Showing papers on "Coupled cluster published in 2000"

CC2 excitation energy calculations on large molecules using the resolution of the identity approximation

Abstract: A new implementation of the approximate coupled cluster singles and doubles method CC2 is reported, which is suitable for large scale integral-direct calculations. It employs the resolution of the identity (RI) approximation for two-electron integrals to reduce the CPU time needed for calculation and I/O of these integrals. We use a partitioned form of the CC2 equations which eliminates the need to store double excitation cluster amplitudes. In combination with the RI approximation this formulation of the CC2 equations leads to a reduced scaling of memory and disk space requirements with the number of correlated electrons (n) and basis functions (N) to, respectively, O(N2) and O(nN2), compared to O(n2N2) in previous implementations. The reduced CPU, memory and disk space requirements make it possible to perform CC2 calculations with accurate basis sets on large molecules, which would not be accessible with conventional implementations of the CC2 method. We present an application to vertical excitation ene...

Low-order scaling local electron correlation methods. III. Linear scaling local perturbative triples correction (T)

Abstract: A new method for the perturbative calculation of the correlation energy due to connected triple excitations (T) in the framework of local coupled cluster theory is presented, for which all computational resources scale linearly with molecular size. One notable complication in the formalism for connected triples introduced by the local approach is the nondiagonality of the Fock matrix in the localized MO (LMO) and projected AO (PAO) basis, which leads to couplings between individual triples amplitudes via the internal–internal and external–external blocks of the Fock matrix, respectively. Further complications and couplings arise due to the nonorthogonality of the PAOs. While the couplings via the external–external block can easily be dealt with, this is more difficult for the internal–internal couplings. In a previous paper we already published preliminary results of an approximation of the method, which neglects these internal–internal couplings entirely and recovers about 97% of the total local triples ...

Analytic second derivatives in high-order many-body perturbation and coupled-cluster theories: Computational considerations and applications

Abstract: The history of analytic first- and second-derivative methods in quantum chemistry is discussed, with special emphasis given to approaches that are associated with electron correlation treatments based on many-body perturbation theory (MBPT) and the coupled-cluster (CC) approximation The computational requirements of recently developed analytical second derivative methods for high-order MBPT and CC methods are discussed in detail and compared with those associated with finite-difference procedures Applications of these techniques to the calculation of anharmonic force fields used to deduce equilibrium geometries and fundamental vibrational frequencies for polyatomic molecules are reviewed

The initial implementation and applications of a general active space coupled cluster method

Abstract: A general coupled cluster method that allows arbitrary excitations from a single reference-determinant is proposed and tested. The method is based on a generalization of the formalism of spin-strings and provides a unified method for the storage and manipulation of coupled cluster operators. An initial implementation of the method is discussed and used to study the convergence of the coupled cluster hierarchy for H2O and CH2 at equilibrium geometry, employing up to eightfold excitations. The energy and wave function contributions of the various excitation levels are examined. The dissociation curve of HF is also studied. Using single and double excitations from a minimal active space, the coupled cluster dissociation curve for HF shows a largest deviation from full configuration interaction curve of 1.3 mEh, which decreases by an order of magnitude up on the addition of triple excitations out of the active space.

An Ab Initio Study of Potential Energy Surfaces for N8 Isomers

Abstract: The potential energy surfaces and the nature of transition structures for the decomposition of three N8 isomers (octaazapentalene, azidopentazole, and diazidodiimide) into 4 N2 are investigated using ab initio methods. These isomers are all high-energy species, relative to molecular nitrogen, but are much lower in energy than the previously studied cubic structure. Second-order perturbation theory (MP2) predicts that the dissociation of octaazapentalene proceeds via isomerization to a linear molecule. The dissociation reaction of azidopentazole prefers ring breaking, at a cost of less than 20 kcal/mol, to breaking a bond in the side chain. The cis isomer of diazidodiimide is found to be slightly more stable than that of the trans isomer at the highest levels of theory used here. The coupled cluster (CCSD(T)) diazidodiimide dissociation barrier is computed to be about 20 kcal/mol. This barrier is only marginally sufficient to make this high energy density molecule metastable.

