Showing papers on "Coupled cluster published in 2006"
TL;DR: A coupled cluster composite approach has been used to accurately determine the spectroscopic constants, bond dissociation energies, and heats of formation for the X1(2)II(3/2) states of the halogen oxides ClO, BrO, and IO, as well as their negative ions ClO-, BrO-, and IO-.
Abstract: A coupled cluster composite approach has been used to accurately determine the spectroscopic constants, bond dissociation energies, and heats of formation for the X12Π3/2 states of the halogen oxides ClO, BrO, and IO, as well as their negative ions ClO-, BrO-, and IO-. After determining the frozen core, complete basis set (CBS) limit CCSD(T) values, corrections were added for core−valence correlation, relativistic effects (scalar and spin−orbit), the pseudopotential approximation (BrO and IO), iterative connected triple excitations (CCSDT), and iterative quadruples (CCSDTQ). The final ab initio equilibrium bond lengths and harmonic frequencies for ClO and BrO differ from their accurate experimental values by an average of just 0.0005 A and 0.8 cm-1, respectively. The bond length of IO is overestimated by 0.0047 A, presumably due to an underestimation of molecular spin−orbit coupling effects. Spectroscopic constants for the spin−orbit excited X22Π1/2 states are also reported for each species. The predicted...
652 citations
TL;DR: In this article, the first-principles calculation of chiroptical properties such as optical rotation, electronic and vibrational circular dichroism, and Raman optical activity are described.
Abstract: This review describes the first-principles calculation of chiroptical properties such as optical rotation, electronic and vibrational circular dichroism, and Raman optical activity. Recent years have witnessed a flurry of activity in this area, especially in the advancement of density-functional and coupled cluster methods, with two ultimate goals: the elucidation of the fundamental relationship between chiroptical properties and detailed molecular structure, and the development of a suite of computational tools for the assignment of the absolute configurations of chiral molecules. The underlying theory and the basic principles of such calculations are given for each property, and a number of representative applications are discussed.
368 citations
TL;DR: The spin-flip approach to multireference situations (e.g., bond breaking, diradicals, and triradicals) is described and can be viewed as an equation-of-motion model, where target states are sought on the basis of determinants conserving the total number of electrons but changing the number of alpha and beta electrons.
Abstract: The spin-flip (SF) approach to multireference situations (e.g., bond breaking, diradicals, and triradicals) is described. Both closed- and open-shell low-spin states are described within a single reference formalism as spin-flipping, e.g., α → β, excitations from a high-spin reference state for which both dynamical and nondynamical correlation effects are much smaller than for the corresponding low-spin state. Formally, the SF approach can be viewed as an equation-of-motion model, where target states are sought on the basis of determinants conserving the total number of electrons but changing the number of α and β electrons.
282 citations
TL;DR: Calculations using the CASSCF based CT method with single and double operators for the potential energy curves for water and nitrogen molecules, the BeH(2) insertion reaction, and hydrogen fluoride and boron hydride bond breaking consistently yield quantitative accuracies typical of equilibrium region coupled cluster theory, but across all geometries, and better than obtained with multireference perturbation theory.
Abstract: We propose a theory to describe dynamic correlations in bonding situations where there is also significant nondynamic character. We call this the canonical transformation (CT) theory. When combined with a suitable description of nondynamic correlation, such as given by a complete-active-space self-consistent Field (CASSCF) or density matrix renormalization group wave function, it provides a theory to describe bonding situations across the entire potential energy surface with quantitative accuracy for both dynamic and nondynamic correlation. The canonical transformation theory uses a unitary exponential ansatz, is size consistent, and has a computational cost of the same order as a single-reference coupled cluster theory with the same level of excitations. Calculations using the CASSCF based CT method with single and double operators for the potential energy curves for water and nitrogen molecules, the BeH_2 insertion reaction, and hydrogen fluoride and boron hydride bond breaking, consistently yield quantitative accuracies typical of equilibrium region coupled cluster theory, but across all geometries, and better than obtained with multireference perturbation theory.
239 citations
TL;DR: For the early transition metal elements (Sc-Mn) the internally contracted multireference averaged coupled pair functional method yielded excellent agreement with experiment; however, the atomic properties for the late transition metals (Mn-Zn) proved to be much more difficult to describe with this level of theory, even with the largest reference function.
