De-perturbative corrections for charge-stabilized double ionization potential equation-of-motion coupled-cluster method

Charge stabilization improves the numeric performance of double ionization potential equation-of-motion (EOM-DIP) method when using unstable (autoionizing) dianion references. However, the stabilization potential introduces an undesirable perturbation to the target states' energies. Here we introduce and benchmark two approaches for removing the perturbation caused by the stabilization. The benchmark calculations of excitation energies in selected diradicals illustrate that the so-called core correction based on evaluating the perturbation in a small basis set is robust and yields reliable EOM-DIP values, i.e., the errors of 0.0-0.3 eV against a similar-level coupled-cluster approach.     

Spin-projected coupled-cluster theory with single and double excitations

Coupled-cluster (CC) theory including single (S) and double (D) excitations and carried out with a spin-unrestricted Hartree–Fock (UHF) reference wave function is free from S + 1 spin contamination as can be confirmed by an analysis of the expectation value of the spin operator, Ŝ ². Contamination by the S + 2 contaminant can be projected out by an approximate procedure (APCCSD) with a projection operator, P^, represented by the product of the spin annihilation operators ? _{s+ 1} and ?_s+2. The computational cost of such a projection scales with O(M ⁶) (M is the number of basis functions). The APCCSD energy obtained after annihilation of the S + 2 contaminant can be improved by adding triple (T) excitations in a perturbative way, thus leading to APCCSD(T) energies. For the 17 examples studied, the deviation of the UHF-CCSD(T) energies from the corresponding full configuaration interaction values is reduced from 4.0 to 2.3 mhartree on the average as a result of annihilating the S + 2 contaminant in an approximate way. In the case of single-bond cleavage, APCSSD leads to a significant improvement of the energy in the region where the bonding electrons recouple from a closed shell to an open shell singlet electron pair. Received: 13 April 2000 / Accepted: 12 July 2000 / Published online: 24 October 2000     

Performance of the general-model-space state-universal coupled-cluster method

The capabilities of the recently developed multireference, general-model-space (GMS), state-universal (SU) coupled-cluster (CC) method have been extended in order to enable the handling of any excited state that represents a single (S) or a double (D) excitation relative to the ground state. A series of calculations concerning the ground and excited states of the CH(+), HF, F(2), H(2)O, NH(2), and CH(2) molecules were carried out so as to assess the performance of the GMS SU CCSD method. For diatomics we have computed the entire potential energy curves, while for triatomics we have focused on vertical excitation energies. We demonstrate how a systematic enlargement of the model space enables a consideration of a larger and larger number of excited states. A comparison of the CC and full configuration interaction or large-scale CI results enables an assessment of the accuracy and reliability of the GMS SU CCSD method within a given basis set. In all cases very good results have been obtained, including highly excited states and those having a doubly-excited character.     

General implementation of the relativistic coupled-cluster method

We report the development of a general order relativistic coupled-cluster (CC) code. Our implementation is based on Kramers-paired molecular spinors, utilizes double group symmetry, and is applicable with the full Dirac-Coulomb and several approximate relativistic Hamiltonians. The available methods include iterative and perturbative single-reference CC approaches with arbitrary excitations as well as a state-selective multi-reference CC ansatz. To illustrate the performance of the new code, benchmark calculations have been performed for the total energies, bond lengths, and vibrational frequencies of the monoxides of Group IVa elements. The trends due to the simultaneous inclusion of relativity as well as higher-order electron correlation effects are analyzed. The newly developed code significantly widens the scope of the ab initio relativistic calculations, for both molecules and atoms alike, surpassing the accuracy and reliability of the currently available implementations in the literature.     