Performance of CCSDT for diatomic dissociation energies

Abstract: Calculations of 11 diatomic dissociation energies with coupled cluster theory through iterative triple excitations highlight both the strength and limitations of this method. By combining very large basis sets (through septuple zeta in some cases) and complete basis set extrapolations with corrections for core/valence correlation, scalar relativistic and atomic/molecular spin–orbit effects, it was possible to achieve excellent agreement with experiment in most cases. However, for C2 and CN the extent of the multiconfigurational nature of the molecules caused problems for the single configuration-based couple cluster methods. In the worse case, the inclusion of iterative triples resulted in a change with respect to the perturbative triples result which was of the opposite sign to the full configuration interaction change. This work emphasizes the difficulties in achieving uniform chemical accuracy even for ground state, first and second row diatomics.

Size-extensivity correction for the state-specific multireference Brillouin–Wigner coupled-cluster theory

Abstract: We present a simple a posteriori correction for the state-specific multireference Brillouin–Wigner coupled-cluster (MR BWCCSD) theory, which eliminates its size-extensivity error. In the converged amplitudes we drop terms that were identified to be responsible for the lack of size extensivity. We performed MR BWCCSD calculations with this correction on CH2, SiH2, twisted ethylene, F2, and ozone that are all, from the computational point of view, typical representatives of two-reference problems. Comparison with rigorously size-extensive calculations and experiment shows that the size-extensivity error of the corrected MR BWCCSD is only a few tenths of kcal/mol.

Second order perturbation corrections to singles and doubles coupled-cluster methods: General theory and application to the valence optimized doubles model

Abstract: We present a general perturbative method for correcting a singles and doubles coupled-cluster energy. The coupled-cluster wave function is used to define a similarity-transformed Hamiltonian, which is partitioned into a zeroth-order part that the reference problem solves exactly plus a first-order perturbation. Standard perturbation theory through second-order provides the leading correction. Applied to the valence optimized doubles ~VOD! approximation to the full-valence complete active space self-consistent field method, the second-order correction, which we call ~2!, captures dynamical correlation effects through external single, double, and semi-internal triple and quadruple substitutions. A factorization approximation reduces the cost of the quadruple substitutions to only sixth order in the size of the molecule. A series of numerical tests are presented showing that VOD~2! is stable and well-behaved provided that the VOD reference is also stable. The second-order correction is also general to standard unwindowed coupled-cluster energies such as the coupled-cluster singles and doubles ~CCSD! method itself, and the equations presented here fully define the corresponding CCSD~2! energy. © 2000 American Institute of Physics. @S0021-9606~00!30130-1#

A study of water clusters using the effective fragment potential and Monte Carlo simulated annealing

Abstract: Simulated annealing methods have been used with the effective fragment potential to locate the lowest energy structures for the water clusters (H2O)n with n=6, 8, 10, 12, 14, 16, 18, and 20. The most successful method uses a local minimization on each Monte Carlo step. The effective fragment potential method yielded interaction energies in excellent agreement with those calculated at the ab initio Hartree–Fock level and was quite successful at predicting the same energy ordering as the higher-level perturbation theory and coupled cluster methods. Analysis of the molecular interaction energies in terms of its electrostatic, polarization, and exchange-repulsion/charge-transfer components reveals that the electrostatic contribution is the dominant term in determining the energy ordering of the minima on the (H2O)n potential energy surfaces, but that differences in the polarization and repulsion components can be important in some cases.

MC-QCISD: Multi-coefficient correlation method based on quadratic configuration interaction with single and double excitations

Abstract: This paper presents a multi-coefficient correlation method based on quadratic configuration interaction with single and double excitations (MC-QCISD) and basis sets using segmented contraction and having the same exponential parameters in the s and p spaces. The results are comparable to a previous multi-coefficient correlation method based on coupled cluster theory with less efficient correlation-consistent basis sets, and they are better than a previous multi-coefficient correlation method based on Moller−Plesset fourth order perturbation theory with single, double, and quadruple excitations with correlation-consistent basis functions. The mean unsigned error per bond of the MC-QCISD method is 0.72 kcal/mol. The new method should be very efficient for computing geometries of open-shell transition states.

