Showing papers on "Coupled cluster published in 2001"

Interaction energies of van der Waals and hydrogen bonded systems calculated using density functional theory: Assessing the PW91 model

Abstract: The performance of density functional theory using the Perdew and Wang’s exchange and correlation functionals (PW91) functional for the prediction of intermolecular interactionenergies is evaluated based on calculations on the neon, argon, methane, ethylene, and benzene dimers, as well as on 12 hydrogen bonded complexes (water, methanol, formic acid, hydrogen fluoride, ammonia, formamide dimers and water–methanol, water–dimethyl ether, water–formaldehyde, hydrogen cyanide–hydrogen fluoride, water–ammonia, water–formamide complexes). The results were compared with those obtained from Becke’s exchange and Lee, Yang, and Parr’s correlation functionals (BLYP), Becke’s 3 parameter functional combined with Lee, Yang, and Parr’s correlation functional (B3LYP), second order Mo/ller–Plesset perturbation (MP2), and coupled cluster calculations with single and double substitutions and with non-iterative triple corrections [CCSD(T)] calculations. The calculated interactionenergies show that the PW91 functional performs much better than the BLYP or B3LYP functionals. The error in the computed binding energies of the hydrogen bonded complexes is 20% in the worst case. The most demanding cases are the systems with large dispersion contributions to the binding energy, such as the benzene dimer. In contrast to the BLYP and B3LYP functionals which fail to account for dispersion, the PW91 functional at least partly recovers the attraction. The basis set dependence of the PW91 functionals is relatively small in contrast to the MP2 and CCSD(T) methods. Despite its occasional difficulties with dispersion interaction, the PW91 functional may be a viable alternative to the ab initio methods, certainly in situations where large complexes are being studied.

Higher excitations in coupled-cluster theory

Abstract: 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.

Low-order scaling local electron correlation methods. IV. Linear scaling local coupled-cluster (LCCSD)

Abstract: A new implementation of local coupled-cluster theory with single and double excitations (LCCSD) is presented for which asymptotically all computational resources (CPU, memory, and disk) scale only linearly with the molecular size. This is achieved by: (i) restricting the correlation space for each electron pair to domains that are independent of molecular size; (ii) classifying the pairs according to a distance criterion and treating only strong pairs at the highest level; (iii) using efficient prescreening algorithms in the integral transformation and other integral-direct procedures; and (iv) neglect of small couplings of electron pairs that are far apart from each other. The errors caused by the various approximations are negligible. LCCSD calculations on molecules including up to 300 correlated electrons and over 1000 basis functions in C1 symmetry are reported, all carried out on a workstation.

Extended benchmark studies of coupled cluster theory through triple excitations

Abstract: Coupled cluster theory through quasiperturbative triple excitations [CCSD(T)] was used with large correlation consistent basis sets to obtain optimized structures, harmonic vibrational frequencies and atomization energies for 37 molecules from the G2/97 test set. In some cases, it proved possible to include the triple excitations iteratively via CCSDT. Use of various correlation consistent basis set sequences facilitated estimation of frozen core energies in the complete basis set limit. Tight d functions were added for all second row atoms in order to improve the basis set convergence properties. Core/valence correlation corrections were obtained from all electron CCSD(T)/cc-pCVQZ calculations. Scalar relativistic contributions to the atomization energy were obtained from configuration interaction mass-velocity/one-electron Darwin calculations and CCSD(T) Douglas–Kroll–Hess calculations. By combining results from the present work with previously reported findings, a total of 114 comparisons with reliable...

Coupled-cluster theory for excited electronic states: The full equation-of-motion coupled-cluster single, double, and triple excitation method

Abstract: The equation-of-motion coupled-cluster method with the full inclusion of the single, double, and triple excitations (EOM-CCSDT) has been formulated and implemented. The proper factorization procedure ensures that the method scales as n8, i.e., in the same manner as the standard CCSDT method for ground states. The method has been tested on the vertical excitation energies of the N2 and CO molecules for several basis sets up to 92 basis functions. The full inclusion of the triple excitations improves the EOM-CCSD results by up to 0.2 eV for considered systems.