Improvement of the coupled-cluster singles and doubles method via scaling same- and opposite-spin components of the double excitation correlation energy

There has been much interest in cost-free improvements to second-order M?ller-Plesset perturbation theory (MP2) via scaling the same- and opposite-spin components of the correlation energy (spin-component scaled MP2). By scaling the same- and opposite-spin components of the double excitation correlation energy from the coupled-cluster of single and double excitations (CCSD) method, similar improvements can be achieved. Optimized for a set of 48 reaction energies, scaling factors were determined to be 1.13 and 1.27 for the same- and opposite-spin components, respectively. Preliminary results suggest that the spin-component scaled CCSD (SCS-CCSD) method will outperform all MP2 type methods considered for describing intermolecular interactions. Potential energy curves computed with the SCS-CCSD method for the sandwich benzene dimer and methane dimer reproduce the benchmark CCSD(T) potential curves with errors of only a few hundredths of 1 kcal mol(-1) for the minima. The performance of the SCS-CCSD method suggests that it is a reliable, lower cost alternative to the CCSD(T) method.     

Equation-of-motion coupled-cluster methods for ionized states with an approximate treatment of triple excitations

The accuracy of geometries and harmonic vibrational frequencies is evaluated for two equation-of-motion ionization potential coupled-cluster methods including CC3 and CCSDT-3 triples corrections. The first two Sigma states and first Pi state of the N2 +, CO+, CN, and BO diatomic radicals are studied. The calculations show a tendency for the CC3 variant to overestimate the bond lengths and to underestimate the vibrational frequencies, while the CCSDT-3 variant seems to be more reliable. It is also demonstrated that the accuracy of such methods is comparable to sophisticated traditional multireference approaches and the full configuration interaction method.     

A coupled-cluster method for quasidegenerate states

A size-extensive, multireferences coupled-cluster method for studies of quasidegenerate states based on the Jeziorski–Monkhorst [16] ansatz for the cluster operator (Ω = ∑eP_j, where the sum is extended over the configurations spanning the model space), is presented and applied in pilot calculations. The method is referred to as multireference coupled electron-pair method (MR CEPM ), because it is assumed that the individual cluster operators can be approximated by their two-body parts, i.e., T_j ≈ T_j(2). The linear version of this method (MR L-CEPM ) is also discussed. Both methods are applied to two simple model systems: (1) a minimum basis set model involving eight hydrogen atoms in various spacial arrangements for which the degree of quasidegeneracy can be continuously varied; (2) a model involving the C_2ν insertion of Be into H₂. For the first time in multireference coupled-cluster calculations, the nonlinear parts of the equations are completely accounted for. The MR CEPM results are very encouraging for strongly quasidegenerate states. The MR L -CEPM results are slightly below the accurate (FCI ) values.     

A natural linear scaling coupled-cluster method

It is shown that using an appropriate localized molecular orbital (LMO) basis, one is able to calculate coupled-cluster singles and doubles (CCSD) wave functions and energies for very large systems by performing full CCSD calculations on small subunits only. This leads to a natural linear scaling coupled-cluster method (NLSCC), in which total correlation energies of extended systems are evaluated as the sum of correlation energy contributions from individual small subunits within that system. This is achieved by defining local occupied orbital correlation energies. These are quantities, which in the LMO basis become transferable between similar molecular fragments. Conventional small scale existing molecular CCSD codes are all that is needed, the local correlation effect being simply transmitted via the appropriate LMO basis. Linear scaling of electronic correlation energy calculations is thus naturally achieved using the NLSCC approach, which in principle can treat nonperiodic extended systems of infinite basis set size. Results are shown for alkanes and several polyglycine molecules and the latter compared to recent results obtained via an explicit large scale LCCSD calculation. (c) 2004 American Institute of Physics.     