Abstract: Recently developed correlation consistent basis sets for the first row transition metal elements Sc–Zn have been utilized to determine complete basis set (CBS) scalar relativistic electron affinities, ionization potentials, and 4s23dn−2–4s1dn−1 electronic excitation energies with single reference coupled cluster methods [CCSD(T), CCSDT, and CCSDTQ] and multireference configuration interaction with three reference spaces: 3d4s, 3d4s4p, and 3d4s4p3d′. The theoretical values calculated with the highest order coupled cluster techniques at the CBS limit, including extrapolations to full configuration interaction, are well within 1kcal∕mol of the corresponding experimental data. For the early transition metal elements (Sc-Mn) the internally contracted multireference averaged coupled pair functional method yielded excellent agreement with experiment; however, the atomic properties for the late transition metals (Mn-Zn) proved to be much more difficult to describe with this level of theory, even with the largest ...
229 citations
TL;DR: In this paper, the advantages and possibilities of unitary coupled-cluster (CC) theory are examined, and it is shown that using a unitary parameterization of the wave function guarantees agreement between a sum-over-states polarization propagator and response theory calculation of properties of arbitrary order.
Abstract: The advantages and possibilities of a unitary coupled-cluster (CC) theory are examined. It is shown that using a unitary parameterization of the wave function guarantees agreement between a sum-over-states polarization propagator and response theory calculation of properties of arbitrary order, as opposed to the case in conventional CC theory. Then, using the Zassenhaus expansion for noncommuting exponential operators, explicit diagrams for an extensive and variational method based on unitary CC theory are derived. Possible extensions to the approximations developed are discussed as well. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2006
229 citations
TL;DR: High-order excitations have been studied in three multireference couple cluster theories built on the wave operator formalism and the BW and Mk methods are found to provide more accurate results than the state-universal SU approach at all levels of truncation of the cluster operator.
Abstract: For the first time high-order excitations (n>2) have been studied in three multireference couple cluster (MRCC) theories built on the wave operator formalism: (1) the state-universal (SU) method of Jeziorski and Monkhorst (JM) (2) the state-specific Brillouin-Wigner (BW) coupled cluster method, and (3) the state-specific MRCC approach of Mukherjee (Mk). For the H4, P4, BeH(2), and H8 models, multireference coupled cluster wave functions, with complete excitations ranging from doubles to hextuples, have been computed with a new arbitrary-order string-based code. Comparison is then made to corresponding single-reference coupled cluster and full configuration interaction (FCI) results. For the ground states the BW and Mk methods are found, in general, to provide more accurate results than the SU approach at all levels of truncation of the cluster operator. The inclusion of connected triple excitations reduces the nonparallelism error in singles and doubles MRCC energies by a factor of 2-10. In the BeH(2) and H8 models, the inclusion of all quadruple excitations yields absolute energies within 1 kcal mol(-1) of the FCI limit. While the MRCC methods are very effective in multireference regions of the potential energy surfaces, they are outperformed by single-reference CC when one electronic configuration dominates.
216 citations
TL;DR: DF-SCS-LMP2 is computationally inexpensive and represents an attractive method for the study of larger pi-stacked systems such as truncated sections of DNA.
Abstract: Potential energy curves for the parallel-displaced, T-shaped and sandwich structures of the benzene dimer are computed with density fitted local second-order Moller–Plesset perturbation theory (DF-LMP2) as well as with the spin-component scaled (SCS) variant of DF-LMP2. While DF-LMP2 strongly overestimates the dispersion interaction, in common with canonical MP2, the DF-SCS-LMP2 interaction energies are in excellent agreement with the best available literature values along the entire potential energy curves. The DF-SCS-LMP2 dissociation energies for the three structures are also compared with new complete basis set estimates of the interaction energies obtained from accurate coupled cluster (CCSD(T)) and DF-SCS-MP2 calculations. Since LMP2 is essentially free of basis set superposition errors, counterpoise corrections are not required. As a result, DF-SCS-LMP2 is computationally inexpensive and represents an attractive method for the study of larger π-stacked systems such as truncated sections of DNA.
214 citations
TL;DR: The CCSD(T) method is found to provide results that are closer to the CCSDTQ and full configuration-interaction results than the less approximate CCS DT method.
