Showing papers on "Coupled cluster published in 1995"

Response functions in the CC3 iterative triple excitation model

Abstract: The derivation of response functions for coupled cluster models is discussed in a context where approximations can be introduced in the coupled cluster equations. The linear response function is derived for the approximate coupled cluster singles, doubles, and triples model CC3. The linear response functions for the approximate triples models, CCSDT‐1a and CCSDT‐1b, are obtained as simplifications to the CC3 linear response function. The consequences of these simplifications are discussed for the evaluation of molecular properties, in particular, for excitation energies. Excitation energies obtained from the linear response eigenvalue equation are analyzed in orders of the fluctuation potential. Double replacement dominated excitations are correct through second order in all the triples models mentioned, whereas they are only correct to first order in the coupled cluster singles and doubles model (CCSD). Single replacement dominated excitation energies are correct through third order in CC3, while in CCSD...

Equation of motion coupled cluster method for electron attachment

Abstract: The electron attachment equation of motion coupled cluster (EA‐EOMCC) method is derived which enables determination of the various bound states of an (N+1)‐electron system and the corresponding energy eigenvalues relative to the energy of an N‐electron CCSD reference state Detailed working equations for the EA‐EOMCC method are derived using diagrammatic techniques for both closed‐shell and open‐shell CCSD reference states based upon a single determinant The EA‐EOMCC method is applied to a variety of different problems, the main purpose being to establish its prospects and limitations The results from EA‐EOMCC calculations are compared to other EOMCC approaches, starting from different reference states, as well as other theoretical methods and experimental values, where available We have investigated electron affinities for a wide selection of both closed‐shell and open‐shell systems Excitation spectra of atoms and molecules with an odd number of electrons are obtained, taking the closed‐shell ground state of the ion as a reference in the EA‐EOMCC calculation Finally we consider excitation spectra of some closed‐shell systems, and find in particular that the electron attachment approach is capable of yielding accurate triplet excitation energies in an efficient way

Modification of the gaussian-2 theoretical model : the use of coupled-cluster energies, density-functional geometries, and frequencies

Abstract: A family of modified GAUSSIAN−2 (G2M) calculational schemes have been proposed, based on geometry optimization and vibrational frequency calculations using the hybrid density‐functional approach, and electron correlation evaluation using the coupled‐cluster methods. The most accurate model, called G2M(RCC), gives the average absolute deviation of calculated atomization energies from experiment for 32 first‐row compounds of 0.88 kcal/mol. The other two methods, called G2M(RCC,MP2) and G2M(rcc,MP2), exhibit the average absolute deviations of 1.15 and 1.28 kcal/mol, respectively, and can be used for the calculations of molecules and radicals of larger sizes containing up to six to seven heavy atoms. The G2M(rcc,MP2) model demonstrates an accuracy comparable to that of G2(MP2) and requires less intensive computations than the latter. The preference of the G2M(RCC) methods over the original G2 is expected to be particularly significant for the open shell systems with large spin contamination.

The anharmonic force field of ethylene, C2H4, by means of accurate ab initio calculations

Abstract: The quartic force field of ethylene, C2H4, has been calculated ab initio using augmented coupled cluster, CCSD(T), methods and correlation consistent basis sets of spdf quality. For the C-12 isotopomers C2H4, C2H3D, H2CCD2, cis-C2H2D2, trans-C2H2D2, C2HD3, and C2D4, all fundamentals could be reproduced to better than 10 per centimeter, except for three cases of severe Fermi type 1 resonance. The problem with these three bands is identified as a systematic overestimate of the Kiij Fermi resonance constants by a factor of two or more; if this is corrected for, the predicted fundamentals come into excellent agreement with experiment. No such systematic overestimate is seen for Fermi type 2 resonances. Our computed harmonic frequencies suggest a thorough revision of the accepted experimentally derived values. Our computed and empirically corrected re geometry differs substantially from experimentally derived values: both the predicted rz geometry and the ground-state rotational constants are, however, in excellent agreement with experiment, suggesting revision of the older values. Anharmonicity constants agree well with experiment for stretches, but differ substantially for stretch-bend interaction constants, due to equality constraints in the experimental analysis that do not hold. Improved criteria for detecting Fermi and Coriolis resonances are proposed and found to work well, contrary to the established method based on harmonic frequency differences that fails to detect several important resonances for C2H4 and its isotopomers. Surprisingly good results are obtained with a small spd basis at the CCSD(T) level. The well-documented strong basis set effect on the v8 out-of-plane motion is present to a much lesser extent when correlation-optimized polarization functions are used. Complete sets of anharmonic, rovibrational coupling, and centrifugal distortion constants for the isotopomers are available as supplementary material to the paper.

