Showing papers on "Coupled cluster published in 2009"

A diagnostic for determining the quality of single‐reference electron correlation methods

Abstract: It was recently proposed that the Euclidian norm of the t(sub 1) vector of the coupled cluster wave function (normalized by the number of electrons included in the correlation procedure) could be used to determine whether a single-reference-based electron correlation procedure is appopriate. This diagnostic, T(sub 1) is defined for use with self-consistent-field molecular orbitals and is invariant to the same orbital rotations as the coupled cluster energy. T(sub 1) is investigated for several different chemical systems which exhibit a range of multireference behavior, and is shown to be an excellent measure of the importance of non-dynamical electron correlation and is far superior to C(sub 0) from a singles and doubles configuration interaction wave function. It is further suggested that when the aim is to recover a large fraction of the dynamical electron correlation energy, a large T(sub 1) (i.e., greater than 0.02) probably indicates the need for a multireference electron correlation procedure.

Efficient and accurate approximations to the local coupled cluster singles doubles method using a truncated pair natural orbital basis

Abstract: A production level implementation of the closed-shell local quadratic configuration interaction and coupled cluster methods with single and double excitations (QCISD and CCSD) based on the concept of pair natural orbitals [local pair natural orbital LPNO-QCISD and LPNO-CCSD) is reported, evaluated, and discussed. This work is an extension of the earlier developed LPNO coupled-electron pair approximation (LNPO-CEPA) method [F. Neese et al., Chem. Phys. 130, 114108 (2009)] and makes extended use of the resolution of the identity (RI) or density fitting (DF) approximation. Two variants of each method are compared. The less accurate approximations (LPNO2-QCISD/LPNO2-CCSD) still recover 98.7%-99.3% of the correlation energy in the given basis and have modest disk space requirements. The more accurate variants (LPNO1-QCISD/LPNO1-CCSD) typically recover 99.75%-99.95% of the correlation energy in the given basis but require the Coulomb and exchange operators with up to two-external indices to be stored on disk. Both variants have comparable computational efficiency. The convergence of the results with respect to the natural orbital truncation parameter (T(CutPNO)) has been studied. Extended numerical tests have been performed on absolute and relative correlation energies as function of basis set size and T(CutPNO) as well as on reaction energies, isomerization energies, and weak intermolecular interactions. The results indicate that the errors of the LPNO methods compared to the canonical QCISD and CCSD methods are below 1 kcal/mol with our default thresholds. Finally, some calculations on larger molecules are reported (ranging from 40-86 atoms) and it is shown that for medium sized molecules the total wall clock time required to complete the LPNO-CCSD calculations is only two to four times that of the preceding self-consistent field (SCF). Thus these methods are highly suitable for large-scale computational chemistry applications. Since there are only three thresholds involved that have been given conservative default values, the methods can be confidentially used in a "black-box" fashion in the same way as their canonical counterparts.

An Assessment of Theoretical Methods for Nonbonded Interactions: Comparison to Complete Basis Set Limit Coupled-Cluster Potential Energy Curves for the Benzene Dimer, the Methane Dimer, Benzene−Methane, and Benzene−H2S†

Abstract: Large, correlation-consistent basis sets have been used to very closely approximate the coupled-cluster singles, doubles, and perturbative triples [CCSD(T)] complete basis set potential energy curves of several prototype nonbonded complexes, the sandwich, T-shaped, and parallel-displaced benzene dimers, the methane−benzene complex, the H2S−benzene complex, and the methane dimer. These benchmark potential energy curves are used to assess the performance of several methods for nonbonded interactions, including various spin-component-scaled second-order perturbation theory (SCS-MP2) methods, the spin-componet-scaled coupled-cluster singles and doubles method (SCS-CCSD), density functional theory empirically corrected for dispersion (DFT-D), and the meta-generalized-gradient approximation functionals M05-2X and M06-2X. These approaches generally provide good results for the test set, with the SCS methods being somewhat more robust. M05-2X underbinds for the test cases considered, while the performances of DFT...

The electronic couplings in electron transfer and excitation energy transfer.