Abstract: The sources of error in electronic structure calculations arising from the truncation of the one-particle and n-particle expansions are examined with very large correlation consistent basis sets, in some cases up through valence 10-zeta quality, and coupled cluster methods, up through connected quadruple excitations. A limited number of full configuration interaction corrections are also considered. For cases where full configuration interaction calculations were unavailable or prohibitively expensive, a continued fraction approximation was used. In addition, errors arising from corevalence and relativistic corrections are also probed for a number of small chemical systems. The accuracies of several formulas for estimating total energies and atomization energies in the complete basis set limit are compared in light of the present large basis set findings. In agreement with previous work, the CCSD(T) method is found to provide results that are closer to the CCSDTQ and full configuration-interaction results than the less approximate CCSDT method.
188 citations
TL;DR: The importance of electron-correlation contributions to the DBOC is illustrated in the computation of the corresponding corrections for the reaction energy and activation barrier of the F + H2 --> FH + H reaction as well as of the atomization energy for trans-butadiene.
Abstract: Schemes for the analytic calculation of the diagonal Born-Oppenheimer correction (DBOC) are formulated and implemented for use with general single-reference configuration-interaction and coupled-cluster wave function models. Calculations are reported to demonstrate the convergence of the DBOC with respect to electron-correlation treatment and basis set as well as to investigate the size-consistency error in configuration-interaction calculations of the DBOC. The importance of electron-correlation contributions to the DBOC is illustrated in the computation of the corresponding corrections for the reaction energy and activation barrier of the F+H2→FH+H reaction as well as of the atomization energy for trans-butadiene.
186 citations
TL;DR: The results show very good agreement with density functional theory calculations, reproducing the individual CSOV energy contributions for a given interaction as well as the B3LYP total interaction energies with errors below kBT at room temperature.
Abstract: Total intermolecular interaction energies are determined with a first version of the Gaussian electrostatic model (GEM-0), a force field based on a density fitting approach using s-type Gaussian functions. The total interaction energy is computed in the spirit of the sum of interacting fragment ab initio (SIBFA) force field by separately evaluating each one of its components: electrostatic (Coulomb), exchange repulsion, polarization, and charge transfer intermolecular interaction energies, in order to reproduce reference constrained space orbital variation (CSOV) energy decomposition calculations at the B3LYP/aug-cc-pVTZ level. The use of an auxiliary basis set restricted to spherical Gaussian functions facilitates the rotation of the fitted densities of rigid fragments and enables a fast and accurate density fitting evaluation of Coulomb and exchange-repulsion energy, the latter using the overlap model introduced by Wheatley and Price [Mol. Phys. 69, 50718 (1990)]. The SIBFA energy scheme for polarization and charge transfer has been implemented using the electric fields and electrostatic potentials generated by the fitted densities. GEM-0 has been tested on ten stationary points of the water dimer potential energy surface and on three water clusters (n=16,20,64). The results show very good agreement with density functional theory calculations, reproducing the individual CSOV energy contributions for a given interaction as well as the B3LYP total interaction energies with errors below kBT at room temperature. Preliminary results for Coulomb and exchange-repulsion energies of metal cation complexes and coupled cluster singles doubles electron densities are discussed.
TL;DR: The CR-CC(2, 3) method proposed in this article is a completely renormalized (CR) coupled-cluster (CC) approach, in which the CCSD (CC singles and doubles) energy is corrected for the effect of triples, and is size extensive, competitive with CCSd(T) in calculations for non-degenerate states, and as accurate as the expensive CC approach with singles, doubles, and triples in the bond-breaking region.
TL;DR: In this article, a short-range gradient-corrected density functional from the closed-shell to the open-shell case was extended with long-range coupled-cluster methods (CCSD, CCSD(T)), and applied to the weakly bound alkali-metal rare-gas dimers AmRg (Am = Li-Cs; Rg = Ne-Xe).
TL;DR: The results show that the CAM-B3LYP functional, when used in conjuction with a one-particle basis-set containing diffuse functions, has much promise; however, care must still be exercised for diffuse Rydberg-type states.
Abstract: We present a detailed study of the effects of electron correlation on two-photon absorption calculated by coupled cluster quadratic response theory. The hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3 has been used to investigate the effects of electron correlation on the two-photon absorption cross sections of formaldehyde (CH2O), diacetylene (C4H2), and water (H2O). In particular, the effects of triple excitations on two-photon transition cross sections are determined for the first time. In addition, we present a detailed comparison of the coupled cluster results with those obtained from Hartree-Fock and density-functional response theories. We have investigated the local-density approximation, the pure Becke-Lee-Yang-Parr (BLYP) functional, the hybrid Becke-3-parameter-Lee-Yang-Parr (B3LYP), and the Coulomb-attenuated B3LYP (CAM-B3LYP) functionals. Our results show that the CAM-B3LYP functional, when used in conjuction with a one-particle basis-set containing diffuse functions, has much promise; however, care must still be exercised for diffuse Rydberg-type states.