The effect of lone pairs and electronegativity on the indirect nuclear spin–spin coupling constants in CH2X (X=CH2, NH, O, S): Ab initio calculations using optimized contracted basis sets

Abstract: The indirect nuclear spin–spin coupling constants of C2H4, CH2NH, CH2O, and CH2S were investigated by means of correlated ab initio calculations at the level of the second order polarization propagator approximation (SOPPA) and the second order polarization propagator approximation with coupled cluster singles and doubles amplitudes—SOPPA(CCSD) using large basis sets, which are optimized for the calculation of coupling constants. It is found that at the self-consistent-field (SCF) level CH2NH and CH2S exhibit triplet instabilities whereas CH2CH2 and CH2O show triplet quasi-instabilities, which renders the SCF results meaningless. Our best results deviate between 0.3 and 2.7 Hz from the experimental values. We find that although the one-bond C–H and Y–H couplings as well as the two- and three-bond H–H couplings are dominated by the Fermi contact term, significant contributions of the orbital paramagnetic and sometimes even spin–dipolar terms are observed for the one-bond C–Y and two-bond C–H and Y–H coupli...

Highly accurate coupled-cluster singlet and triplet pair energies from explicitly correlated calculations in comparison with extrapolation techniques

Abstract: Coupled-cluster singles and doubles (CCSD) valence shell correlation energies of the systems CH2 (<1A1 state), H2O, HF, N2, CO, Ne, and F2 are computed by means of standard calculations with correlation-consistent basis sets of the type cc-pVxZ (x = D, T, Q, 5, 6) and by means of explicitly correlated coupled-cluster calculations (CCSD-R12/B) with large uncontracted basis sets of the type 19s14p8d6f4g3h for C, N, O, F, and Ne and 9s6p4d3f for H. These CCSD-R12/B calculations provide reference values for the basis set limit of CCSD theory. The computed correlation energies are decomposed into singlet and triplet pair energies. It is established that the singlet pair energies converge as X−3 and the triplet pair energies as X−5 with the cardinal number of the correlation-consistent basis sets, and an extrapolation technique is proposed that takes into account their different convergence behaviour. Applied to the cc-pV5Z and cc-pV6Z results, this new extrapolation yields pair energies with a mean absolute de...

Formulation and implementation of the relativistic Fock-space coupled cluster method for molecules

Abstract: An implementation of the relativistic multireference Fock-space coupled cluster method is presented which allows simultaneous calculation of potential surfaces for different oxidation states and electronic levels of a molecule, yielding values for spectroscopic constants and transition energies. The method is tested in pilot calculations on the I2 and HgH molecules, and is shown to give a good and balanced description of various electronic states and energies.

Ab initio study of the absorption spectra of Agn (n=5–8) clusters

Abstract: The absorption spectra of Ag5–8 have been determined in the framework of the linear response equation-of-motion coupled cluster method and related techniques employing 11-electron relativistic effective core potential. In these treatments electron correlation effects for 11 electrons per atom are included, providing an accurate description of excited states of silver clusters. The calculations of transition energies and oscillator strengths have been carried out in a large energy interval for the stable structures and for the isomeric forms higher in energy. This allowed us to investigate the influence of structural properties on the spectroscopic patterns and to determine the role of d-electrons. Inclusion of d-electrons in the correlation treatment is mandatory to obtain accurate values for transition energies, but the excitations of s-electrons are primarily responsible for the spectroscopic patterns. They are characterized by the interference phenomena known in molecular spectroscopy which lead to a s...

Benchmark ab Initio Energy Profiles for the Gas-Phase SN2 Reactions Y- + CH3X → CH3Y + X- (X,Y = F,Cl,Br). Validation of Hybrid DFT Methods

Abstract: The energetics of the gas-phase SN2 reactions Y- + CH3X- → CH3Y + X- (where X,Y = F,Cl,Br), were studied using (variants on) the recent W1 and W2 ab initio computational thermochemistry methods. These calculations involve CCSD and CCSD(T) coupled cluster methods, basis sets of up to spdfgh quality, extrapolations to the one-particle basis set limit, and contributions of inner-shell correlation, scalar relativistic effects, and (where relevant) first-order spin−orbit coupling. Our computational predictions are in excellent agreement with experimental data where these have small error bars; in a number of other instances reexamination of the experimental data may be in order. Our computed benchmark data (including cases for which experimental data are unavailable altogether) are used to assess the quality of a number of compound thermochemistry schemes such as G2 theory, G3 theory, and CBS-QB3, as well as a variety of density functional theory methods. Upon applying some modifications to the level of theory...

