Excitation Coupled-cluster Theory Research Articles

Accurate Theoretical Thermochemistry for Fluoroethyl Radicals.

An accurate coupled-cluster (CC) based model chemistry was applied to calculate reliable thermochemical quantities for hydrofluorocarbon derivatives including radicals 1-fluoroethyl (CH3-CHF), 1,1-difluoroethyl (CH3-CF2), 2-fluoroethyl (CH2F-CH2), 1,2-difluoroethyl (CH2F-CHF), 2,2-difluoroethyl (CHF2-CH2), 2,2,2-trifluoroethyl (CF3-CH2), 1,2,2,2-tetrafluoroethyl (CF3-CHF), and pentafluoroethyl (CF3-CF2). The model chemistry used contains iterative triple and perturbative quadruple excitations in CC theory, as well as scalar relativistic and diagonal Born-Oppenheimer corrections. To obtain heat of formation values with better than chemical accuracy perturbative quadruple excitations and scalar relativistic corrections were inevitable. Their contributions to the heats of formation steadily increase with the number of fluorine atoms in the radical reaching 10 kJ/mol for CF3-CF2. When discrepancies were found between the experimental and our values it was always possible to resolve the issue by recalculating the experimental result with currently recommended auxiliary data. For each radical studied here this study delivers the best heat of formation as well as entropy data.

Dissociation of the Fluorine Molecule

The primary purpose of the present study is to resolve the discrepancy that exists between the two most recently published dissociation energies for the fluorine molecule [D0(F2)] and, consequently, for the associated heats of formation of the fluorine atom [ΔfH0°(F)]. We hope to provide a reliable, well-established theoretical estimate for these thermochemical quantities. To this end, a high-accuracy coupled-cluster-based composite ab initio model chemistry has been utilized. The protocol involves contributions of up to pentuple excitations in coupled-cluster theory augmented with basis set extrapolation techniques and additional corrections beyond the nonrelativistic and Born–Oppenheimer approximations. The augmented core–valence correlation consistent basis set families, aug-cc-pCVXZ, have been successively used, in some cases, up to octuple-ζ quality. Our best theoretical results for D0(F2) and ΔfH0°(F) obtained in this study are 154.95 ± 0.48 and 77.48 ± 0.24 kJ/mol, respectively. Because conflicting theoretical results are also reported about the existence of a barrier along the dissociation curve of F2, extensive multireference configuration interaction and coupled-cluster calculations have been performed using reference orbitals taken from all-electron complete active space self-consistent field computations. Extrapolations from the results obtained with the aug-cc-pCVXZ (X = T, Q, 5) basis sets clearly indicate that the barrier indeed exists. It is located at 3.80 ± 0.20 Å along the dissociation curve with a height of 42 ± 10 μEh (∼0.11 ± 0.03 kJ/mol). Because of the neglect of this effect during the evaluation of the raw experimental data used to obtain D0(F2) = 154.52 ± 0.12 kJ/mol and ΔfH0°(F) = 77.26 ± 0.06 kJ/mol [Stevens; et al. J. Phys. Chem. A 2010, 114, 13134], an additional error should be attached to these latter values. Obviously, the barrier does not affect either the experimental results, D0(F2) = 154.92 ± 0.10 kJ/mol and ΔfH0°(F) = 77.46 ± 0.05 kJ/mol [Yang; et al. J. Chem. Phys. 2005, 122, 134308; 2007, 127, 209901], which are based on the ion-pair dissociation of the molecule, or the data calculated theoretically. It is also noteworthy that our best estimates are in excellent agreement with those obtained from the ion-pair dissociation experiment.

Alternative perturbation theories for triple excitations in coupled-cluster theory

The dominant method of small molecule quantum chemistry over the last twenty years is CCSD(T). Despite this success, RHF-based CCSD(T) fails for systems away from equilibrium. Work over the last ten years has lead to modifications of CCSD(T) that improve the description of bond breaking. These new methods include ΛCCSD(T), CCSD(2) T , CCSD(2) and CR-CC(2,3), which are new perturbative corrections to single-reference CCSD. We present a unified derivation of these methods and compare them at the level of formal theory and computational accuracy. None of the methods is clearly superior, although formal considerations favour ΛCCSD(T) and computational accuracy for the systems considered favours CR-CC(2,3).

Explicitly correlated connected triple excitations in coupled-cluster theory

A way to incorporate explicit electron correlation into connected triple excitations in coupled-cluster theory is proposed. The new ansatz is applied to the coupled-cluster singles and doubles model with noniterative triple excitations [CCSD(T)] and does not introduce any further sets of equations to be solved. A first implementation using automated generation and string-based evaluation of the explicit expressions is reported. The results demonstrate that the ansatz significantly enhances the basis set convergence of the noniterative triple excitation correction and thus improves upon previous approaches to explicitly correlated CCSD(T).

