Showing papers on "Coupled cluster published in 2012"
469 citations
TL;DR: The current state of the art in wave function-based electronic structure methods is illustrated via discussions of the most important effects incorporated into a selection of high-accuracy methods chosen from the chemical literature as discussed by the authors.
Abstract: The current state of the art in wavefunction-based electronic structure methods is illustrated via discussions of the most important effects incorporated into a selection of high-accuracy methods chosen from the chemical literature. If one starts with a high-quality correlation treatment, such as provided by the CCSD(T) coupled cluster method, the leading effects include convergence of the results with respect to the 1-particle basis set, (outer)core/valence correlation, scalar relativistic effects and a number of smaller effects. For thermochemical properties such as the heat of formation, the zero-point vibrational energy also becomes important, introducing its own set of difficulties to the computational approach. Changes in the various components as the chemical systems incorporate heavier elements and as the size of the systems grows are also considered. Finally, challenges arising from the desire to extend existing methods to transition metal and heavier elements are considered.
396 citations
TL;DR: This brief overview of coupled‐cluster theory will describe formal aspects of the theory which should be understood by perspective users of CC methods and comment on some current developments that are improving the theory's accuracy or applicability.
Abstract: Coupled-cluster theory offers today's reference quantum chemical method for most of the problems encountered in electronic structure theory. It has been instrumental in establishing the now well-known paradigm of converging, many-body methods,
Many-body perturbation theory (MBPT) for second, MBPT2, and fourth-order MBPT4; and coupled-cluster (CC) theory for different categories of excitations, singles, doubles, triples, quadruples (SDTQ). Although built on the same basic concept as configuration interaction (CI), many-body methods fundamentally improve upon CI approximations by introducing the property of size extensivity, meaning that contrary to any truncated CI all terms properly scale with the number of electrons in the problem. This fundamental aspect of many-electron methods leads to the exceptional performance of CC theory and its finite-order MBPT approximations plus its equation-of-motion extensions for excited, ionized, and electron attached states. This brief overview will describe formal aspects of the theory which should be understood by perspective users of CC methods. We will also comment on some current developments that are improving the theory's accuracy or applicability. © 2011 John Wiley & Sons, Ltd.
301 citations
TL;DR: Spin component-scaled (SCS) electron correlation methods for electronic structure theory can be derived theoretically by applying special conditions to the underlying wave functions in perturbation theory as mentioned in this paper, based on the insight that low-order wave function expansions treat the correlation effects of electron pairs with opposite spin (OS) and same spin (SS) differently.
Abstract: Spin-component-scaled (SCS) electron correlation methods for electronic structure theory are reviewed The methods can be derived theoretically by applying special conditions to the underlying wave functions in perturbation theory They are based on the insight that low-order wave function expansions treat the correlation effects of electron pairs with opposite spin (OS) and same spin (SS) differently because of their different treatment at the underlying Hartree–Fock level Physically, this is related to the different average inter-electronic distances in the SS and OS electron pairs The overview starts with the original SCS-MP2 method and discusses its strengths and weaknesses and various ways to parameterize the scaling factors Extensions to coupled-cluster and excited state methods as well the connection to virtual-orbital dependent density functional approaches are highlighted The performance of various SCS methods in large thermochemical benchmarks and for excitation energies is discussed in comparison with other common electronic structure methods
197 citations
TL;DR: It is found that the compact representation of the amplitudes in the OSV approach affords various advantages, including smaller computational time requirements (for comparable accuracy), as well as a more systematic control of the error through a single energy threshold.
Abstract: We extend the orbital-specific-virtual tensor factorization, introduced for local Moller-Plesset perturbation theory in Ref. [J. Yang, Y. Kurashige, F. R. Manby and G. K. L. Chan, J. Chem. Phys. 134, 044123 (2011)10.1063/1.3528935], to local coupled cluster singles and doubles theory (OSV-LCCSD). The method is implemented by modifying an efficient projected-atomic-orbital local coupled cluster program (PAO-LCCSD) described recently, [H.-J. Werner and M. Schutz, J. Chem. Phys. 135, 144116 (2011)10.1063/1.3641642]. By comparison of both methods we find that the compact representation of the amplitudes in the OSV approach affords various advantages, including smaller computational time requirements (for comparable accuracy), as well as a more systematic control of the error through a single energy threshold. Overall, the OSV-LCCSD approach together with an MP2 correction yields small domain errors in practical calculations. The applicability of the OSV-LCCSD is demonstrated for molecules with up to 73 atoms and realistic basis sets (up to 2334 basis functions).