Perturbative corrections to coupled-cluster and equation-of-motion coupled-cluster energies: A determinantal analysis

Abstract: We develop a combined coupled-cluster (CC) or equation-of-motion coupled-cluster (EOM-CC) theory and Rayleigh–Schrodinger perturbation theory on the basis of a perturbation expansion of the similarity-transformed Hamiltonian H=exp(−T)H exp(T). This theory generates a series of perturbative corrections to any of the complete CC or EOM-CC models and hence a hierarchy of the methods designated by CC(m)PT(n) or EOM-CC(m)PT(n). These methods systematically approach full configuration interaction (FCI) as the perturbation order (n) increases and/or as the cluster and linear excitation operators become closer to complete (m increases), while maintaining the orbital-invariance property and size extensivity of CC at any perturbation order, but not the size intensivity of EOM-CC. We implement the entire hierarchy of CC(m)PT(n) and EOM-CC(m)PT(n) into a determinantal program capable of computing their energies and wave functions for any given pair of m and n. With this program, we perform CC(m)PT(n) and EOM-CC(m)PT...

A second-order perturbative correction to the coupled-cluster singles and doubles method: CCSD(2)

Abstract: Recently, we introduced a new ansatz for developing perturbative corrections to methods based on coupled-cluster theory. In this article we apply this ansatz to the coupled-cluster singles and doubles (CCSD) method, generating the CCSD(2) method. We use the CCSD(2) method to study the double dissociation of water and to calculate spectroscopic constants of first row diatomic molecules. As long as Hartree–Fock is a reasonable approximation, CCSD(2) works very well.

Heats of formation and ionization energies of NHx, x=0–3

Abstract: The heats of formation of NH3, NH2, NH and the ionization energies of NH3, NH2, NH, and N have been calculated at high levels of ab initio molecular orbital theory at 0 K. Geometries and frequencies were calculated with coupled cluster theory, including a perturbative treatment of the connected triple excitations and with correlation consistent basis sets up through augmented sextuple zeta in quality. Subsequent extrapolation of the total energies to the complete one-particle basis set limit was performed 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, spin–orbit, and higher order correlation effects. Zero point energies were taken from anharmonic force fields where available or are based on appropriately scaled values. Using the R/UCCSD(T) method, we find the following heats of formation (kcal/mol) at 0 K: ΔHf(NH3)=−9.10±0.17 (calc.) versus −9.30±0.10 (expt.); ΔHf(N...

New type of noniterative energy corrections for excited electronic states: Extension of the method of moments of coupled-cluster equations to the equation-of-motion coupled-cluster formalism

Abstract: The recently proposed method of moments of coupled-cluster equations (MMCC) is extended to excited states via the equation-of-motion coupled-cluster (EOMCC) formalism. The main idea of the new MMCC theory is that of the noniterative energy corrections which, when added to the excited-state energies obtained in standard approximate EOMCC calculations, recover the exact energies. The MMCC corrections are expressed in terms of the generalized moments of the EOMCC equations. Approximate variants of the excited-state MMCC formalism, including the MMCC(2,3) approach, are introduced. In the MMCC(2,3) method, very simple energy corrections, expressed in terms of matrix elements of the triples-reference, triples-singles, and triples-doubles blocks of the EOMCCSD (EOMCC singles and doubles) similarity-transformed Hamiltonian, are added to the excited-state energies obtained in EOMCCSD calculations. The performance of the MMCC(2,3) approach is illustrated by the results of pilot calculations for the potential energy...