Achieving Chemical Accuracy with Coupled-Cluster Theory

Abstract: Due to formal and computational advances in coupled-cluster theory over the past few years, it is now possible to obtain very accurate molecular geometries, vibrational frequencies, heats of formation, binding energies, and vertical electronic excitation energies. For example, based on statistical analyses of a large number of calculations, it is shown that the CCSD(T)/spdfg level of theory gives rXH,rXY (double bonds), and rXY (triple bonds) with an average error of 0.0010, 0.0020, and 0.0026 A, respectively, with the theoretical bond distances usually too long relative to experiment. This level of theory yields bond angle predictions that are too small by 0.21 degrees on average. Fundamental vibrational frequencies predicted at the CCSD(T)/spdfg level of theory are accurate to better than 8.0 cm-1 on average, but the remaining errors are less systematic than those found for the geometrical parameters, except for X–Y stretches which are usually underestimated relative to experiment. For molecules described reasonably well by a single determinant reference function, single- and multiple-bond energies are given to within 1.0 and 2.0 kcal/mol, respectively, at the CCSD(T)/spdfg level of theory. The present monograph reviews the advances that have lead to the current state-of-the art, and also summarizes selected examples from the published literature.

Benchmark calculations with correlated molecular wave functions. vii: binding energy and structure of the hf dimer

Abstract: The hydrogen bond energy and geometry of the HF dimer have been investigated using the series of correlation consistent basis sets from aug‐cc‐pVDZ to aug‐cc‐pVQZ and several theoretical methods including Mo/ller–Plesset perturbation and coupled cluster theories. Estimates of the complete basis set (CBS) limit have been derived for the binding energy of (HF)2 at each level of theory by utilizing the regular convergence characteristics of the correlation consistent basis sets. CBS limit hydrogen bond energies of 3.72, 4.53, 4.55, and 4.60 kcal/mol are estimated at the SCF, MP2, MP4, and CCSD(T) levels of theory, respectively. CBS limits for the intermolecular F–F distance are estimated to be 2.82, 2.74, 2.73, and 2.73 A, respectively, for the same correlation methods. The effects of basis set superposition error (BSSE) on both the binding energies and structures have also been investigated for each basis set using the standard function counterpoise (CP) method. While BSSE has a negligible effect on the intramolecular geometries, the CP‐corrected F–F distance and binding energy differ significantly from the uncorrected values for the aug‐cc‐pVDZ basis set; these differences decrease regularly with increasing basis set size, yielding the same limits in the CBS limit. Best estimates for the equilibrium properties of the HF dimer from CCSD(T) calculations are De=4.60 kcal/mol, RFF=2.73 A, r1=0.922 A, r2=0.920 A, Θ1=7°, and Θ2=111°.

Coupled-cluster calculations of nuclear magnetic resonance chemical shifts

Abstract: Theory and implementation of the gauge‐including atomic orbital (GIAO) ansatz for the gauge‐invariant calculation of nuclear magnetic resonance chemical shifts are described for the coupled‐cluster singles and doubles (CCSD) approach. Results for the shielding constants of the hydrides HF, H2O, NH3, and CH4 as well as for a few multiply bonded systems such as CO, N2, and HCN demonstrate the importance of higher‐order correlation corrections, as good agreement with experiment is only obtained at the CCSD level and to some extent at partial fourth‐order many‐body perturbation theory [SDQ‐MBPT(4)] with the latter slightly overestimating correlation effects due to single and double excitations. For relative chemical shifts, GIAO‐CCSD calculations provide in difficult cases (e.g., CO and CF4) more accurate results than previous GIAO‐MBPT(2) calculations. But, it seems that it is often more important to include rovibrational effects (as well as possible molecule–solvent interactions) than higher‐order correlation corrections. Despite that, GIAO‐CCSD proves to be a powerful tool for the accurate calculation of NMR chemical shifts. Its capabilities as well as its limitations are demonstrated in shielding calculations for formaldehyde, diazomethane, and ozone. At least for the latter, the description provided by the CCSD ansatz is not sufficient and even higher excitations need to be considered.