Gaussian basis sets for use in correlated molecular calculations. VIII. Standard and augmented sextuple zeta correlation consistent basis sets for aluminum through argon

Abstract: Standard and augmented correlation consistent sextuple zeta (cc-pV6Z and aug-cc-pV6Z) basis sets have been determined for the second-row atoms aluminum through argon. Using these sets, dissociation energies and spectroscopic constants for the ground states of HCl, PN, and P2 have been calculated using several theoretical methods, including Moller–Plesset perturbation theory, coupled cluster theory, and multireference configuration interaction theory (MRCI). The aug-cc-pV6Z and cc-pV6Z sets yield dissociation energies that are estimated to be within 0.1–0.2 kcal/mol of the complete basis set limit for HCl and within 1–1.5 kcal/mol for PN and P2. The MRCI and CCSD(T) methods are found to give the most consistently reliable results for the spectroscopic constants of all three species investigated. Use of the counterpoise correction improves the convergence behavior of the spectroscopic constants with increasing n for both the cc-pVnZ and aug-cc-pVnZ sets and should allow more accurate estimates of the complete basis set limit to be predicted. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 76: 205–221, 2000

The active-space equation-of-motion coupled-cluster methods for excited electronic states: The EOMCCSDt approach

Abstract: The idea of selecting the most important higher-than-doubly excited configurations in single-reference coupled-cluster (CC) calculations for quasidegenerate ground states of molecular systems through the use of active orbitals is extended to excited electronic states via the equation-of-motion (EOM) CC formalism. The resulting EOMCCSDt method, in which triexcited clusters T3 and the corresponding three-body components of the EOMCC excitation operator R are restricted to internal and semiinternal components defined through active orbitals, is capable of significantly improving the vertical excitation energies obtained with the conventional EOMCCSD (EOMCC singles and doubles) approach at a fraction of the computer cost associated with the full EOMCCSDT (EOMCC singles, doubles, and triples) calculations. The results of pilot calculations for the H8, CH2, and CH+ molecules indicate that the EOMCCSDt method using small active spaces is as accurate as the EOMCCSDT approach. In particular, the EOMCCSDt method is...

Predicting the heats of formation of model hydrocarbons up to benzene

Abstract: The heats of formation of benzene and seven other small hydrocarbons (allyl, allene, cyclopropene, propene, propyne, cyclopropane, and propane) have been calculated at high levels of ab initio molecular orbital theory. Geometries and frequencies were determined, in general, with coupled cluster theory, including a perturbative treatment of the connected triple excitations and with basis sets up through augmented quadruple-ζ in quality or, in some cases, augmented quintuple-ζ. Subsequent extrapolation of the total energies to the complete 1-particle basis set limit was performed, in an effort to further reduce the basis set truncation error. Additional improvements in the atomization energy were achieved by applying corrections for core/valence correlation, scalar relativistic, atomic spin−orbit, and higher-order correlation effects. Zero-point energies were based on an average of the vibrational energies obtained from the experimental fundamentals and theoretical harmonic frequencies. Using restricted ope...

Benchmark variational coupled cluster doubles results

Abstract: We present the first application of the Rayleigh–Ritz variational procedure to the coupled cluster doubles trial function. The variational approach is applied to the potential surface of H4, the double dissociation of water and the dissociation of N2, and the results are compared to standard coupled cluster doubles calculations. It is found that the variational approach gives a greatly improved description of strongly correlated systems, where the standard approach is known to fail. Some examination of the basis set dependence of the results is presented.

