This naturally leads us to an approach which has previously been examined in the context of cost-saving approximations to CCSD for equilibrium properties by Nooijen [ J. Chem. Phys. 111, 10815 (1999) ]. The hybrid MP2–CCSD approach, which has the same formal scaling as conventional MP2 theory, provides potential curves with a correct shape for bond-breaking reactions of BH, CH₄, and HF. The error of the MP2–CCSD method (measured against full configuration-interaction data) is smaller than that of MP2 at all interfragment separations and is qualitatively similar to that of full CCSD.
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    A general diagrammatic algorithm for contraction and subsequent simplification of second-quantized expressions
    (Georgia Institute of Technology, 2004-08) Bochevarov, Arteum D. ; Sherrill, C. David
    We present a general computer algorithm to contract an arbitrary number of second-quantized expressions and simplify the obtained analytical result. The functions that perform these operations are a part of the program Nostromo which facilitates the handling and analysis of the complicated mathematical formulas which are often encountered in modern quantum-chemical models. In contrast to existing codes of this kind, Nostromo is based solely on the Goldstone-diagrammatic representation of algebraic expressions in Fock space and has capabilities to work with operators as well as scalars. Each Goldstone diagram is internally represented by a line of text which is easy to interpret and transform. The calculation of matrix elements does not exploit Wick’s theorem in a direct way, but uses diagrammatic techniques to produce only nonzero terms. The identification of equivalent expressions and their subsequent factorization in the final result is performed easily by analyzing the topological structure of the diagrammatic expressions.