175 citations
TL;DR: In this article, a review of coupled cluster (CC) theory for electronic excited states is presented, and the basics of a CC response theory framework that allows the transfer of the attractive accuracy and convergence properties associated with CC methods over to the calculation of electronic excitation energies and properties.
Abstract: We review coupled cluster (CC) theory for electronically excited states. We outline the basics of a CC response theory framework that allows the transfer of the attractive accuracy and convergence properties associated with CC methods over to the calculation of electronic excitation energies and properties. Key factors affecting the accuracy of CC excitation energy calculations are discussed as are some of the key CC models in this field. To aid both the practitioner as well as the developer of CC excited state methods, we also briefly discuss the key computational steps in a working CC response implementation. Approaches aimed at extending the application range of CC excited state methods either in terms of molecular size and phenomena or in terms of environment (solution and proteins) are also discussed. © 2011 John Wiley & Sons, Ltd.
166 citations
TL;DR: This work shows how THC can be used to both reduce the scaling with respect to molecular size of coupled cluster singles and doubles (CCSD) by two orders and remove the memory bottleneck associated with storage of the doubles amplitudes.
Abstract: The manipulation of the rank-four tensor of double excitation amplitudes represents a challenge to the efficient implementation of many electronic structure methods. We present a proof of concept for the approximation of doubles amplitudes in the tensor hypercontraction (THC) representation. In particular, we show how THC can be used to both reduce the scaling with respect to molecular size of coupled cluster singles and doubles (CCSD) (and related methods) by two orders [from O(N6) to O(N4)] and remove the memory bottleneck associated with storage of the doubles amplitudes. The accuracy of correlated methods as integral and amplitude approximations are introduced is examined. For a set of 20 small molecules, single and double-excitation configuration interaction (CISD), quadratic CISD (QCISD), and CCSD correlation energies could be reproduced with millihartree accuracy after the introduction of these approximations. Our approach exploits otherwise hidden factorizable tensor structure in both the electron...
160 citations
TL;DR: In this paper, a composite approach based on coupled cluster theory was used to predict the atomization energies and equilibrium structures of 13 small, first-row compounds, and the composite approach was found to yield a mean absolute deviation of 0.19
Abstract: A flexible, high-level, composite approach based on coupled cluster theory has been used to predict the atomization energies and equilibrium structures of 13 small, first-row compounds. Each of the major components in this approach can be systematically improved, thereby providing a practical measure of the inherent uncertainty (or degree of convergence) in the final results. Comparison with Active Thermochemical Table data, which relies on a network of experimental and theoretical data, showed excellent agreement for the atomization energies. With the addition of the latest molecular systems to the Computational Results Database, the composite approach was found to yield a mean absolute deviation of 0.19 kcal mol−1 and a root-mean-square deviation of 0.31 kcal mol−1 across 142 comparisons. If the analysis is limited to experimental data with estimated uncertainties of 0.2 kcal mol−1 or less, the error metrics are cut in half. Similar good agreement is found with experimental structures, but the relative ...
155 citations
TL;DR: Based on an asymmetric Lanczos-chain subspace algorithm, damped coupled cluster linear response functions have been implemented for the hierarchy of coupled cluster (CC) models including CC with si....
Abstract: Based on an asymmetric Lanczos-chain subspace algorithm, damped coupled cluster linear response functions have been implemented for the hierarchy of coupled cluster (CC) models including CC with si ...
152 citations
TL;DR: This perspective addresses selected recent developments in the theoretical calculation of vibrational spectra, energies, wave functions and properties and emphasis is put on vibrational self-consistent field (VSCF) based methods and in particular vibrational coupled cluster (VCC) theory.