TL;DR: Subotnik and Head-Gordon as mentioned in this paper proposed an algorithm for computing smooth local coupled-cluster singles-doubles (LCCSD) correlation energies of quantum mechanical systems, which leads to smooth potential energy surfaces and yields large computational savings.
Abstract: We demonstrate near linear scaling of a new algorithm for computing smooth local coupled-cluster singles-doubles (LCCSD) correlation energies of quantum mechanical systems. The theory behind our approach has been described previously, [J. Subotnik and M. Head-Gordon, J. Chem. Phys. 123, 064108 (2005)], and requires appropriately multiplying standard iterative amplitude equations by a bump function, creating local amplitude equations (which are smooth according to the implicit function theorem). Here, we provide an example that this theory works in practice: we show that our algorithm leads to smooth potential energy surfaces and yields large computational savings. As an example, we apply our LCCSD approach to measure the post-MP2 correction to the energetic gap between two different alanine tetrapeptide conformations.
TL;DR: A simple approach for constructing virtual LMOs of clusters, and new ways of constructing clusters and extracting the correlation contributions from calculations on clusters, which are more efficient than those suggested in the original work are proposed.
Abstract: An efficient implementation of the “cluster-in-molecule” (CIM) approach is presented for performing local electron correlation calculations in a basis of orthogonal occupied and virtual localized molecular orbitals (LMOs). The main idea of this approach is that significant excitation amplitudes can be approximately obtained by solving the coupled cluster (or Moller-Plesset perturbation theory) equations of a series of “clusters,” each of which contains a subset of occupied and virtual LMOs. In the present implementation, we have proposed a simple approach for constructing virtual LMOs of clusters, and new ways of constructing clusters and extracting the correlation contributions from calculations on clusters, which are more efficient than those suggested in the original work. More importantly, linear scaling of computational time of the CIM approach is achieved by evaluating the transformed two-electron integrals over LMOs using simple truncation techniques in limited operations (independent of the molecu...
TL;DR: In this article, two classes of non-iterative coupled-cluster (CC) methods derived from the method of moments of CC equations (MMCC) are discussed, which combine the MMCC formalism with a simplified form of multi-reference perturbation theory.
Abstract: Two recently proposed classes of non-iterative coupled-cluster (CC) methods derived from the method of moments of CC equations (MMCC) are discussed. The first approach, termed MMCC/PT, combines the MMCC formalism with a simplified form of multi-reference perturbation theory. The second approach, which leads to completely renormalized (CR) CC methods employing the left eigenstates of the similarity-transformed Hamiltonian, such as CR-CCSD , exploits the recently developed biorthogonal formulation of the MMCC theory. Both approaches are capable of improving the results of standard CC and equation-of-motion CC (EOMCC) calculations for ground-state potential energy surfaces along bond breaking coordinates and excited states dominated by two-electron transitions with computer costs similar to those characterizing the popular (and failing) CCSD(T) approximation. The performance of the basic MMCC/PT and CR-CCSD approximations, in which non-iterative corrections due to triple excitations are added to the ground-s...
TL;DR: The application of these methods to Koopmans and satellite ionizations of N2 and CO has shown that IP-EOM-CCSD frequently accounts for orbital relaxation inadequately and displays errors exceeding a couple of eV, but these errors can be systematically reduced to tenths or even hundredths of an eV by IP-CCSDTT or CCSDTQ.
Abstract: Compact algebraic equations defining the equation-of-motion coupled-cluster (EOM-CC) methods for ionization potentials (IP-EOM-CC) have been derived and computer implemented by virtue of a symbolic algebra system largely automating these processes. Models with connected cluster excitation operators truncated after double, triple, or quadruple level and with linear ionization operators truncated after two-hole-one-particle (2h1p), three-hole-two-particle (3h2p), or four-hole-three-particle (4h3p) level (abbreviated as IP-EOM-CCSD, CCSDT, and CCSDTQ, respectively) have been realized into parallel algorithms taking advantage of spin, spatial, and permutation symmetries with optimal size dependence of the computational costs. They are based on spin-orbital formalisms and can describe both α and β ionizations from open-shell (doublet, triplet, etc.) reference states into ionized states with various spin magnetic quantum numbers. The application of these methods to Koopmans and satellite ionizations of N2 and C...
