John F. Stanton

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.

HEAT: High accuracy extrapolated ab initio thermochemistry

A theoretical model chemistry designed to achieve high accuracy for enthalpies of formation of atoms and small molecules is described. This approach is entirely independent of experimental data and contains no empirical scaling factors, and includes a treatment of electron correlation up to the full coupled-cluster singles, doubles, triples and quadruples approach. Energies are further augmented by anharmonic zero-point vibrational energies, a scalar relativistic correction, first-order spin-orbit coupling, and the diagonal Born-Oppenheimer correction. The accuracy of the approach is assessed by several means. Enthalpies of formation (at 0 K) calculated for a test suite of 31 atoms and molecules via direct calculation of the corresponding elemental formation reactions are within 1 kJ mol(-1) to experiment in all cases. Given the quite different bonding environments in the product and reactant sides of these reactions, the results strongly indicate that even greater accuracy may be expected in reactions that preserve (either exactly or approximately) the number and types of chemical bonds.

Analytic energy derivatives for ionized states described by the equation‐of‐motion coupled cluster method

The theory for analytic energy derivatives of excited electronic states described by the equation‐of‐motion coupled cluster (EOM‐CC) method has been generalized to treat cases in which reference and final states differ in the number of electrons. While this work specializes to the sector of Fock space that corresponds to ionization of the reference, the approach can be trivially modified for electron attached final states. Unlike traditional coupled cluster methods that are based on single determinant reference functions, several electronic configurations are treated in a balanced way by EOM‐CC. Therefore, this quantum chemical approach is appropriate for problems that involve important nondynamic electron correlation effects. Furthermore, a fully spin adapted treatment of doublet electronic states is guaranteed when a spin restricted closed shell reference state is used—a desirable feature that is not easily achieved in standard coupled cluster approaches. The efficient implementation of analytic gradien...

Perturbative treatment of triple excitations in coupled‐cluster calculations of nuclear magnetic shielding constants

A theory for the calculation of nuclear magnetic shielding constants at the coupled‐cluster singles and doubles level augmented by a perturbative correction for connected triple excitations (CCSD(T)) has been developed and implemented. The approach, which is based on the gauge‐including atomic orbital (GIAO) ansatz, is illustrated by several numerical examples. These include a comparison of CCSD(T) and other highly correlated methods with full configuration interaction for the BH molecule, and a systematic comparison with experiment for HF, H2O,NH3, CH4, N2, CO, HCN, and F2. The results demonstrate the importance of triple excitations in establishing quantitative accuracy. Finally, the ability of GIAO‐CCSD(T) to make accurate predictions for difficult cases is explored in calculations for formaldehyde (CH2O), diazomethane(CH2NN), and ozone (O3).

The accurate determination of molecular equilibrium structures

Equilibrium structures have been determined for 19 molecules using least-squares fits involving rotational constants from experiment and vibrational corrections from high-level electronic-structure calculations. Equilibrium structures obtained by this procedure have a uniformly high quality. Indeed, the accuracy of the results reported here likely surpasses that reported in most experimental determinations. In addition, the accuracy of equilibrium structures obtained by energy minimization has been calibrated for the following standard models of ab initio theory: Hartree–Fock, MP2, CCSD, and CCSD(T). In accordance with previous observations, CCSD(T) is significantly more accurate than the other models; the mean and maximum absolute errors for bond distances of the 19 molecules are 0.09 and 0.59 pm, respectively, in CCSD(T)/cc-pCVQZ calculations. The maximum error is obtained for ROO in H2O2 and is so large compared with the mean absolute error that an experimental reinvestigation of this molecule is warra...

WHY CCSD(T) WORKS : A DIFFERENT PERSPECTIVE

Abstract The CCSD(T) method was originally motivated as an attempt to treat the effects of triply excited determinants upon both single and double excitation operators on an equal footing. Hence, conventional analyses based on perturbation theory cannot satisfactorily explain why the particular fifth-order term included in CCSD(T) should be chosen over a number of other possibilities. This work demonstrates that the terms appearing in CCSD(T) can be justified if one takes the biorthogonal representation of the CCSD state as the zeroth-order wavefunction. This perspective provides some additional insight as to why the method works so well in practice.

High-accuracy extrapolated ab initio thermochemistry. III. Additional improvements and overview

Effects of increased basis-set size as well as a correlated treatment of the diagonal Born-Oppenheimer approximation are studied within the context of the high-accuracy extrapolated ab initio thermochemistry (HEAT) theoretical model chemistry. It is found that the addition of these ostensible improvements does little to increase the overall accuracy of HEAT for the determination of molecular atomization energies. Fortuitous cancellation of high-level effects is shown to give the overall HEAT strategy an accuracy that is, in fact, higher than most of its individual components. In addition, the issue of core-valence electron correlation separation is explored; it is found that approximate additive treatments of the two effects have limitations that are significant in the realm of <1 kJ mol(-1) theoretical thermochemistry.

Analytic CCSD(T) second derivatives

A general-purpose implementation of analytic CCSD(T) second derivatives is presented. Its applicability is demonstrated by calculations of vibration-rotation interaction constants for the astrophysically important molecule cyclopropenylidene (C3H2) in which the required cubic force constants have been determined by numerical differentiation of analytically evaluated second derivatives of the energy.

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.

Coupled‐cluster open‐shell analytic gradients: Implementation of the direct product decomposition approach in energy gradient calculations

Analytic energy gradients for the coupled‐cluster singles and doubles (CCSD) method have been implemented for closed‐shell systems using restricted Hartree–Fock (RHF) and open‐shell systems using unrestricted Hartree–Fock (UHF) reference functions. To achieve maximum computational efficiency, the basic theory has been reformulated in terms of intermediates, thus reducing the number of required floating‐point operations, and all computational steps are given in terms of matrix products in order to exploit the vector capabilities of modern supercomputers. Furthermore, the implementation has been designed to take full advantage of Abelian symmetry operations. To illustrate the computational efficiency of our implementation and in particular to demonstrate the possible savings due to the exploitation of symmetry, computer timings and hardware requirements are given for several representative chemical systems. In addition, the newly developed analytic CCSD gradient methods are applied to calculate the equilibr...