Equation-of-motion coupled-cluster method for the study of shape resonance

The equation-of-motion coupled-cluster method (EOM-CC) is applied for the first time to calculate the energy and width of a shape resonance in an electron-molecule scattering. The procedure is based on inclusion of complex absorbing potential with EOM-CC theory. We have applied this method to investigate the shape resonance in e(-)N(2), e(-)CO, and e(-)C(2)H(2).     

pCCSD: parameterized coupled-cluster theory with single and double excitations

The primary characteristics of single reference coupled-cluster (CC) theory are size-extensivity and size-consistency, invariance under orbital rotations of the occupied or virtual space, the exactness of CC theory for N electron systems when the cluster operator is truncated to N-tuple excitations, and the relative insensitivity of CC theory to the choice of the reference determinant. In this work, we propose a continuous class of methods which display the desirable features of the coupled-cluster approach with single and double excitations (CCSD). These methods are closely related to the CCSD method itself and are inspired by the coupled electron pair approximation (CEPA). It is demonstrated that one can systematically improve upon CCSD and obtain geometries, harmonic vibrational frequencies, and total energies from a parameterized version of CCSD or pCCSD(α,β) by selecting a specific member from this continuous family of approaches. In particular, one finds that one such approach, the pCCSD(-1,1) method, is a significant improvement over CCSD for the calculation of equilibrium structures and harmonic frequencies. Moreover, this method behaves surprisingly well in the calculation of potential energy surfaces for single bond dissociation. It appears that this methodology has significant promise for chemical applications and may be particularly useful in applications to larger molecules within the framework of a high accuracy local correlation approach.     

A spin-adapted coupled-cluster based linear response theory for double ionization potentials

We developed in this article a spin-adapted formulation of the coupled-cluster based linear response theory (CC-LRT) for computing double-ionization potentials (DIPs), which may be experimentally observed by Auger spectroscopy. CC-LRT is a multireference generalization of the CC theory where the energy differences have no disconnected vacuum (core) diagrams, signifying core-extensivity. For the spin-adaptation of the CC-LRT equations for the singlet and triplet manifolds, we used the Young-Yamanouchi orthogonal spin-eigenfunctions. The orbital version of the CC-LRT equations are then automatically generated by the conjugate projection operators of Young-Yamanouchi spin functions. We illustrated the working of our spin-adaptation procedure by confining our CC-LRT equations to the space of 2h and 1p–3h ionized determinants. As numerical application of our formalism, we computed the Auger kinetic energies of HF and H₂O. We also analyzed the nature of size-extensivity of the DIPs generated by CC-LRT and showed explicitly that when the molecule is composed of two noninteracting fragments the computed DIPs are either DIPs of fragment A or B or a composite DIP depending on both A and B, which are just not sum of ionization potentials (IPs) of A and B. This analysis is done to underscore the fact that DIPs from CC-LRT is only core-extensive and not fully extensive. © 1996 John Wiley & Sons, Inc.     

The coupled-cluster method in high sectors of the Fock space

The coupled-cluster method is applied to high sectors of the Fock space (up to five electrons outside a closed shell). Ionization potentials and excitation energies are calculated for atomic N, O, F, P, and S and their ions. The effect of virtual triple excitations is included, exactly or at several levels of appoximation. These terms are important for accurate results in the high sectors. © 1995 John Wiley & Sons, Inc.     

Model study of the impact of orbital choice on the accuracy of coupled-cluster energies. II. Valence-universal coupled-cluster method

The impact of the choice of molecular orbital sets on the results of the valence-universal coupled cluster method involving up to three-body amplitudes (VU-CCSDT) was studied for the H4 model. This model offers a straightforward way of representing all possible symmetry-adapted orbitals. Moreover, the degree of quasi-degeneracy of its lowest ¹A₁ states can be varied over a wide range by changing its geometry. Calculations were performed both for 13 sets of standard quantum chemical orbitals and for a vast variety of nonstandard orbital sets defined by nodes of a two-dimensional orbital grid. The performance of various standard orbital sets in VU-CCSDT calculations is compared. It is also documented that for every quasi-degeneracy region there exist nonstandard orbital sets which allow one to obtain more accurate VU-CCSDT energies than the standard orbital sets. In an attempt to provide a general interpretation for some of the alternative orbital sets, we defined a set of orbitals which maximize the proximity of the model and target spaces—maximum proximity orbitals (MPO). It is demonstrated that outside the strong quasi-degeneracy region the energies obtained for the VU-CCSDT approach based on the MPOs are more accurate than for the standard orbital sets. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 67: 221–237, 1998     