TL;DR: The problem of the double bond flipping interconversion of the two equivalent ground state structures of cyclobutadiene (CBD) is addressed at the multireference average-quadratic coupled cluster level of theory, which is capable of optimizing the structural parameters of the ground, transition, and excited states on an equal footing.
Abstract: The problem of the double bond flipping interconversion of the two equivalent ground state structures of cyclobutadiene (CBD) is addressed at the multireference average-quadratic coupled cluster level of theory, which is capable of optimizing the structural parameters of the ground, transition, and excited states on an equal footing. The barrier height involving both the electronic and zero-point vibrational energy contributions is 6.3 kcal mol(-1), which is higher than the best earlier theoretical estimate of 4.0 kcal mol(-1). This result is confirmed by including into the reference space the orbitals of the CC sigma bonds beyond the standard pi orbital space. It places the present value into the middle of the range of the measured data (1.6-10 kcal mol(-1)). An adiabatic singlet-triplet energy gap of 7.4 kcal mol(-1) between the transition state (1)B(tg) and the first triplet (3)A(2g) state is obtained. A low barrier height for the CBD automerization and a small DeltaE((3)A(2g),(1)B(1g)) gap bear some relevance on the highly pronounced reactivity of CBD, which is briefly discussed.
TL;DR: The results of benchmark calculations for the low-lying doublet and quartet states of the CH and SH radicals reveal that the active-space EA-EOMCCSDt and IP-Eom CCSDt methods are capable of producing results for the electronic excitations in open-shell systems that match the high accuracy of EA- and IP, EOMCC calculations with a full treatment of 3p-2h and 3h-2p excitations.
Abstract: The efficient, general-purpose implementations of the active-space electron-attached (EA) and ionized (IP) equation-of-motion coupled-cluster (EOMCC) methods including up to 3p-2h and 3h-2p excitations, called EA-EOMCCSDt and IP-EOMCCSDt, respectively, are discussed. The details of the algorithm that enables one to achieve a high degree of code vectorization for the active-space methods and the factorized forms of the EA- and IP-EOMCCSDt equations that maximize the benefits of using active orbitals in the process of selecting the dominant 3p-2h and 3h-2p excitations are presented. The results of benchmark calculations for the low-lying doublet and quartet states of the CH and SH radicals reveal that the active-space EA-EOMCCSDt and IP-EOMCCSDt methods are capable of producing results for the electronic excitations in open-shell systems that match the high accuracy of EA- and IP-EOMCC calculations with a full treatment of 3p-2h and 3h-2p excitations, even when the excited states of interest display a manifestly multideterminantal nature, with the costs that can be on the same order of those characterizing the basic EOMCC singles and doubles approach.
TL;DR: In this paper, Moszynski et al. proposed a time independent coupled cluster theory of the polarization propagator at the single and double excitations (CCSD) level and investigated the performance of the new approach by carrying out calculations of static and dynamic electric dipole polarizabilities for various molecules.
Abstract: Recently proposed time-independent coupled cluster theory of the polarization propagator [R. Moszynski, P. S. Żuchowski, and B. Jeziorski, Collect. Czech. Chem. Commun. 70, 1109, 2005] has been implemented at the single and double excitations (CCSD) level. The performance of the new approach was investigated by carrying out calculations of static and dynamic electric dipole polarizabilities for various molecules and by making a comparison with values obtained from other ab initio methods, including the full configuration interaction (FCI) technique. Our results show that the polarizabilities computed with the new approach are in a good agreement with the time-dependent CCSD and (when available) FCI values. The isotropic C 6 dispersion coefficients for several benchmark van der Waals complexes, e.g. dimers of helium, argon, water, and benzene, are also reported. They compare very well with existing experimental and best theoretical data. The new propagator, implemented already in the MOLPRO package, is com...
TL;DR: To assess the separation of dynamic and nondynamic correlations and orbital choice, the molecular structure and harmonic vibrational frequencies of ozone are calculated with the recently developed tailored coupled cluster singles and doubles method (TCCSD).