Abstract: This perspective addresses selected recent developments in the theoretical calculation of vibrational spectra, energies, wave functions and properties. The theoretical foundation and recently developed computational protocols for constructing hierarchies of vibrational Hamiltonian operators are reviewed. A many-mode second quantization (SQ) formulation is discussed prior to the discussion of anharmonic wave functions. Emphasis is put on vibrational self-consistent field (VSCF) based methods and in particular vibrational coupled cluster (VCC) theory. Other issues are also reviewed briefly, such as inclusion of thermal effects, response theoretical calculation of spectra, and the difficulty in treating dense spectra.
121 citations
TL;DR: The orbital-adaptive time-dependent coupled-cluster (ATCC) method as mentioned in this paper is a hierarchy of approximations to the now standard multi-configurational Hartree method for fermions.
Abstract: The curse of dimensionality (COD) limits the current state-of-the-art ab initio propagation methods for non-relativistic quantum mechanics to relatively few particles. For stationary structure calculations, the coupled-cluster (CC) method overcomes the COD in the sense that the method scales polynomially with the number of particles while still being size-consistent and extensive. We generalize the CC method to the time domain while allowing the single-particle functions to vary in an adaptive fashion as well, thereby creating a highly flexible, polynomially scaling approximation to the time-dependent Schrodinger equation. The method inherits size-consistency and extensivity from the CC method. The method is dubbed orbital-adaptive time-dependent coupled-cluster, and is a hierarchy of approximations to the now standard multi-configurational time-dependent Hartree method for fermions. A numerical experiment is also given.
TL;DR: The performance and some of the potentialities of the approach are investigated in calculations of the visible/ultraviolet absorption spectrum and the dispersion of the real polarizability in near-resonant regions of pyrimidine, the near-edge absorption fine structure (NEXAFS) of ammonia, and the direct determination of the C6 dipole-dipole dispersion coefficient of the benzene dimer.
Abstract: We present an implementation of the damped coupled-cluster linear response function based on an asymmetric Lanczos chain algorithm for the hierarchy of coupled-cluster approximations CCS (coupled-c ...
TL;DR: In this article, the Feller-Peterson-Dixon approach to reliable prediction of thermochemical properties to chemical accuracy is described, which is based on extrapolating coupled cluster CCSD(T) calculations of the valence electronic energy to the complete basis set limit.
Abstract: The Feller–Peterson–Dixon approach to the reliable prediction of thermochemical properties to chemical accuracy is described. The method calculates the total atomization energy of a molecule and then uses experimental atomic heats of formation to calculate the heat of formation. The method is based on extrapolating coupled cluster CCSD(T) calculations of the valence electronic energy to the complete basis set limit followed by additive corrections to the electronic energy including: core–valence interactions, scalar relativistic, spin–orbit, and higher order corrections beyond CCSD(T). Corrections for the nuclear motion in terms of the zero-point energy need to be included and for high-accuracy, Born–Oppenheimer corrections may be added. Issues with these terms and the experimental atomic data are described. A summary of the reliability of the approach is presented.
TL;DR: A consistent derivation of a density functional theory (DFT) based embedding method which encompasses wave-function theory-in-DFT and the DFT-based subsystem formulation of response theory by Neugebauer as special cases is presented.
Abstract: In this article, we present a consistent derivation of a density functional theory (DFT) based embedding method which encompasses wave-function theory-in-DFT (WFT-in-DFT) and the DFT-based subsystem formulation of response theory (DFT-in-DFT) by Neugebauer [J. Neugebauer, J. Chem. Phys. 131, 084104 (2009)] as special cases. This formulation, which is based on the time-averaged quasi-energy formalism, makes use of the variation Lagrangian techniques to allow the use of non-variational (in particular: coupled cluster) wave-function-based methods. We show how, in the time-independent limit, we naturally obtain expressions for the ground-state DFT-in-DFT and WFT-in-DFT embedding via a local potential. We furthermore provide working equations for the special case in which coupled cluster theory is used to obtain the density and excitation energies of the active subsystem. A sample application is given to demonstrate the method.
TL;DR: Four diagnostic criteria have been examined and new criteria are proposed as a gauge for 4d transition metal-containing molecules to predict the possible need to employ multireference (MR) wave function-based methods to describe energetic and spectroscopic properties.