Reduced multireference coupled-cluster method: barrier heights for heavy atom transfer, nucleophilic substitution, association, and unimolecular reactions

The recently developed reduced multireference coupled-cluster method with singles and doubles (RMR CCSD) that is perturtatively corrected for triples [RMR CCSD(T)] is employed to compute the forward and reverse barrier heights for 19 non-hydrogen-transfer reactions. The method represents an extension of the conventional single-reference (SR) CCSD(T) method to multireference situations. The results are compared with a benchmark database, which is essentially based on the SR CCSD(T) results. With the exception of seven cases, the RMR CCSD(T) results are almost identical with those based on SR CCSD(T), implying the abatement of MR effects at the SD(T) level relative to the SD level. Using the differences between the RMR CCSD(T) and CCSD(T) barrier heights as a measure of MR effects, modified values for barrier heights of studied reactions are given.     

Breaking bonds with the left eigenstate completely renormalized coupled-cluster method

The recently developed [P. Piecuch and M. Wloch, J. Chem. Phys. 123, 224105 (2005)] size-extensive left eigenstate completely renormalized (CR) coupled-cluster (CC) singles (S), doubles (D), and noniterative triples (T) approach, termed CR-CC(2,3) and abbreviated in this paper as CCL, is compared with the full configuration interaction (FCI) method for all possible types of single bond-breaking reactions between C, H, Si, and Cl (except H2) and the H2Si[Double Bond]SiH2 double bond-breaking reaction. The CCL method is in excellent agreement with FCI in the entire region R=1-3Re for all of the studied single bond-breaking reactions, where R and Re are the bond distance and the equilibrium bond length, respectively. The CCL method recovers the FCI results to within approximately 1 mhartree in the region R=1-3Re of the H-SiH3, H-Cl, H3Si-SiH3, Cl-CH3, H-CH3, and H3C-SiH3 bonds. The maximum errors are -2.1, 1.6, and 1.6 mhartree in the R=1-3Re region of the H3C-CH3, Cl-Cl, and H3Si-Cl bonds, respectively, while the discrepancy for the H2Si[Double Bond]SiH2 double bond-breaking reaction is 6.6 (8.5) mhartree at R=2(3)Re. CCL also predicts more accurate relative energies than the conventional CCSD and CCSD(T) approaches, and the predecessor of CR-CC(2,3) termed CR-CCSD(T).     

An open-shell coupled-cluster response method for static properties

This paper deals with a multideterminantal model space-based coupled-cluster response approach suitable for the calculation of static properties of quasi-degenerate systems. The firstorder static property of one-valence-hole/particle system using this approach has been specifically discussed.     

An efficient closed-shell singles and doubles coupled-cluster method

A reformulated set of equations for the closed-shell singles and doubles coupled-cluster (CCSD) method is presented. A computational cost of n_v⁴n₀²+7n_v³n₀³+1n_v²n₀⁴ for the n⁶ steps is obtained, where n_v is the number of virtual molecular orbitals included in the CCSD procedure, n₀ is the number of doubly occupied molecular orbitals and n=n₀+n_v. Test calculations for the cis and trans isomers of FNNF and planar and pyramidal CH₃⁻ are presented. Equilibrium structures determined with large Gaussian basis sets at the second-order Møller-Plesset (MP2) perturbation level of theory are reported and used for the other electron correlation methods. With the largest one-particle basis set (144 contracted Gaussian functions), the equilibrium geometries of cis- and trans-FNNF agree with experiment. Based on analyses of planar and pyramidal CH₃⁻ wavefunctions and the calculated inversion barrier, it is suggested that the molecular anion may not exist in a planar configuration but that autodetachment of an electron occurs before the transition state is reached. Comparisons of our new CCSD procedure demonstrate that coupled-cluster methods are not significantly more expensive than similar electron correlation techniques.