Perturbative treatment of the similarity transformed Hamiltonian in equation‐of‐motion coupled‐cluster approximations

Abstract: A series of size‐consistent approximations to the equation‐of‐motion coupled cluster method in the singles and doubles approximation (EOM‐CCSD) are developed by subjecting the similarity transformed Hamiltonian H=exp(−T)H exp(T) to a perturbation expansion Attention is directed to N and N−1 electron final state realizations of the method defined by truncation of H at second order Explicit spin–orbital equations for the energy and its first derivative are documented for both approaches [EOMEE‐CCSD(2) and EOMIP‐CCSD(2), respectively], and have been implemented in a large‐scale quantum chemistry program Vertical ionization potentials calculated by EOMIP‐CCSD(2) are shown to be equivalent to those of an approach presented recently by Nooijen and Snijders [J Chem Phys 102, 1681 (1995)] Applications of both EOMIP‐CCSD(2) and EOMEE‐CCSD(2) provide results for final state properties that compare favorably with those obtained in full EOM‐CCSD calculations Analysis of the computational aspects of the approximate and full EOM‐CCSD methods shows that the cost of EOMIP‐CCSD(2) energy and gradient calculations scales in proportion to the fifth power of the basis set size, a significant savings over the sixth power dependence of EOMIP‐CCSD This feature is of great practical importance, as it shows that this N−1 electron final state approach has a large domain of applicability and is therefore likely to become a valuable tool for application calculations On the other hand, the same cannot be said for EOMEE‐CCSD(2) since its asymptotic computational dependence and storage requirements are the same as the full EOMEE‐CCSD method

Theoretical study of the first transition row oxides and sulfides

Abstract: The first transition row oxides and sulfides are studied using several different levels of theory. The calculations show the bonding mechanism in the sulfides and oxides to be very similar. For the oxides, accurate experimental data allow the theoretical methods to be calibrated. The same level of theory is used to study the sulfides where there is far less experimental information. For ScO through MnO and CuO the coupled cluster singles and doubles technique including a perturbational estimate of the unliked triple excitations [CCSD(T)] yields spectroscopic constants ((tau)e, (omega)e, and D0) in good agreement with experiment. The triple excitations are found to be very important in achieving this accuracy. For FeO to NiO, the single determinant self-consistent-field (SCF) approach yields pi orbitals that are localized on the metal or oxygen. This appears to cause problems for the single reference techniques; this is discussed in detail for NiO. The complete-active-space SCF/internally contracted averaged coupled pair functional approach (CASSCF/ICACPF) works well for FeO to NiO. The calculation of accurate dipole moments is found to be very difficult.

Approximately extensive modifications of the multireference configuration interaction method: A theoretical and practical analysis

Abstract: The extensivity error of configuration interaction (CI) is well understood and unlinked diagram corrections must be applied to get reliable results. Besides the well known a posteriori Davidson‐type corrections, several methods attempt to modify the CI equations a priori to obtain nearly extensive results, while retaining the convenience of working in a configuration space. Such unlinked diagram corrections are particularly important for multireference cases for which coupled‐cluster (CC) calculations, which require a many‐body, integral‐based calculation, are more difficult. Several such multireference methods have been presented recently, ranging from the multireference linearized coupled cluster method (MR‐LCCM), averaged coupled pair functional (MR‐ACPF), through various quasidegenerate variational perturbation theory (QD‐VPT), MR‐coupled electron pair method (MR‐CEPA) to size‐consistent, self‐consistent, selected CI [(SC)2SCI]. We analyze all of these methods theoretically and numerically, paying par...