A systematic theoretical investigation of the valence excited states of the diatomic molecules B2, C2, N2 and O2

Abstract: A quantitative survey on the performance of multireference (MR), configuration interaction with all singles and doubles (CISD), MRCISD with the Davidson correction and MR-average quadratic coupled cluster (AQCC) methods for a wide range of excited states of the diatomic molecules B2, C2, N2 and O2 is presented. The spectroscopic constants r e, ωe, T e and D e for a total of 60 states have been evaluated and critically compared with available experimental data. Basis set extrapolations and size-extensivity corrections are essential for highly accurate results: MR-AQCC mean-errors of 0.001 A, 10 cm−1, 300 cm−1 and 300 cm−1 have been obtained for r e, ωe, T e and D e, respectively. Owing to the very systematic behavior of the results depending on the basis set and the choice of method, shortcomings of the calculations, such as Rydberg state coupling or insufficient configuration spaces, can be identified independently of experimental data. On the other hand, significant discrepancies with experiment for states which indicate no shortcomings whatsoever in the theoretical treatment suggest the re-evaluation of experimental results. The broad variety of states included in our survey and the uniform quality of the results indicate that the observed systematics is a general feature of the methods and, hence, is molecule-independent.

Triple excitation effects in coupled-cluster calculations of indirect spin–spin coupling constants

Abstract: The effect of triple excitations in coupled-cluster calculations of indirect spin-spin coupling constants is investigated in coupled-cluster singles and doubles (CCSD) calculations augmented by a perturbative treatment of triples [CCSD(T)], in calculations based on the CC3 model as well as in coupled-cluster singles, doubles, and triples (CCSDT) calculations. Though triple excitation effects are in most cases not particularly pronounced, it is demonstrated that among the approximate schemes for handling triples only the CC3 model with no orbital relaxation included (unrelaxed CC3) provides an adequate description. The otherwise successful CCSD(T) aproach appears to either significantly overestimate triple excitation effects or to yield corrections with the wrong sign in comparison to CCSDT.

Theoretical study of the protolytic dissociation of HCl in water clusters

Abstract: Reaction mechanisms for the acidic dissociation of HCl in water clusters are considered. Intermediates in the reaction are obtained from stationary points on the potential energy surface of the systems HCl–(H2O)n with n=4 and 5. These points have been determined by the B3LYP density functional method in an aug-cc-pVDZ atomic orbital (AO) basis. The total energies of the stationary points are checked by the coupled cluster single-double-triple [CCSD(T)] method in the same AO basis. For the case of n=4 a multibody analysis of the interaction energies is performed by the CCSD(T) method as well as by symmetry adapted perturbation theory. The clusters have a completely dissociated form as their energetically lowest minimum.

Structure and Stability of N6 Isomers and Their Spectroscopic Characteristics

Abstract: Among homonuclear nitrogen molecules, N6 isomers occupy a critical position as a possible diazide or a benzene analogue. However, the character of stationary points on the N6 potential-energy hypersurface is known to be a strong function of choice of calculation methods and basis set. We present results with density functional theory (B3LYP and PW91 functionals) and coupled cluster theory (CCSD(T)) to investigate the shape of the potential-energy surface. The CCSD(T) suggests fewer minima on the potential-energy surface compared with the density functional theory. The stability and amount of internally stored energy of N6 isomers as well as their spectroscopic characteristics are important. Structure, vibrational frequencies including IR and CCSD Raman intensities, heats of formation, vertical ionization potentials, electron affinities, and excitation energies are reported.

Gauge invariant coupled cluster response theory using optimized nonorthogonal orbitals

Abstract: Using the time-dependent Lagrangian response approach, the recently revived orbital optimized coupled cluster (OCC) model is reformulated using nonorthogonal orbital rotations in a manner that conserves the commutativity of the cluster excitation operators. The gauge invariance and the simple pole structure of the OCC linear response function are retained, while the dimension of the eigenvalue problem is reduced by a factor of 2. Restricting the cluster operator to double excitations, we have carried out the first implementation of gauge invariant coupled cluster response theory. Test calculations of the excitation energy, and length and velocity gauge oscillator strengths are presented for the lowest electric dipole allowed transitions of the CH + molecular ion and the Ne atom. Additionally, the excitation energies to the four lowest-lying states of water are calculated.