Computing coupled-cluster wave functions with arbitrary excitations

Abstract: An algorithm is presented for solving coupled-cluster (CC) equations by successive diagonalization of 2×2 matrices. It is more expensive than usual procedures, but it is capable of solving a CC problem where any arbitrary excitation is included in the cluster operator. Equation-of-motion coupled-cluster (EOMCC) excitation energies can also be determined by this method regardless of the type of excitations in the cluster operator and the space where the effective Hamiltonian is diagonalized. The algorithm is applied to the study of the convergence of CC and EOMCC series in some small bases.

Excited states theory for optimized orbitals and valence optimized orbitals coupled-cluster doubles models

Abstract: We introduce an excited state theory for the optimized orbital coupled cluster doubles (OO-CCD) and valence optimized orbital coupled cluster doubles (VOO-CCD) models. The equations for transition energies are derived using a similarity transformed Hamiltonian. The effects of orbital relaxation are discussed. We present results for several single-reference molecules (H2O, CH2O, C2H4O, C2H4, BeO), as well as for molecules with significant nondynamical correlation in the ground state (CH+, BH, A 1A1 CH2), and for rectangular O4+. We find that: (i) OO-CCD excitation energies are very close to CCSD excitation energies; (ii) similarly to the complete active space SCF (CASSCF) model, the effects of orbital relaxation are very important for VOO-CCD excited states such that the excitation energies calculated by VOO-CCD and CASSCF with orbitals optimized for the ground state are very close to each other and unsatisfactory; (iii) the VOO-CCD model with an approximate treatment of orbital relaxation describes singly...

Full configuration interaction benchmarking of coupled-cluster models for the lowest singlet energy surfaces of N2

Abstract: The potential-energy curves for the X 1Σg+, a 1Πg, a′ 1Σu−, w 1Δu, c3 1Πu, and b 1Πu states of N2 have been investigated in full configuration interaction (FCI) and coupled-cluster response calculations. The equilibrium bond lengths, adiabatic excitation energies, and harmonic frequencies have been obtained with the coupled-cluster singles model (CCS), an approximate coupled-cluster singles and doubles model (CC2), the coupled-cluster singles and doubles model (CCSD), and an approximate coupled-cluster singles, doubles, and triples model (CC3), and subsequently compared to FCI results. The weak and strong features of the coupled-cluster models are discussed and illustrated. Overall, improvements towards FCI are obtained in the hierarchy CCS–CC2–CCSD–CC3. CC3 is always consistently better than CCSD, and for all the considered spectroscopic constants CC3 provides excellent results. Examples where the CC3 model fails are also given. The noniterative triples model, CCSDR(3), is compared to the iterative tripl...

Ab initio coupled-cluster calculations for the fcc and hcp structures of rare-gas solids

Abstract: In order to gain more insight into factors governing the relative stability of the fcc and hcp structures of the rare-gas solids Ne through Xe, we performed ab initio coupled-cluster calculations for the most important three- and four-body terms in the many-body expansion of the cohesive energy. These terms are combined with empirical two-body potentials derived from dimer data and with a multipole expansion for the long-range three-body terms. In addition, we calculated phonon spectra, in harmonic approximation, for the two structures. Including zero-point energies, our results agree very well with experimental data for the fcc structure. The hypothetical hcp structure, which is lower in energy with two-body potentials, is destabilized by short-range three-body terms and, even more important, by the contribution of zero-point vibration.

Relativistic coupled cluster calculations for neutral and singly charged Au3 clusters

Abstract: Relativistic coupled cluster studies are performed for the structures, dissociation energies, ionization potentials and electron affinities for Au, Au2 and Au3. The calculations show that the upward shifts of the ionization potentials and electron affinities of Aun clusters by approximately 2 eV compared to Cun or Agn base on relativistic effects. Au3+ is predicted to adopt a trigonal planar structure (D3h, 1A1), Au3 a E⊗e Jahn–Teller distorted structure (C2v,2A1) 0.1 eV below the linear 2Σu+ arrangement, and Au3− adopts a linear structure (1Σg+).

