The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties
01 May 1993-Journal of Chemical Physics (American Institute of Physics)-Vol. 98, Iss: 9, pp 7029-7039
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.
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TL;DR: In this paper, the three-parameter Lee-Yang-Parr (B3LYP) functional was used to compute low-lying electronic excitations of N2, ethylene, formaldehyde, pyridine and porphin.
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TL;DR: In this article, the essential aspects of coupled-cluster theory are explained and illustrated with informative numerical results, showing that the theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules.
Abstract: Today, coupled-cluster theory offers the most accurate results among the practical ab initio electronic-structure theories applicable to moderate-sized molecules. Though it was originally proposed for problems in physics, it has seen its greatest development in chemistry, enabling an extensive range of applications to molecular structure, excited states, properties, and all kinds of spectroscopy. In this review, the essential aspects of the theory are explained and illustrated with informative numerical results.
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Cites background or methods from "The equation of motion coupled‐clus..."
...Limiting Rk to single and double excitations, h = h1h2 , defines EOM-CCSD Comeau and Bartlett, 1993; Stanton and Bartlett, 1993b; Geertsen et al., 1989 see Figs....
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...So, in practice, to avoid evaluation of the inverse resolvent, one solves the linear equation Stanton and Bartlett, 1993a h1 E − H̄ h1 h1 E − H̄ h2 h2 E − H̄ h1 h2 E − H̄ h2 C1 C2 = h1 1 + h̄ 0 h2 1 + h̄ 0 , which can be accomplished much more efficiently using the same kind of numerical methods…...
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...…reason for this is that these states have a large component of double excitation character, which can be judged by the large weight of double excitations in the excitedstate wave function, perhaps most easily measured by the magnitude of the amplitudes from R1 and R2 Stanton and Bartlett, 1993b ....
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TL;DR: Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.
Abstract: Advances in theory and algorithms for electronic structure calculations must be incorporated into program packages to enable them to become routinely used by the broader chemical community. This work reviews advances made over the past five years or so that constitute the major improvements contained in a new release of the Q-Chem quantum chemistry package, together with illustrative timings and applications. Specific developments discussed include fast methods for density functional theory calculations, linear scaling evaluation of energies, NMR chemical shifts and electric properties, fast auxiliary basis function methods for correlated energies and gradients, equation-of-motion coupled cluster methods for ground and excited states, geminal wavefunctions, embedding methods and techniques for exploring potential energy surfaces.
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TL;DR: In this article, an approximate coupled cluster singles and doubles model is presented, denoted CC2, where the total energy is of second-order Moller-Plesset perturbation theory (MP2) quality.
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References
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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 general procedure for calculation of the electron correlation energy, starting from a single Hartree-Fock determinant, is introduced, and the relation of this method to coupled-cluster (CCSD) theory is discussed.
Abstract: A general procedure is introduced for calculation of the electron correlation energy, starting from a single Hartree–Fock determinant. The normal equations of (linear) configuration interaction theory are modified by introducing new terms which are quadratic in the configuration coefficients and which ensure size consistency in the resulting total energy. When used in the truncated configuration space of single and double substitutions, the method, termed QCISD, leads to a tractable set of quadratic equations. The relation of this method to coupled‐cluster (CCSD) theory is discussed. A simplified method of adding corrections for triple substitutions is outlined, leading to a method termed QCISD(T). Both of these new procedures are tested (and compared with other procedures) by application to some small systems for which full configuration interaction results are available.
4,194 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: Manybody perturbation theory (MBPT) and coupled-cluster methcoder (CCM) were defined in this paper as a subset of the N-body problem.
Abstract: Ten years ago in the Annual Review of Physical Chemistry. there was a review article entitled "Many-Body Theories of the Electronic Structure of Atoms and Molecules," by Karl Freed ( 1 ) . In that article many-body methods were defined to be those techniques which derive their impetus from theories of the N-body problem for which N --+ 00. For the purposes of this review, we further specify these methods as many-body perturba tion theory (MBPT) (2-5) and the closely related coupled-cluster meth ods (CCM) (6-9) . In the ten years since that review appeared, probably no area in theo retical chemistry has undergone more development than has the theory, methodology, and applications of such ab initio many-body methods for
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