Extension of the method of moments of coupled-cluster equations to a multireference wave operator formalism ☆

Abstract: The recently proposed method of moments of coupled-cluster equations (MMCC) is extended to a multireference wave operator formalism. After reviewing the single-reference MMCC theory and its performance in calculations of potential energy surfaces involving bond breaking, we introduce the method of moments of the generalized Bloch equation and the method of moments of the state-universal coupled-cluster equations (MM-SUCC). The main idea of the MM-SUCC theory is that of the noniterative energy corrections that, when added to the ground- and excited-state energies obtained in approximate SUCC calculations, recover the exact energies. Approximate variants of the MM-SUCC formalism that may lead to significant improvements in the results of the standard SUCC calculations are discussed.

The helium–, neon–, and argon–cyclopropane van der Waals complexes: Ab initio ground state intermolecular potential energy surfaces and intermolecular dynamics

Abstract: Using the coupled cluster singles and doubles including connected triples model and the augmented correlation consistent polarized valence double zeta basis set extended with a set of 3s3p2d1f1g midbond functions, ab initio helium–, neon–, and argon–cyclopropane ground state intermolecular potential energies are evaluated and fitted to an analytic function including up to four-body interactions. These are the first ab initio potential energy surfaces available for these complexes and are characterized by an absolute minimum of −73.3 cm−1 at a distance on the cyclopropane C3-axis of 3.291 A, −125.3 cm−1 at 3.435 A, and −301.1 cm−1 at 3.696 A for helium, neon, and argon, respectively. The bound van der Waals states are calculated. Two types of tunneling motion cause splittings of these levels: a C3 tunneling between the three equivalent local minima placed in the cyclopropane plane, and a C2 tunneling motion of the rare gas atom between the global minima above and below the cyclopropane plane.

Energy versus amplitude corrected coupled-cluster approaches. II. Breaking the triple bond

Abstract: We examine the effectiveness of various energy corrections to the standard CCSD and to the reduced multireference (RMR) CCSD methods. These corrections are based on the asymmetric energy formula, but instead of projecting onto the reference configuration, as in the standard CCSD method, we employ for this purpose either the MR CISD wave function that is based on a suitable model space of the kind used in RMR CCSD, or simply the zero-order wave function in that model space. Both full complete-active-space and severely-truncated model spaces are employed. The method is applied to the prototypical case of the triple-bond dissociation, namely, to the exactly solvable double-zeta model of the N2 molecule. It is shown that in this way we can eliminate the breakdown of the standard CCSD method in the region of highly stretched geometries and obtain reliable potential energy curves. The comparison with the recently proposed renormalized CCSD(T) and variational CCD methods is also briefly addressed.

Analytical energy gradients for local coupled-cluster methods

Abstract: Analytical expressions for evaluating energy gradients for local coupled-cluster wavefunctions are derived, and relations between the conventional and local coupled-cluster theories are elaborated. In the more general local case additional terms arise from the geometry dependence of the localization transformation and the non-orthogonality of the projected atomic orbitals (PAOs) which are used to span the virtual space. Furthermore, if the excitations from a given orbital pair are restricted to subsets (domains) of PAOs, new terms arise from the geometry dependence of these subspaces. The gradient theory is also generalized to the case in which weakly correlated electron pairs are treated by local second-order Moller–Plesset theory (LMP2) while the contributions of strong pairs are computed at the coupled-cluster level. A number of test calculations are presented in which optimized equilibrium structures are compared for local and conventional calculations, and it is concluded that the local approximations hardly affect the accuracy.

On the accuracy of the fixed-node diffusion quantum Monte Carlo method

Abstract: The accuracy of the fixed-node diffusion quantum Monte Carlo (FN-DQMC) method is compared to the coupled cluster method CCSD(T). For a test set of 20 small molecules and 17 reactions the electronic contribution to the reaction enthalpy is calculated with the FN-DQMC method using the nodes of a Slater determinant calculated at the HF/cc-pVTZ level. By comparison with reference reaction enthalpies the FN-DQMC method is shown to be more accurate than the CCSD(T)/cc-pVDZ method and almost as accurate as CCSD(T)/cc-pVTZ. The deviation from the reference data is comparable to the CCSD(T)/cc-pVTZ deviation, but, with only two exceptions, of opposite sign.