Abstract: Four diagnostic criteria have been examined to identify the suitability of single-reference wave function-based quantum chemistry methods for a set of 118 4d transition metal species. These diagnostics include the weight of the leading configuration of the CASSCF wave function, C02; the Frobenius norm of the coupled cluster amplitude vector related to single excitations, T1; the matrix 2-norm of the coupled cluster T1 amplitude vector arising from coupled cluster calculations, D1; and the percent total atomization energy, %TAE, corresponding to a relationship between energies determined with CCSD and CCSD(T) calculations. New criteria, namely, T1 ≥ 0.045, D1 ≥ 0.120, and %TAE ≥ 10%, are herein proposed as a gauge for 4d transition metal-containing molecules to predict the possible need to employ multireference (MR) wave function-based methods to describe energetic and spectroscopic properties.
TL;DR: In this paper, a review of recent developments in molecular relativistic electronic-structure theory is reviewed, with a particular emphasis on post-Hartree-Fock electron correlation methodology.
TL;DR: The coupled-cluster method overcomes the COD in the sense that the method scales polynomially with the number of particles while still being size-consistent and extensive, and is a hierarchy of approximations to the now standard multi-configurational time-dependent Hartree method for fermions.
Abstract: The curse of dimensionality (COD) limits the current state-of-the-art {\it ab initio} propagation methods for non-relativistic quantum mechanics to relatively few particles. For stationary structure calculations, the coupled-cluster (CC) method overcomes the COD in the sense that the method scales polynomially with the number of particles while still being size-consistent and extensive. We generalize the CC method to the time domain while allowing the single-particle functions to vary in an adaptive fashion as well, thereby creating a highly flexible, polynomially scaling approximation to the time-dependent Schrodinger equation. The method inherits size-consistency and extensivity from the CC method. The method is dubbed orbital-adaptive time-dependent coupled-cluster (OATDCC), and is a hierarchy of approximations to the now standard multi-configurational time-dependent Hartree method for fermions. A numerical experiment is also given.
TL;DR: The results clearly show that it is only the EOMEE-CCSD(T) that is capable of providing accuracy of about 0.1 eV, whereas CC2 is surprisingly accurate for ππ* transitions but fails (often badly) for nπ* and Rydberg transitions and DFT and CASPT2 seem to give reliable results for the lowest transition, but the error increases fast with the excitation level.
Abstract: Equation of motion excitation energy coupled-cluster (EOMEE-CC) methods including perturbative triple excitations have been used to set benchmark results for the excitation energy and oscillator strength of the building units of DNA, i.e., cytosine, guanine, adenine and thymine. In all cases the lowest twelve transitions have been considered including valence and Rydberg ones. Triple-ζ basis sets with diffuse functions have been used and the results are compared to CC2, CASPT2, TDDFT, and DFT/MRCI results from the literature. The results clearly show that it is only the EOMEE-CCSD(T) that is capable of providing accuracy of about 0.1 eV. EOMEE-CCSD systematically overshoots the energy of all types of transitions by 0.1–0.3 eV, whereas CC2 is surprisingly accurate for ππ* transitions but fails (often badly) for nπ* and Rydberg transitions. DFT and CASPT2 seem to give reliable results for the lowest transition, but the error increases fast with the excitation level. The differences in the excitation energie...
TL;DR: This work provides a comprehensive investigation of alternative schemes where the MP2 extrapolation is replaced by the coupled-electron pair approximation, version 1 or the local pair natural orbital version of this method (LPNO-CEPA/1).