Gauge‐invariant calculation of nuclear magnetic shielding constants at the coupled–cluster singles and doubles level

Abstract: The gauge‐including atomic orbital (GIAO) method for the gauge‐invariant calculation of nuclear magnetic shielding constants has been implemented at the coupled‐cluster singles and doubles (CCSD) level. A brief description of the theory and its computational requirements is provided. Finally, the GIAO–CCSD method is applied to calculate nuclear shielding constants of N2O with two different basis sets, the larger of which contains 153 contracted Gaussian functions.

A comparison of single reference methods for characterizing stationary points of excited state potential energy surfaces

Abstract: The accuracy of geometries, vibrational frequencies and dipole moments of stationary points on excited state potential energy surfaces is assessed for three single reference excited state theories—configuration interaction (CIS), a perturbative doubles correlation correction to CIS, termed CIS(D), and equation‐of‐motion coupled cluster theory with single and double substitutions (EOM‐CCSD). Two groups of systems are studied: the diatomic molecules H2, BH, BF, C2, CO, and N2; and the lowest singlet excited states of ammonia, formaldehyde and acetylene. The calculations demonstrate that CIS systematically underestimates bond lengths and overestimates frequencies and dipole moments, a pattern often associated with the Hartree–Fock method for ground states. CIS(D) fails to provide a systematic improvement to CIS for all geometries and frequencies, often overestimating correlation corrections. EOM‐CCSD, by contrast, performs significantly better than CIS for all properties considered.

Basis set convergence and performance of density functional theory including exact exchange contributions for geometries and harmonic frequencies

Abstract: The performance of the Becke three-parameter Lee-Yang-Parr (B3LYP) method for geometries and harmonic frequencies has been compared with other density functional methods and accurate coupled cluster calculations, and its basis set convergence investigated. In a basis of [3s2p1d] quality, B3LYP geometries are more accurate than CCSD(T) due to an error compensation. Using simple additivity corrections, B3LYP/[4s3p2d1f] calculations allow the prediction of geometries to within 0·002 A, on average. Except for certain special cases where frequencies are especially sensitive to the basis set, B3LYP/[4s3p2d1f] frequencies do not represent a clear improvement over B3LYP/[3s2p1d], while the latter are of nearly the same quality as CCSD(T)/[3s2p1d]. Applications to ethylene, benzene, furan and pyrrole are presented. For the latter three molecules, our best structures and harmonic frequencies are believed to be the most accurate computed values available.

Description of core‐excitation spectra by the open‐shell electron‐attachment equation‐of‐motion coupled cluster method

Abstract: The theoretical description of core‐excitation spectra presents a difficult problem due to the large excitation energies involved, and the extensive relaxation effects that occur upon promotion of a core electron to a valence or Rydberg level. For this reason we follow a two‐step procedure to evaluate core‐excitation energies. We start from a coupled cluster singles‐doubles (CCSD) description of the core ion to include the large relaxation effects, followed by adding an extra electron to the core‐ionized state to obtain the various core‐excited states of the neutral by using the open‐shell electron attachment equation‐of‐motion coupled cluster method (EA‐EOMCC). An important feature of the approach is that the term values, the core‐excitation energies relative to the relevant core‐ionization potential, are calculated directly and this allows us to achieve high accuracy. This work describes the extension of the EA‐EOMCC method to open‐shell reference states and we make applications to a number of molecular systems. The assignment of recently obtained high‐resolution core‐excitation spectra for acetylene and ethylene is discussed, and we compare our open‐shell EA‐EOMCC results to results obtained from closed‐shell EA‐EOMCC calculations based on the equivalent core ion corresponding to the core‐excited molecular system. Special attention is paid to the singlet–triplet splitting for core‐excited states, and we address the multireference character of core‐ionized and core‐excited states for molecules that contain symmetry‐equivalent heavy nuclei, which relates to a persistent controversy in the literature concerning localized versus delocalized core holes.

Second order many-body perturbation approximations to the Coupled Cluster Green's Function.