The potential energy curve and dipole polarizability tensor of mercury dimer

Abstract: Scalar relativistic coupled cluster calculations for the potential energy curve and the distance dependence of the static dipole polarizability tensor of Hg2 are presented and compared with current experimental work. The role of the basis set superposition error for the potential energy curve and the dipole polarizability is discussed in detail. Our recently optimized correlation consistent valence basis sets together with energy adjusted pseudopotentials are well suited to accurately describe the van der Waals system Hg2. The vibrational–rotational analysis of the best spin–orbit corrected potential energy curve yields re=3.74 A, D0=328 cm−1, ωe=18.4 cm−1, and ωexe=0.28 cm−1 in reasonable agreement with experimental data (re=3.69±0.01 A, De=380±25 cm−1, ωe=19.6±0.3 cm−1 and ωexe=0.25±0.05 cm−1). We finally present a scaled potential energy curve of the form ∑ja2jr−2j which fits the experimental fundamental vibrational transition of 19.1 cm−1 and the form of our calculated potential energy curve best (re=3.69 A, D0=365 cm−1, ωe=19.7 cm−1, and ωexe=0.29 cm−1). We recommend these accurate two-body potentials as the starting point for the construction of many-body potentials in dynamic simulations of mercury clusters.

State-Specific Brillouin-Wigner Multireference Coupled Cluster Study of the Singlet-Triplet Separation in the Tetramethyleneethane Diradical

Abstract: The potential energy curves for the twisting of tetramethyleneethane in its lowest singlet and triplet states were calculated by the state-specific two-reference Brillouin−Wigner coupled-cluster method with single and double excitations. The calculated potential energy curves are essentially the same as those obtained by the two-determinant CCSD method, and they are also in agreement with the previously reported density functional theory results. Our data bring support for the previously suggested interpretation of experimental data on tetramethyleneethane in the gas phase and in the matrix.

Coupled-cluster theory, pseudo-Jahn–Teller effects and conical intersections

Abstract: A detailed analysis of the strengths and weaknesses of coupled-cluster and many-body perturbation theories in treating strongly interacting potential energy surfaces is presented. Standard coupled cluster theory is shown to provide a qualitative treatment of Herzberg–Teller coupling that is vastly superior to that associated with perturbation theory. However, it also predicts unphysical effects that will always cause it to fail in describing the topology of potential energy surfaces in the immediate vicinity of conical intersections. To treat problems involving strong interstate coupling (notably those involving radicals subject to pseudo-Jahn–Teller effects), methods based on equation-of-motion (linear response) coupled-cluster theory appear to be considerably more suitable. In particular, they provide a description of intersecting surfaces that is qualitatively correct in all respects. It is also shown that there is no reason to believe that the noniterative inclusion of triple excitation contributions ...

The accuracy of atomization energies from explicitly correlated coupled-cluster calculations

Abstract: The accuracy of atomization energies obtained from explicitly correlated coupled-cluster R12 calculations (CC-R12)—including single and double excitation operators (CCSD-R12) and a posteriori perturbative corrections for triple excitations [CCSD[T]-R12 and CCSD(T)-R12]—is studied for CH2(1A1), NH3, H2O, HF, N2, CO, and F2. The basis-set convergence with functions of high angular momentum is demonstrated. Unlike for conventional calculations, already the spdf saturation on nonhydrogen atoms and spd saturation on hydrogen are sufficient for CC-R12 calculations to provide results accurate to within 1 kJ/mol of the limit of a complete basis. Remaining small uncertainties at the CCSD[T]-R12 or CCSD(T)-R12 levels are attributed to the insufficient convergence within the coupled-cluster hierarchy towards the limit of full configuration interaction. It is shown that near the basis-set limit (as provided by CC-R12 calculations) the CCSD[T] variant of the triples correction gives, on average, results closer to the ...