Abstract: It is well-known that the basis set limit is difficult to reach in correlated post Hartree-Fock ab initio calculations. One possible route forward is to employ basis set extrapolation schemes. In order to avoid prohibitively expensive calculations, the highest level calculation (typically based on the "gold standard" coupled cluster theory with single, double, and perturbative triple excitations, CCSD(T)) is only performed with the smallest basis set, and the remaining basis set incompleteness is estimated at a lower level of theory, typically second-order Moller-Plesset perturbation theory (MP2). In this work, we provide a comprehensive investigation of alternative schemes where the MP2 extrapolation is replaced by the coupled-electron pair approximation, version 1 (CEPA/1) or the local pair natural orbital version of this method (LPNO-CEPA/1). It is shown that the MP2 method achieves apparent accuracy only due to error cancellation. Systematically more accurate results at small additional computational cost are obtained if the MP2 step is replaced by LPNO-CEPA/1. The errors of LPNO-CEPA/1 relative to canonical CEPA/1 are negligible. Owing to the highly systematic nature of the deviations between canonical and LPNO methods, basis set extrapolation reduces the LPNO errors in the total energies by 1 order of magnitude (~0.2 kcal/mol) and errors in energy differences to essentially zero. Using the CCSD(T)/LPNO-CEPA/1-based extrapolation scheme, new reference values are proposed for the recently published S66 set of interaction energies. The deviations between the new values and the original interactions energies are mostly very small but reach values up to 0.3 kcal/mol.
TL;DR: It is demonstrated that for all choices of virtual orbitals much smaller domains are needed in the explicitly correlation methods than without the explicitly correlated terms, since the latter correct a large part of the domain error, as found previously.
Abstract: Explicitly correlated local coupled-cluster (LCCSD-F12) methods with pair natural orbitals (PNOs), orbital specific virtual orbitals (OSVs), and projected atomic orbitals (PAOs) are compared. In all cases pair-specific virtual subspaces (domains) are used, and the convergence of the correlation energy as a function of the domain sizes is studied. Furthermore, the performance of the methods for reaction energies of 52 reactions involving 58 small and medium sized molecules is investigated. It is demonstrated that for all choices of virtual orbitals much smaller domains are needed in the explicitly correlated methods than without the explicitly correlated terms, since the latter correct a large part of the domain error, as found previously. For PNO-LCCSD-F12 with VTZ-F12 basis sets on the average only 20 PNOs per pair are needed to obtain reaction energies with a root mean square deviation of less than 1 kJ mol−1 from complete basis set estimates. With OSVs or PAOs at least 4 times larger domains are needed for the same accuracy. A new hybrid method that combines the advantages of the OSV and PNO methods is proposed and tested. While in the current work the different local methods are only simulated using a conventional CCSD program, the implications for low-order scaling local implementations of the various methods are discussed.
TL;DR: Calculations suggest that CASSCF and CASPT2 may have difficulties with providing a reliable description of the Co-CMe bond breaking in MeCbl, since using adequate active spaces is prohibitively expensive.
Abstract: The Co–CMe bond dissociation in methylcobalamin (MeCbl), modeled by the Im–[CoIIIcorrin]–Me+ system consisting of 58 atoms, is examined using the coupled-cluster (CC), density-functional theory (DFT), complete-active-space self-consistent-field (CASSCF), and CASSCF-based second-order perturbation theory (CASPT2) approaches. The multilevel variant of the local cluster-in-molecule framework, employing the completely renormalized (CR) CC method with singles, doubles, and noniterative triples, termed CR-CC(2,3), to describe higher-order electron correlation effects in the region where the Co–CMe bond breaking takes place, and the canonical CC approach with singles and doubles (CCSD) to capture the remaining correlation effects, abbreviated as CR-CC(2,3)/CCSD, is used to obtain the benchmark potential energy curve characterizing the Co–CMe dissociation in the MeCbl cofactor. The Co–CMe bond dissociation energy (BDE) resulting from the CR-CC(2,3)/CCSD calculations for the Im–[CoIIIcorrin]–Me+ system using the 6...
TL;DR: Comparisons of results indicate that the ic-MRCCSD(T) method provides a highly accurate and efficient treatment of both static and dynamic electron correlation in connection with minimal active spaces.