Abstract: The time‐consuming step in coupled cluster Green’s function or equivalently equation of motion coupled cluster calculations of ionization potentials is the solution of the CCSD equations. We investigate here the accuracy that can be obtained if the CCSD coefficients are replaced by their MBPT(2) analogs. We discuss some additional diagonal approximations that might prove especially useful in polymer calculations, and compare with traditional Green’s function calculations based on a second order approximation to the irreducible self‐energy.

Detailed study of the water trimer potential energy surface

Abstract: The potential energy surface of the water trimer has been studied through the use of ab initio quantum mechanical methods. Five stationary points were located, including one minimum and two transition states. All geometries were optimized at levels up to the double-[Zeta] plus polarization plus diffuse (DZP + diff) single and double excitation coupled cluster (CCSD) level of theory. CCSD single energy points were obtained for the minimum, two transition states, and the water monomer using the triple-[Zeta] plus double polarization plus diffuse (TZ2P + diff) basis at the geometries predicted by the DZP + diff CCSD method. Reported are the following: geometrical parameters, total and relative energies, harmonic vibrational frequencies and infrared intensities for the minimum, and zero point vibrational energies for the minimum, two transition states, and three separated water molecules. 27 refs., 5 figs., 10 tabs.

Limiting values for Mo/ller–Plesset second‐order correlation energies of polyatomic systems: A benchmark study on Ne, HF, H2O, N2, and He...He

Abstract: Limiting values for Mo/ller–Plesset second‐order (MP2) correlation energies are provided for the ten‐electron systems Ne, HF, and H2O, for the N2 molecule, and for the weak He...He interatomic interaction energy. These limiting values were obtained by the MP2‐R12 approach. This approach differs from traditional MP2 theory by employing first‐order wave functions which explicitly depend on the interelectronic coordinates rij. With the MP2‐R12 method, the atomic orbital (AO) basis set limits for the systems under study are reached. The calculations provide insight into AO basis set requirements for methods with linear rij dependence (R12 methods), e.g., for coupled cluster methods, or multireference configuration interaction methods. Moreover, it is expected that the results have the potential to serve as valuable benchmarks for further developments in the field of explicitly correlated wave functions, for example for expansions in terms of Gaussian geminals (Gaussian functions which depend on rij). The pres...

Intrinsic Errors in Several ab Initio Methods: The Dissociation Energy of N2

Abstract: Using sequences of correlation consistent basis sets, complete basis set (CBS) limits for the dissociation energy D{sub c} of N{sub 2} have been estimated for a variety of commonly used electron correlation methods. After extrapolation to the CBS limit, the difference between theory and experiment corresponds to the error intrinsic to the chosen theoretical method. Correlated wave functions (valence electrons correlated only) for which intrinsic errors have been estimated include internally contracted multireference configuration interaction (CMRCI), singles and doubles coupled cluster theory with and without perturbative triple excitations [CCSD, CCSD(T)], and second-, third-, and fourth-order Moller-Plesset perturbation theory (MP2, MP3, MP4). For CMRCI and CCSD(T), D{sub c} converges smoothly from below the experimental value and yields the smallest intrinsic errors, -0.8 and -1.6 kcal/mol, respectively. In contrast, for MP2 and MP4, D{sub c} exhibits fortuitously good agreement with experiment for small basis sets but leads to CBS limits that are 11.6 and 3.4 kcal/mol larger than experiment, respectively. Correlation of the 1s core electrons is predicted to yield intrinsic errors of less than 1 kcal/mol for CMRCI and CCSD(T), while those for MP2 and MP4 increase still further. 38 refs., 1 fig., 1 tab.