Abstract: To assess the separation of dynamic and nondynamic correlations and orbital choice, we calculate the molecular structure and harmonic vibrational frequencies of ozone with the recently developed tailored coupled cluster singles and doubles method (TCCSD). We employ the Hartree-Fock and complete active space (CAS) self-consistent field (SCF) orbitals to perform TCCSD calculations. When using the Hartree-Fock orbitals, it is difficult to reproduce the experimental vibrational frequency of the asymmetric stretching mode. On the other hand, the TCCSD based on the CASSCF orbitals in a correlation consistent polarized valence triple zeta basis yields excellent results with the two symmetric vibrations differing from the experimental harmonic values by 2 cm^(−1) and the asymmetric vibration differing by 9 cm^(−1).
TL;DR: In this paper, the authors compared different strategies to improve the accuracy of local coupled-cluster calculations by domain extensions at fixed geometries, which allows approaching the non-local solution to arbitrary precision.
Abstract: Publisher Summary This chapter discusses and compares different strategies to improve the accuracy by domain extensions at fixed geometries This allows approaching the non-local solution to arbitrary precision However, the computational effort increases rather quickly with the domain sizes, in particular for local coupled cluster with single and double excitations and perturbative treatment of triple excitations [LCCSD(T)], and therefore, it is important to find a best compromise between accuracy and cost The accuracy of local coupled-cluster calculations depends on (1) the domain sizes and (2) the definition of the strong-pair list included in the LCCSD These approximations can be controlled using connectivity or distance criteria In most cases, the domain and the weak-pair approximations in LCCSD(T0)|LMP2 calculations compensate each other to a large extent Therefore, rather accurate results are obtained with the standard approximation in which the domains are determined by the BP procedure and strong orbital pairs are determined by the condition that the domains of the two orbitals overlap
TL;DR: C coupled cluster models and density functional theory methods are used to calculate the vibrational contributions to the gas-phase specific rotation and it is found that all vibrational modes contribute significantly to the optical rotation and that temperature effects must be taken into account.
Abstract: In a previous study (Chemical Physics Letters 2005, 401, 385) we computed the optical rotatory dispersion of (S)-propylene oxide in gas phase and solution using the hierarchy of coupled cluster models CCS, CC2, CCSD, and CC3. Even for the highly correlated CC3 model combined with a flexible basis set, the theoretical gas-phase specific rotation at 355 nm was found to be negative in contrast to the experimental result. We argued that vibrational contributions could be crucial for obtaining a complete understanding of the experimental result. Here, we show that this indeed is the case by using coupled cluster models and density functional theory methods to calculate the vibrational contributions to the gas-phase specific rotation at 355, 589.3, and 633 nm. While density functional theory (B3LYP and SAOP functionals) overestimates the specific rotation at 355 nm by approximately 1 order of magnitude and yields an incorrect sign at 589.3 and 633 nm, the coupled cluster results are in excellent agreement with the experimentally measured optical rotations. We find that all vibrational modes contribute significantly to the optical rotation and that temperature effects must be taken into account.
TL;DR: A local coupled cluster approach based on a dynamical screening scheme, in which amplitudes are either calculated at the coupled cluster level (in this case CCSD) or at the level of perturbation theory, employing a threshold driven procedure based on MP2 energy increments is presented.
Abstract: In this paper we present a local coupled cluster approach based on a dynamical screening scheme, in which amplitudes are either calculated at the coupled cluster level (in this case CCSD) or at the level of perturbation theory, employing a threshold driven procedure based on MP2 energy increments. This way, controllable accuracy and smooth convergence towards the exact result are obtained in the framework of an a posteriori approximation scheme. For the representation of the occupied space a new set of local orbitals is presented with the size of a minimal basis set. This set is atom centered, is nonorthogonal, and has shapes which are fairly independent of the details of the molecular system of interest. Two slightly different versions of combined local coupled cluster and perturbation theory equations are considered. In the limit both converge to the untruncated CCSD result. Benchmark calculations for four systems (heptane, serine, water hexamer, and oxadiazole-2-oxide) are carried out, and decay of the amplitudes, truncation error, and convergence towards the exact CCSD result are analyzed.
TL;DR: The state-specific Brillouin-Wigner coupled cluster method with singles, doubles, and noniterative perturbative triples, called MR BWCCSD(T), for a general number of closed- and open-shell reference configurations, and the effect of connected triples was found to be minor.
