Rodney J. Bartlett

A full coupled‐cluster singles and doubles model: The inclusion of disconnected triples

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.

The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties

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.

Coupled‐cluster methods with noniterative triple excitations for restricted open‐shell Hartree–Fock and other general single determinant reference functions. Energies and analytical gradients

A new, noniterative triples correction to the coupled‐cluster singles and doubles (CCSD), method, for general single determinant reference functions is proposed and investigated numerically for various cases, including non‐Hartree–Fock (non‐HF) reference functions. It is correct through fourth‐order of perturbation theory for non‐HF references, and unlike other such methods, retains the usual invariance properties common to CC methods, while requiring only a single N7 step. In the canonical Hartree–Fock case, the method is equivalent to the usual CCSD(T) method, but now permits the use of restricted open‐shell Hartree‐Fock (ROHF) and quasirestricted Hartree–Fock (QRHF) reference determinants, along with many others. Comparisons with full configuration interaction (FCI) results are presented for CH2, CH2+, CH3, NH2, and SiH2. The paper also reports the derivation and initial computational implementation of analytical gradients for the ROHF‐CCSD(T) method, which includes unrestricted Hartree–Fock (UHF) CCSD...

The full CCSDT model for molecular electronic structure

The full coupled‐cluster model (CCSDT) single, double, and triple excitation method defined by the wave function exp(T1+T2+T3)‖Φ0〉 is formulated and computationally implemented for the first time. Explicit computational equations are presented. The method is applied to numerous examples including BH, FH, C2H2, CO, Ne, F−, and H2O to assess its applicability to the correlation problem. Results from CCSDT agree with full CI, to an average error of less than 1 kcal/mol even for difficult bond breaking examples. A series of results for various approximate, but computationally more efficient versions of the full CCSDT model are also studied and shown to give results in excellent agreement with CCSDT. Additional comparisons with fifth‐order MBPT are reported.

Towards a full CCSDT model for electron correlation

Coupled cluster models for electron correlation which include the effects of single, double, and triple excitation operators are analyzed. An alternate version of the approximate CCSDT‐1 method is implemented. In this version, the full CCSDT cluster operator eT1+T2+T3 is preserved in the creation of single and double excitation coefficients, but in calculation of triple excitation coefficients only the T2 operator is used. We also present a theoretical analysis of the simplest improvement for the evaluation of the contribution of triples beyond that obtained with fourth‐order MBPT. In this approximation, an MBPT(4)‐like calculation of the triples energy is evaluated with converged CCSD T2 coefficients. This is found to offer a good approximation to the converged CCSDT‐1 results.

Non-iterative fifth-order triple and quadruple excitation energy corrections in correlated methods

Abstract In critical cases, single-reference correlated methods like coupled-cluster theory or its quadratic CI approximations fail because of the importance of additional highly excited excitations that cannot usually be included, like connected triple and quadruple excitations. Here we present the first, non-iterative method to evaluate the full set of fifth-order corrections to CCSD and QCISD and assess their accuracy compared to full CI for the very sensitive Be 2 curve and other cases.

The equation-of-motion coupled-cluster method: Excitation energies of Be and CO

Abstract The equation-of-motion coupled-cluster (EOM-CC) method for the calculation of excitation energies is presented. The procedure is based upon representing an excited state as an excitation from a coupled-cluster ground state and the excitation energies are obtained by solving a non-Hermitian eigenvalue problem. Numerical applications are reported for Be and CO, and compared to full CI, Fock space multi-reference coupled-cluster, multi-reference MBPT, and propagator results.

Analytic energy derivatives in many‐body methods. I. First derivatives

Second derivatives of the energy correspond to second‐order response properties and molecular force constants. Currently, both the theory and application of analytic second derivatives in many‐body methods are limited to second‐order perturbation theory. The general theory of analytic second derivatives for the coupled‐cluster (CC) model is presented. The analytic expressions for the second derivative of the energy are given in terms of the response (or ‘‘relaxed’’) density, discussed in part I, and the first‐derivative t amplitudes for efficient evaluation. Explicit expressions for the second derivatives of the coupled‐cluster singles, doubles, and linearized triples model (CCSDT‐1) are presented. Analytic derivatives for the finite‐order MBPT(3) and MBPT(4) models are derived as special cases of the theory.

A coupled cluster approach with triple excitations

The coupled‐cluster model for electron correlation is generalized to include the effects of connected triple excitation contributions. The detailed equations for triple excitation amplitudes are presented, and a simplified version implemented that retains the dominant terms. The model presented, CCSDT‐1, provides the energy correct through fourth order and the wave function through second order. The CCSDT‐1 model is illustrated by comparing with full CI results for HF, BH, and H2O, the latter at several geometries.

Equation of motion coupled cluster method for electron attachment

The electron attachment equation of motion coupled cluster (EA‐EOMCC) method is derived which enables determination of the various bound states of an (N+1)‐electron system and the corresponding energy eigenvalues relative to the energy of an N‐electron CCSD reference state. Detailed working equations for the EA‐EOMCC method are derived using diagrammatic techniques for both closed‐shell and open‐shell CCSD reference states based upon a single determinant. The EA‐EOMCC method is applied to a variety of different problems, the main purpose being to establish its prospects and limitations. The results from EA‐EOMCC calculations are compared to other EOMCC approaches, starting from different reference states, as well as other theoretical methods and experimental values, where available. We have investigated electron affinities for a wide selection of both closed‐shell and open‐shell systems. Excitation spectra of atoms and molecules with an odd number of electrons are obtained, taking the closed‐shell ground ...