Abstract: Internally contracted multireference coupled cluster (ic-MRCC) methods with perturbative treatment of triple excitations are formulated based on Dyall's definition of a zeroth-order Hamiltonian. The iterative models ic-MRCCSDT-1, ic-MRCC3, and their variants ic-MRCCSD(T), ic-MRCC(3) which determine the energy correction from triples by a non-iterative step are consistent in the single-reference limit with CCSDT-1a, CC3, CCSD(T), and CC(3), respectively. Numerical tests on the potential energy surfaces of BeH2, H2O, and N2 as well as on the structure and harmonic vibrational frequencies of the ozone molecule show that these methods account very well for higher order correlation effects. The ic-MRCCSD(T) method is further applied to the geometry optimization and harmonic frequencies of the symmetric vibrational modes of the binuclear transition metal oxide Ni2O2, to the singlet-triplet splittings of o-, m-, and p-benzyne and to a ring-opening reaction of an azirine compound with the molecular formula C6H7NO. The size of the active spaces used in this study ranges from CAS(2,2) to CAS(8,8). Comparisons of results based on differently sized active spaces indicate that the ic-MRCCSD(T) method provides a highly accurate and efficient treatment of both static and dynamic electron correlation in connection with minimal active spaces.
TL;DR: It is shown that the correlation energy may alternatively be expressed using a virtual space partitioning, and that the Lagrangian correlationEnergy may be partitioned using elements from both the occupied and virtual partitioning schemes.
Abstract: Previously, we have introduced the linear scaling coupled cluster (CC) divide-expand-consolidate (DEC) method, using an occupied space partitioning of the standard correlation energy. In this article, we show that the correlation energy may alternatively be expressed using a virtual space partitioning, and that the Lagrangian correlation energy may be partitioned using elements from both the occupied and virtual partitioning schemes. The partitionings of the correlation energy leads to atomic site and pair interaction energies which are term-wise invariant with respect to an orthogonal transformation among the occupied or the virtual orbitals. Evaluating the atomic site and pair interaction energies using local orbitals leads to a linear scaling algorithm and a distinction between Coulomb hole and dispersion energy contributions to the correlation energy. Further, a detailed error analysis is performed illustrating the error control imposed on all components of the energy by the chosen energy threshold. This error control is ultimately used to show how to reduce the computational cost for evaluating dispersion energy contributions in DEC.
TL;DR: A wave function-based method for the decomposition of intermolecular interaction energies into chemically-intuitive components, isolating both mean-field- and explicit correlation-level contributions, and demonstrating the stability of energy components with basis set extension.
Abstract: We propose a wave function-based method for the decomposition of intermolecular interaction energies into chemically-intuitive components, isolating both mean-field- and explicit correlation-level contributions. We begin by solving the locally-projected self-consistent field for molecular interactions equations for a molecular complex, obtaining an intramolecularly polarized reference of self-consistently optimized, absolutely-localized molecular orbitals (ALMOs), determined with the constraint that each fragment MO be composed only of atomic basis functions belonging to its own fragment. As explicit inter-electronic correlation is integral to an accurate description of weak forces underlying intermolecular interaction potentials, namely, coordinated fluctuations in weakly interacting electronic densities, we add dynamical correlation to the ALMO polarized reference at the coupled-cluster singles and doubles level, accounting for explicit dispersion and charge-transfer effects, which map naturally onto th...
TL;DR: The motivation is to develop an accurate and economical methodology that, when coupled with a robust local correlation framework based on localized pair natural orbitals, is suitable for large-scale thermochemical applications for sizeable molecular systems.
Abstract: We have recently introduced a parameterized coupled-cluster singles and doubles model (pCCSD(α, β)) that consists of a bivariate parameterization of the CCSD equations and is inspired by the coupled electron pair approximations. In our previous work, it was demonstrated that the pCCSD(−1, 1) method is an improvement over CCSD for the calculation of geometries, harmonic frequencies, and potential energy surfaces for single bond-breaking. In this paper, we find suitable pCCSD parameters for applications in reaction thermochemistry and thermochemical kinetics. The motivation is to develop an accurate and economical methodology that, when coupled with a robust local correlation framework based on localized pair natural orbitals, is suitable for large-scale thermochemical applications for sizeable molecular systems. It is demonstrated that the original pCCSD(−1, 1) method and several other pCCSD methods are a significant improvement upon the standard CCSD approach and that these methods often approach the accu...
TL;DR: It is demonstrated that the two-photon absorption involving low-lying excited states with increased double excitation character can be adequately studied using the ADC(2)-x scheme, explicitly accounting for interaction of doubly excited configurations.