Intermediate Hamiltonian Fock-space coupled-cluster method: Excitation energies of barium and radium

Abstract: An intermediate Hamiltonian Fock-space coupled cluster method is introduced, based on the formalism developed by Malrieu and co-workers in the context of perturbation theory. The method is designed to make possible the use of large P spaces while avoiding convergence problems traceable to intruder states, which often beset multireference coupled cluster schemes. The essence of the method is the partitioning of P into a main Pm and an intermediate Pi serving as buffer, with concomitant definition of two types of wave and excitation operators. Application to atomic barium and radium yields converged results for a large number of states not accessible by traditional Fock-space coupled cluster. Moreover, states calculated by both methods exhibit better accuracy (by a factor of 2–5) in the intermediate Hamiltonian approach. Energies are given for low-lying states of Ra which have not been observed experimentally.

A CCSDT study of the effects of higher order correlation on spectroscopic constants. I. First row diatomic hydrides

Abstract: Spectroscopic constants have been determined for 13 first row diatomic hydrides using coupled cluster theory with explicit inclusion of (iterative) triple excitations (CCSDT). Comparison of the predicted dissociation energies, bond lengths, harmonic frequencies, and anharmonicities was made with experiment and other high-level theoretical treatments. These include complete active space configuration interaction wave functions, coupled cluster theory with perturbative triples [CCSD(T)], and new benchmark full configuration interaction calculations. Excellent overall agreement with experiment was found, even without correcting for small changes due to core/valence and relativistic effects. The intrinsic CCSDT error with respect to experiment for each molecule and property was estimated by extrapolating to the complete basis set limit. Among the various properties examined in this study, no significant differences were found between CCSD(T) and CCSDT. In light of the substantial increase in computational cos...

Extended similarity transformed equation-of-motion coupled cluster theory (extended-STEOM-CC): Applications to doubly excited states and transition metal compounds

Abstract: The diagonalization manifold in similarity transformed equation-of-motion coupled cluster (STEOM-CC) theory is extended to include doubly excited determinants. In the resulting extended-STEOM approach accurate results are obtained for doubly excited states in small model systems for which full configuration interaction (CI) benchmark results are available (∼0.1 eV errors). On the other hand, extended-STEOM results are found to be virtually identical (<0.1 eV shifts) to the original STEOM results for states that are dominated by single excitations, at least in prototypical organic molecules. The extended-STEOM method is also applied to the transition metal complexes TiCl4, Ni(CO)4, and MnO4−, and yields improved results compared to STEOM and EOM-CCSD. For highly correlated systems, like the permangenate anion, results are not yet fully satisfactory however. In these cases the dominant source of error appears to be the description of ground, ionized, and attached states that underly the similarity transform...

Computational Aspects of Interaction Hyperpolarizability Calculations. A Study on H2···H2, Ne···HF, Ne···FH, He···He, Ne···Ne, Ar···Ar, and Kr···Kr†

Abstract: We report an extensive investigation of the interaction hyperpolarizability of a number of model systems: the hydrogen molecule dimer, the interaction of hydrogen fluoride with a neon atom, and the rare gas diatoms He2, Ne2, Ar2, and Kr2. Our approach relies on finite-field many-body perturbation theory and coupled cluster calculations. The exploration of the various aspects of interaction hyperpolarizability calculations has brought forth the necessity for well-defined computational strategies that can lead to reliable theoretical predictions for such quantities.

Spin-orbit coupling constants from coupled-cluster response theory

Abstract: A scheme for the calculation of spin-orbit coupling constants using coupled-cluster (CC) electronic structure methods is described based on response-theory expressions for transition properties An implementation is reported for singlet–triplet transitions within the coupled-cluster singles and doubles (CCSD) approximation An atomic mean-field representation of the spin-orbit interaction is used to simplify the calculation of spin-orbit coupling constants Sample calculations are presented for spin-orbit couplings for the 11Σ+→13Π transitions for BH and AlH and for the 11A′→13A″ and the 13A″→11A″ transitions for the silylenes HSiX, X=F, Cl, Br, and are compared to results obtained from full configuration interaction (FCI) calculations with the full Breit-Pauli spin-orbit operator