Perturbative treatment of the similarity transformed Hamiltonian in equation‐of‐motion coupled‐cluster approximations
15 Jul 1995-Journal of Chemical Physics (American Institute of Physics)-Vol. 103, Iss: 3, pp 1064-1076
TL;DR: A series of sizeconsistent approximations to the equation-of-motion coupled cluster method in the singles and doubles approximation (EOM•CCSD) are developed by subjecting the similarity transformed Hamiltonian H=exp(−T)H exp(T) to a perturbation expansion as mentioned in this paper.
Abstract: A series of size‐consistent approximations to the equation‐of‐motion coupled cluster method in the singles and doubles approximation (EOM‐CCSD) are developed by subjecting the similarity transformed Hamiltonian H=exp(−T)H exp(T) to a perturbation expansion Attention is directed to N and N−1 electron final state realizations of the method defined by truncation of H at second order Explicit spin–orbital equations for the energy and its first derivative are documented for both approaches [EOMEE‐CCSD(2) and EOMIP‐CCSD(2), respectively], and have been implemented in a large‐scale quantum chemistry program Vertical ionization potentials calculated by EOMIP‐CCSD(2) are shown to be equivalent to those of an approach presented recently by Nooijen and Snijders [J Chem Phys 102, 1681 (1995)] Applications of both EOMIP‐CCSD(2) and EOMEE‐CCSD(2) provide results for final state properties that compare favorably with those obtained in full EOM‐CCSD calculations Analysis of the computational aspects of the approximate and full EOM‐CCSD methods shows that the cost of EOMIP‐CCSD(2) energy and gradient calculations scales in proportion to the fifth power of the basis set size, a significant savings over the sixth power dependence of EOMIP‐CCSD This feature is of great practical importance, as it shows that this N−1 electron final state approach has a large domain of applicability and is therefore likely to become a valuable tool for application calculations On the other hand, the same cannot be said for EOMEE‐CCSD(2) since its asymptotic computational dependence and storage requirements are the same as the full EOMEE‐CCSD method
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Pacific Northwest National Laboratory1, Lawrence Berkeley National Laboratory2, National Center for Computational Sciences3, Brookhaven National Laboratory4, Argonne National Laboratory5, Intel6, University of Texas at Arlington7, State University of New York System8, Pennsylvania State University9, Oak Ridge National Laboratory10, Washington University in St. Louis11, Wellesley College12, Maria Curie-Skłodowska University13, Iowa State University14, Academy of Sciences of the Czech Republic15, University of Tennessee at Martin16, Université libre de Bruxelles17, Facebook18, Russian Academy of Sciences19, University of Minnesota20, University of Washington21, United States Naval Research Laboratory22, Georgia Institute of Technology23, University of St Andrews24, Universidad Autónoma Metropolitana25, University of California, San Diego26, Saarland University27, Sandia National Laboratories28, University of Illinois at Urbana–Champaign29, University of Iceland30, Australian National University31, Florida Institute of Technology32, University of Science and Technology of China33, Oswaldo Cruz Foundation34, Cardiff University35, Louisiana State University36, Chinese Academy of Sciences37, National Autonomous University of Mexico38, University of Florida39, Los Alamos National Laboratory40, University of Oviedo41, Prince of Songkla University42, Ames Laboratory43, University of Utah44, Northwestern University45, Universal Display Corporation46, Federal University of Pernambuco47, CD-adapco48, Cray49, Massachusetts Institute of Technology50, Nvidia51, University of Tennessee52, Shandong Normal University53, University of Cambridge54, Advanced Micro Devices55, Technische Universität München56, Stanford University57, Wuhan University of Technology58, Stony Brook University59
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References
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TL;DR: In this paper, a reliable procedure for calculating the electron affinity of an atom and present results for hydrogen, boron, carbon, oxygen, and fluorine (hydrogen is included for completeness).
Abstract: The calculation of accurate electron affinities (EAs) of atomic or molecular species is one of the most challenging tasks in quantum chemistry. We describe a reliable procedure for calculating the electron affinity of an atom and present results for hydrogen, boron, carbon, oxygen, and fluorine (hydrogen is included for completeness). This procedure involves the use of the recently proposed correlation‐consistent basis sets augmented with functions to describe the more diffuse character of the atomic anion coupled with a straightforward, uniform expansion of the reference space for multireference singles and doubles configuration‐interaction (MRSD‐CI) calculations. Comparison with previous results and with corresponding full CI calculations are given. The most accurate EAs obtained from the MRSD‐CI calculations are (with experimental values in parentheses) hydrogen 0.740 eV (0.754), boron 0.258 (0.277), carbon 1.245 (1.263), oxygen 1.384 (1.461), and fluorine 3.337 (3.401). The EAs obtained from the MR‐SD...
12,969 citations
TL;DR: The coupled cluster singles and doubles model (CCSD) as discussed by the authors is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin-orbital form, and the computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are compared with full CI calculations for H2O and BeH2.
Abstract: The coupled‐cluster singles and doubles model (CCSD) is derived algebraically, presenting the full set of equations for a general reference function explicitly in spin–orbital form. The computational implementation of the CCSD model, which involves cubic and quartic terms, is discussed and results are reported and compared with full CI calculations for H2O and BeH2. We demonstrate that the CCSD exponential ansatz sums higher‐order correlation effects efficiently even for BeH2, near its transition state geometry where quasidegeneracy efforts are quite large, recovering 98% of the full CI correlation energy. For H2O, CCSD plus the fourth‐order triple excitation correction agrees with the full CI energy to 0.5 kcal/mol. Comparisons with low‐order models provide estimates of the effect of the higher‐order terms T1T2, T21T2, T31, and T41 on the correlation energy.
5,603 citations
TL;DR: In this article, a method for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one-electron approximation is proposed.
Abstract: A method is suggested for the calculation of the matrix elements of the logarithm of an operator which gives the exact wavefunction when operating on the wavefunction in the one‐electron approximation. The method is based on the use of the creation and annihilation operators, hole—particle formalism, Wick's theorem, and the technique of Feynman‐like diagrams. The connection of this method with the configuration‐interaction method as well as with the perturbation theory in the quantum‐field theoretical form is discussed. The method is applied to the simple models of nitrogen and benzene molecules. The results are compared with those obtained with the configuration‐interaction method considering all possible configurations within the chosen basis of one‐electron functions.
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TL;DR: In this paper, a comprehensive overview of the equation of motion coupled-cluster (EOM•CC) method and its application to molecular systems is presented by exploiting the biorthogonal nature of the theory, it is shown that excited state properties and transition strengths can be evaluated via a generalized expectation value approach that incorporates both the bra and ket state wave functions.
Abstract: A comprehensive overview of the equation of motion coupled‐cluster (EOM‐CC) method and its application to molecular systems is presented. By exploiting the biorthogonal nature of the theory, it is shown that excited state properties and transition strengths can be evaluated via a generalized expectation value approach that incorporates both the bra and ket state wave functions. Reduced density matrices defined by this procedure are given by closed form expressions. For the root of the EOM‐CC effective Hamiltonian that corresponds to the ground state, the resulting equations are equivalent to the usual expressions for normal single‐reference CC density matrices. Thus, the method described in this paper provides a universal definition of coupled‐cluster density matrices, providing a link between EOM‐CC and traditional ground state CC theory.Excitation energy,oscillator strength, and property calculations are illustrated by means of several numerical examples, including comparisons with full configuration interaction calculations and a detailed study of the ten lowest electronically excited states of the cyclic isomer of C4.
2,171 citations