Abstract: An earlier proposed approach to molecular response functions based on the intermediate state representation (ISR) of polarization propagator and algebraic-diagrammatic construction (ADC) approximations is for the first time employed for calculations of nonlinear response properties. The two-photon absorption (TPA) spectra are considered. The hierarchy of the first- and second-order ADC/ISR computational schemes, ADC(1), ADC(2), ADC(2)-x, and ADC(3/2), is tested in applications to H2O, HF, and C2H4 (ethylene). The calculated TPA spectra are compared with the results of coupled cluster (CC) models and time-dependent density-functional theory (TDDFT) calculations, using the results of the CC3 model as benchmarks. As a more realistic example, the TPA spectrum of C8H10 (octatetraene) is calculated using the ADC(2)-x and ADC(2) methods. The results are compared with the results of TDDFT method and earlier calculations, as well as to the available experimental data. A prominent feature of octatetraene and other polyene molecules is the existence of low-lying excited states with increased double excitation character. We demonstrate that the two-photon absorption involving such states can be adequately studied using the ADC(2)-x scheme, explicitly accounting for interaction of doubly excited configurations. Observed peaks in the experimental TPA spectrum of octatetraene are assigned based on our calculations.
TL;DR: It is demonstrated that the self-consistent eigenvalues obtained from these consistent potentials used in ab initio dft approximate all principal ionization potentials as demanded by ionization Potential theorem.
Abstract: Density functional theory (DFT) results are mistrusted at times due to the presence of an unknown exchange correlation functional, with no practical way to guarantee convergence to the right answer. The use of a known exchange correlation functional based on wave-function theory helps to alleviate such mistrust. The exchange correlation functionals can be written exactly in terms of the density-density response function using the adiabatic-connection and fluctuation-dissipation framework. The random phase approximation (RPA) is the simplest approximation for the density-density response function. Since the correlation functional obtained from RPA is equivalent to the direct ring coupled cluster doubles (ring-CCD) correlation functional, meaning only Coulomb interactions are included, one can bracket RPA between many body perturbation theory (MBPT)-2 and CCD with the latter having all ring, ladder, and exchange contributions. Using an optimized effective potential strategy, we obtain correlation potentials corresponding to MBPT-2, RPA (ring-CCD), linear-CCD, and CCD. Using the suitable choice of the unperturbed Hamiltonian, Kohn-Sham self-consistent calculations are performed. The spatial behavior of the resulting potentials, total energies, and the HOMO eigenvalues are compared with the exact values for spherical atoms. Further, we demonstrate that the self-consistent eigenvalues obtained from these consistent potentials used in ab initio dft approximate all principal ionization potentials as demanded by ionization potential theorem.
TL;DR: A generalization of the equation-of-motion coupled cluster theory is proposed, which is built upon a multireference parent state and uses the amplitudes of the generalized normal-ordered transformed Hamiltonian Ĥ as the residual equations for determining the internally contracted cluster amplitudes without any projection onto the excited configurations.
Abstract: A generalization of the equation-of-motion coupled cluster theory is proposed, which is built upon a multireference parent state. This method is suitable for a number of electronic states of a system that can be described by similar active spaces, i.e., different linear combinations of the same set of active space determinants. One of the suitable states is chosen as the parent state and the dominant dynamical correlation is optimized for this state using an internally contracted multireference coupled cluster ansatz. The remaining correlation and orbital relaxation effects are obtained via an uncontracted diagonalization of the transformed Hamiltonian, H¯=e−THeT, in a compact multireference configuration interaction space, which involves configurations with at most single virtual orbital substitution. The latter effects are thus state-specific and this allows us to obtain multiple electronic states in the spirit of the equation-of-motion coupled cluster approach. A crucial aspect of this formulation ...
05 Jun 2012
TL;DR: In this article, the authors proposed a flexible MMCC (Flex-MMCC) formalism to correct the results of the CC calculations with singles, doubles, and active-space triples for the remaining effects due to connected triple excitations that are missing in the CCSDt considerations.