Gaussian‐2 theory: Use of higher level correlation methods, quadratic configuration interaction geometries, and second‐order Mo/ller–Plesset zero‐point energies

Abstract: The performance of Gaussian‐2 theory is investigated when higher level theoretical methods are included for correlation effects, geometries, and zero‐point energies A higher level of correlation treatment is examined using Brueckner doubles [BD(T)] and coupled cluster [CCSD(T)] methods rather than quadratic configuration interaction [QCISD(T)] The use of geometries optimized at the QCISD level rather than the second‐order Mo/ller–Plesset level (MP2) and the use of scaled MP2 zero‐point energies rather than scaled Hartree–Fock (HF) zero‐point energies have also been examined The set of 125 energies used for validation of G2 theory [J Chem Phys 94, 7221 (1991)] is used to test out these variations of G2 theory Inclusion of higher levels of correlation treatment has little effect except in the cases of multiply‐bonded systems In these cases better agreement is obtained in some cases and poorer agreement in others so that there is no improvement in overall performance The use of QCISD geometries yields significantly better agreement with experiment for several cases including the ionization potentials of CS and O2, electron affinity of CN, and dissociation energies of N2, O2, CN, and SO2 This leads to a slightly better agreement with experiment overall The MP2 zero‐point energies gives no overall improvement These methods may be useful for specific systems

An ab initio derived torsional potential energy surface for (H2O)3. II. Benchmark studies and interaction energies

Abstract: A torsional potential energy surface for the cyclic water trimer was calculated at the level of second‐order Mo/ller–Plesset perturbation theory. For the construction of this ab initio surface, the first‐order wave function was expanded in a many‐electron basis which linearly depends on the interelectronic coordinates r12. The one‐electron basis of Gaussian orbitals was calibrated on the water monomer and dimer to ensure that the ab initio surface computed represents the (near‐ ) basis set limit for the level of theory applied. The positions of the free O—H bonds are described by three torsional angles. The respective three‐dimensional torsional space was investigated by 70 counterpoise corrected single‐point calculations for various values of these angles, providing a grid to fit an analytical representation of the potential energy surface. The four symmetry unique stationary points previously found at the Hartree–Fock and conventional Mo/ller–Plesset levels [Schutz et al., J. Chem. Phys. 99, 5228 (1993)] were studied in detail: Relative energies of the structures were calculated by applying second‐order Mo/ller–Plesset and coupled cluster methods; harmonic vibrational frequencies were calculated at the second‐order Mo/ller–Plesset level with a 6‐311++G(d,p) basis set at these stationary points. It is expected that the present torsional potential energy surface for the water trimer will play an important role in the understanding of the vibrational transitions observed by far‐infrared vibration–rotation–tunneling spectroscopy in terms of a nearly free pseudorotational interconversion on a cyclic vibrational–tunneling path.

An explicitly correlated coupled cluster calculation of the helium–helium interatomic potential

Abstract: Explicitly correlated coupled cluster (CCSDT‐1a‐R12) results were obtained for the He2 interatomic potential from a new, integral‐direct implementation. With the new code, Gaussian basis sets as large as 11s8p6d5f4g3h could be employed, and the potential energy curve was calculated over a wide range using a basis of the type 11s8p6d5f4g.This curve is very close to represent the basis set limit of the CCSDT‐1a approach. At the internuclear separation R=5.6 a0, the CCSDT‐1a limiting value for the interaction energy is −10.68 K. As the effect of quadruple substitutions can be estimated as −0.32 K, this limiting value is perfectly consistent with the accurate quantum Monte Carlo calculation of Anderson et al. [J. Chem. Phys. 99, 345 (1993)], who reported a well depth of −11.01±0.10 K. On the other hand, however, CCSDT‐1a‐R12 calculations of the He2 potential energy curve strongly indicate that the most recent semiempirical potentials available in the literature are slightly too repulsive for short (R≤4.0 a0) ...

Analytic energy derivatives for coupled‐cluster methods describing excited states: General formulas and comparison of computational costs

Abstract: It is possible to derive energy derivatives for nonvariational (e.g., coupled-cluster) methods invoking the generalized Hellmann–Feynman theorem. In such a procedure, one constructs a functional which, besides the usual wave-function parameters, contains new ones. One set of stationary conditions will reproduce exactly the original equations of the method, while the others will determine the value of the new parameters. We applied this straightforward procedure to derive analytic energy derivatives for several coupled-cluster (CC) methods applicable to excited states such as the Hilbert-space CC method, two-determinetal (TD) CC method, Fock-space CC method, and equation-of-motion–CC (EOM–CC) method. Finally, we compared the computational requirements for the different methods. © 1995 John Wiley & Sons, Inc.