Abstract: We developed and implemented the state-specific Brillouin-Wigner coupled cluster method with singles, doubles, and noniterative perturbative triples, called MR BWCCSD(T), for a general number of closed- and open-shell reference configurations. To assess the accuracy of the method, we performed calculations of the three lowest electronic states of the oxygen molecule and of the automerization barrier of cyclobutadiene. For the oxygen molecule, the results were in a good agreement in comparison with those of the iterative MR BWCCSDTalpha method. For cyclobutadiene, the effect of connected triples was found to be minor, which is in agreement with the previous study by and Balkova and Bartlett [J. Chem. Phys. 101, 8972 (1994)].
TL;DR: The use of the band-Lanczos algorithm is proposed to evaluate efficiently the resolvent type ADC expressions and the performance of the method is tested in computations of static and dynamic polarizabilities of several small molecules at the second-order (ADC(2)) level of the theory.
TL;DR: An automatic and general procedure for the calculation of geometrical derivatives of the energy and general property surfaces for molecular systems is developed and implemented and may be used for both ground and excited electronic states.
Abstract: An automatic and general procedure for the calculation of geometrical derivatives of the energy and general property surfaces for molecular systems is developed and implemented. General expressions for an n-mode representation are derived, where the n-mode representation includes only the couplings between n or less degrees of freedom. The general expressions are specialized to derivative force fields and property surfaces, and a scheme for calculation of the numerical derivatives is implemented. The implementation is interfaced to electronic structure programs and may be used for both ground and excited electronic states. The implementation is done in the context of a vibrational structure program and can be used in combination with vibrational self-consistent field (VSCF), vibrational configuration interaction (VCI), vibrational Moller-Plesset, and vibrational coupled cluster calculations of anharmonic wave functions and calculation of vibrational averaged properties at the VSCF and VCI levels. Sample calculations are presented for fundamental vibrational energies and vibrationally averaged dipole moments and frequency dependent polarizabilities and hyperpolarizabilities of water and formaldehyde.
TL;DR: A two-component Hartree-Fock and density-functional program that treats spin-orbit coupling self-consistently within the orbital optimization procedure and results show very satisfactory agreement with theoretical coupled cluster as well as experimental data where available, such that the theoretical results can serve as an estimate for the hitherto unknown properties of astatine, element 117, and their dimers.
Abstract: A two-component quasirelativistic Hamiltonian based on spin-dependent effective core potentials is used to calculate ionization energies and electron affinities of the heavy halogen atom bromine through the superheavy element 117 (eka-astatine) as well as spectroscopic constants of the homonuclear dimers of these atoms. We describe a two-component Hartree-Fock and density-functional program that treats spin-orbit coupling self-consistently within the orbital optimization procedure. A comparison with results from high-order Douglas-Kroll calculations—for the superheavy systems also with zeroth-order regular approximation and four-component Dirac results—demonstrates the validity of the pseudopotential approximation. The density-functional (but not the Hartree-Fock) results show very satisfactory agreement with theoretical coupled cluster as well as experimental data where available, such that the theoretical results can serve as an estimate for the hitherto unknown properties of astatine, element 117, and ...
TL;DR: The nCC hierarchy of coupled-cluster approximations has all the attractive features of CC including its size extensivity, orbital invariance, and orbital insensitivity, but in a conceptually appealing form suited to bond breaking, while being computationally less demanding.
Abstract: The nCC hierarchy of coupled-cluster approximations, where n guarantees exactness for n electrons and all products of n electrons are derived and applied to several illustrative problems. The condition of exactness for n=2 defines nCCSD=2CC, with nCCSDT=3CC and nCCSDTQ=4CC being exact for three and four electrons. To achieve this, the minimum number of diagrams is evaluated, which is less than in the corresponding CC model. For all practical purposes, nCC is also the proper definition of a size-extensive CI. 2CC is also an orbitally invariant coupled electron pair approximation. The numerical results of nCC are close to those for the full CC variant, and in some cases are closer to the full CI reference result. As 2CC is exact for separated electron pairs, it is the natural zeroth-order approximation for the correlation problem in molecules with other effects introduced as these units start to interact. The nCC hierarchy of approximations has all the attractive features of CC including its size extensivity, orbital invariance, and orbital insensitivity, but in a conceptually appealing form suited to bond breaking, while being computationally less demanding. Excited states from the equation of motion (EOM-2CC) are also reported, which show results frequently approaching those of EOM-CCSDT.