Abstract: After reviewing recent progress in the area of the development of coupled-cluster (CC) methods for quasi-degenerate electronic states that are characterized by stronger non-dynamical correlation effects, including new generations of single- and multi-reference approaches that can handle bond breaking and excited states dominated by many-electron transitions, and after discussing the key elements of the left-eigenstate completely renormalized (CR) CC and equation-of-motion (EOM) CC methods, and the underlying biorthogonal method of moments of CC (MMCC) equations [P. Piecuch, M. Wloch, J. Chem. Phys. 123 (2005) 224105; P. Piecuch, M. Wloch, J.R. Gour, A. Kinal, Chem. Phys. Lett. 418 (2006) 467; M. Wloch, M.D. Lodriguito, P. Piecuch, J.R. Gour, Mol. Phys. 104 (2006) 2149], it is argued that it is beneficial to merge the CR-CC/EOMCC and active-space CC/EOMCC [P. Piecuch, Mol. Phys. 108 (2010) 2987, and references therein] theories into a single formalism. In order to accomplish this goal, the biorthogonal MMCC theory, which provides compact many-body expansions for the differences between the full configuration interaction and CC or, in the case of excited states, EOMCC energies, obtained using conventional truncation schemes in the cluster operator T and excitation operator Rμ, is generalized, so that one can correct the CC/EOMCC energies obtained with arbitrary truncations in T and Rμ for the selected many-electron correlation effects of interest. The resulting moment expansions, defining the new, Flexible MMCC (Flex-MMCC) formalism, and the ensuing CC(P; Q) hierarchy, proposed in the present work, enable one to correct energies obtained in the active-space CC and EOMCC calculations, in which one selects higher many-body components of T and Rμ via active orbitals and which recover much of the relevant non-dynamical and some dynamical electron correlation effects in applications involving potential energy surfaces (PESs) along bond breaking coordinates, for the effects of higher-order, primarily dynamical, correlations missing in the active-space CC/EOMCC considerations. The Flex-MMCC corrections to the active-space CC/EOMCC energies are mathematically similar to the non-iterative energy corrections defining the existing left-eigenstate CR-CC and CR-EOMCC methods, such as CR-CC(2, 3) and CR-EOMCC(2, 3). The potential advantages of the Flex-MMCC and CC(P; Q) formalisms are illustrated by describing the initial implementation and numerical tests of the novel CC hybrid scheme, abbreviated as CC(t; 3), in which one corrects the results of the CC calculations with singles, doubles, and active-space triples, termed CCSDt, for the remaining effects due to connected triple excitations that are missing in the CCSDt considerations, but are present in the MMCC-based CR-CC(2, 3) approach. By examining bond breaking in the HF, F2, and F 2 + molecules, it is demonstrated that the CC(t; 3) method improves the CCSDt and CR-CC(2, 3) results, providing PESs that agree with those obtained with the full CC theory with singles, doubles, and triples (CCSDT) to within small fractions of a millihartree, at the fraction of the computer costs of the CCSDT calculations. Different strategies for defining active-space triples within the CC(t; 3) scheme and the underlying CCSDt method are discussed. When limited to the ground-state problem, the CC(t; 3) approach can be regarded as an improved and rigorously derived extension of the recently proposed CCSD(T)-h method [J. Shen, E. Xu, Z. Kou, S. Li, J. Chem. Phys. 132 (2010) 114115], in which triples corrections of the CCSD(T) type are replaced by their more robust CR-CC(2, 3)-style analogs.
TL;DR: It is shown that one can greatly improve the description of biradical transition states, both in terms of the resulting energy barriers and total energies, by combining the CC approach with singles, doubles, and active-space triples, termed CCSDt, with the CC(P;Q)-style correction due to missing triple excitations defining theCC(t;3) approximation.
Abstract: We have recently suggested the CC(P;Q) methodology that can correct energies obtained in the active-space coupled-cluster (CC) or equation-of-motion (EOM) CC calculations, which recover much of the nondynamical and some dynamical electron correlation effects, for the higher-order, mostly dynamical, correlations missing in the active-space CC/EOMCC considerations. It is shown that one can greatly improve the description of biradical transition states, both in terms of the resulting energy barriers and total energies, by combining the CC approach with singles, doubles, and active-space triples, termed CCSDt, with the CC(P;Q)-style correction due to missing triple excitations defining the CC(t;3) approximation.