Approximate treatment of higher excitations in coupled-cluster theory. II. Extension to general single-determinant reference functions and improved approaches for the canonical Hartree–Fock case

The theory and implementation of approximate coupled-cluster (CC), in particular approximate CC singles, doubles, triples, and quadruples methods, are discussed for general single-determinant reference functions. While the extension of iterative approximate models to the non-Hartree-Fock case is straightforward, the generalization of perturbative approaches is not trivial. In contrast to the corresponding perturbative triples methods, there are additional terms required for non-Hartree-Fock reference functions, and there are several possibilities to derive approximations to these terms. As it turns out impossible to develop an approach that is consistent with the canonical Hartree-Fock-based theory, several new approximations have been implemented and their performance for total energies and heats of formation has been assessed. The numerical results show that the performance of the methods does not depend strongly on the approximations assumed. Furthermore, the new perturbative quadruples methods, when applied to canonical Hartree-Fock reference functions, outperform at least for absolute energies the existing ones without increasing the computational costs.

Approximate treatment of higher excitations in coupled-cluster theory

The possibilities for the approximate treatment of higher excitations in coupled-cluster (CC) theory are discussed. Potential routes for the generalization of corresponding approximations to lower-level CC methods are analyzed for higher excitations. A general string-based algorithm is presented for the evaluation of the special contractions appearing in the equations specific to those approximate CC models. It is demonstrated that several iterative and noniterative approximations to higher excitations can be efficiently implemented with the aid of our algorithm and that the coding effort is mostly reduced to the generation of the corresponding formulas. The performance of the proposed and implemented methods for total energies is assessed with special regard to quadruple and pentuple excitations. The applicability of our approach is illustrated by benchmark calculations for the butadiene molecule. Our results demonstrate that the proposed algorithm enables us to consider the effect of quadruple excitations for molecular systems consisting of up to 10-12 atoms.

Coupled-cluster methods including noniterative corrections for quadruple excitations

A new method is presented for treating the effects of quadruple excitations in coupled-cluster theory. In the approach, quadruple excitation contributions are computed from a formula based on a non-Hermitian perturbation theory analogous to that used previously to justify the usual noniterative triples correction used in the coupled cluster singles and doubles method with a perturbative treatment of the triple excitations (CCSD(T)). The method discussed in this paper plays a parallel role in improving energies obtained with the full coupled-cluster singles, doubles, and triples method (CCSDT) by adding a perturbative treatment of the quadruple excitations (CCSDT(Q)). The method is tested for an extensive set of examples, and is shown to provide total energies that compare favorably with those obtained with the full singles, doubles, triples, and quadruples (CCSDTQ) method.

Higher excitations in coupled-cluster theory

The viability of treating higher excitations in coupled-cluster theory is discussed. An algorithm is presented for solving coupled-cluster (CC) equations which can handle any excitation. Our method combines the formalism of diagrammatic many-body perturbation theory and string-based configuration interaction (CI). CC equations are explicitly put down in terms of antisymmetrized diagrams and a general method is proposed for the factorization of the corresponding algebraic expressions. Contractions between cluster amplitudes and intermediates are evaluated by a string-based algorithm. In contrast to our previous developments [J. Chem. Phys. 113, 1359 (2000)] the operation count of this new method scales roughly as the (2n+2)nd power of the basis set size where n is the highest excitation in the cluster operator. As a by-product we get a completely new CI formalism which is effective for solving both truncated and full CI problems. Generalization for approximate CC models as well as multireference cases is also discussed.

Triple excitations in coupled-cluster theory: Energies and analytical derivatives

A review is presented of our recent work which deals with some aspects of the inclusion of connected triple excitations in single reference coupled–cluster theory. We first consider basic aspects of the theory and computational cost, noting the need for accurate and economical approximations to the complete coupled–cluster single, double and triple excitation method (CCSDT). Several such approximations are now available, including the CCSD + T(CCSD) and CCSD(T) methods. We have now efficiently implemented analytical derivative methods for these and related methods for open-shell reference determinants, including restricted open-shell Hartree–Fock for CCSD(T). Some results with large basis sets are presented for the HCO radical which further demonstrate the reliability of these methods for the spectroscopic characterization of small open-shell species. The remainder of this article deals with several applications of the complete CCSDT method, a new implementation of which we have recently completed. Like our previous work, this is for general single reference determinants, although we have now incorporated Abelian symmetry. We present a comparison with full configuration interaction data for CH3; a study of the N2 potential curve using restricted and unrestricted Hartree–Fock references; a comparison of the dipole moments and polarizabilities of BeO; and a study of the harmonic force field of 2Σ C. These studies also provide assessments of the accuracy of the approximate schemes for including T3. Finally, we present some timing data for some CCSDT calculations with out new implementation. © 1993 John Wiley & Sons, Inc.

A parallel vectorized implementation of triple excitations in CCSD(T): application to the binding energies of the AlH 3, AlH 2F, AlHF 2 and AlF 3 dimers

An efficient method for evaluating various non-iterative estimates of connected triple excitations in coupled-cluster theory is outlined and related to a similar expression occurring in Møller-Plesset perturbation theory. The method is highly vectorized and capable of utilizing multiple processors on a shared-memory machine, leading to computational rates in excess of one billion floating-point operations per second on four processors of a CRAY Y-MP. Using the new procedure, the binding energies of the D 2h diborane-type dimers of AlH 3, AlH 2F, AlHF 2 and AlF 3 have been determined to be 32, 40, 20 and 47 kcal/mol, respectively. For Al 2F 6, the correlation procedure includes 232 molecular orbitals and over 1.5 × 10 6 single and double coupled-cluster amplitudes, effectively accounting for over 2 × 10 9 connected triple excitations.