Abstract: The transport of charge via electrons and the transport of excitation energy via excitons are two processes of fundamental importance in diverse areas of research. Characterization of electron transfer (ET) and excitation energy transfer (EET) rates are essential for a full understanding of, for instance, biological systems (such as respiration and photosynthesis) and opto-electronic devices (which interconvert electric and light energy). In this Account, we examine one of the parameters, the electronic coupling factor, for which reliable values are critical in determining transfer rates. Although ET and EET are different processes, many strategies for calculating the couplings share common themes. We emphasize the similarities in basic assumptions between the computational methods for the ET and EET couplings, examine the differences, and summarize the properties, advantages, and limits of the different computational methods. The electronic coupling factor is an off-diagonal Hamiltonian matrix element between the initial and final diabatic states in the transport processes. ET coupling is essentially the interaction of the two molecular orbitals (MOs) where the electron occupancy is changed. Singlet excitation energy transfer (SEET), however, contains a Frster dipole-dipole coupling as its most important constituent. Triplet excitation energy transfer (TEET) involves an exchange of two electrons of different spin and energy; thus, it is like an overlap interaction of two pairs of MOs. Strategies for calculating ET and EET couplings can be classified as (1) energy-gap-based approaches, (2) direct calculation of the off-diagonal matrix elements, or (3) use of an additional operator to describe the extent of charge or excitation localization and to calculate the coupling value. Some of the difficulties in calculating the couplings were recently resolved. Methods were developed to remove the nondynamical correlation problem from the highly precise coupled cluster models for ET coupling. It is now possible to obtain reliable ET couplings from entry-level excited-state Hamiltonians. A scheme to calculate the EET coupling in a general class of systems, regardless of the contributing terms, was also developed. In the past, empirically derived parameters were heavily invoked in model description of charge and excitation energy drifts in a solid-state device. Recent advances, including the methods described in this Account, permit the first-principle quantum mechanical characterization of one class of the parameters in such descriptions, enhancing the predictive power and allowing a deeper understanding of the systems involved.

Calculation of properties with the coupled-cluster method

Abstract: The cluster-expansion approach to the correlation problem, pioneered by Coester, Kummel, Cizek and Paldus, is extended to calculation of static and dynamic properties of many-fermion systems. Linear, inhomogeneous equations are obtained for properties of any order. A time-dependent formulation gives frequency-dependent properties, yielding excitation energies, transition probabilities, and (possibly) lifetimes reminiscent of Green's function methods.

On the accurate calculation of polarizabilities and second hyperpolarizabilities of polyacetylene oligomer chains using the CAM-B3LYP density functional.

Abstract: The polarizability and second hyperpolarizability of polyacetylene oligomer chains of increasing size up to C24H26 were investigated by means of the Coulomb-attenuating method (CAM-B3LYP) using response theory. It was found that this long-range corrected density functional removes to large parts the overestimation observed for standard methods and in many cases provides results close to those of coupled cluster calculations. A direct comparison to experimentally observed dynamic hyperpolarizabilities is made to estimate the accuracy of the method. A basis set study revealed a noticeable contribution of diffuse orbitals to the hyperpolarizability also for larger oligomers. Furthermore, CAM-B3LYP is also confirmed to provide molecular geometries close to experimentally observed structures, especially for longer chain lengths.

Dispersion-corrected Møller-Plesset second-order perturbation theory.

Abstract: We show that the often unsatisfactory performance of Moller-Plesset second-order perturbation theory (MP2) for the dispersion interaction between closed-shell molecules can be rectified by adding a correction Delta C(n)/R(n), to its long-range behavior. The dispersion-corrected MP2 (MP2 + Delta vdW) results are in excellent agreement with the quantum chemistry "gold standard" [coupled cluster theory with single, double and perturbative triple excitations, CCSD(T)] for a range of systems bounded by hydrogen bonding, electrostatics and dispersion forces. The MP2 + Delta vdW method is only mildly dependent on the short-range damping function and consistently outperforms state-of-the-art dispersion-corrected density-functional theory.

Local correlation calculations using standard and renormalized coupled-cluster approaches.

Abstract: The linear scaling local correlation approach, termed “cluster-in-molecule” (CIM), is extended to the coupled-cluster (CC) theory with singles and doubles (CCSD) and CC methods with singles, doubles, and noniterative triples, including CCSD(T) and the completely renormalized CR-CC(2,3) approach. The resulting CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) methods are characterized by (i) the linear scaling of the CPU time with the system size, (ii) the use of orthonormal orbitals in the CC subsystem calculations, (iii) the natural parallelism, (iv) the high computational efficiency, enabling calculations for much larger systems and at higher levels of CC theory than previously possible, and (v) the purely noniterative character of local triples corrections. By comparing the results of the canonical and CIM-CC calculations for normal alkanes and water clusters, it is shown that the CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) approaches accurately reproduce the corresponding canonical CC correlation and relative energies, while offering savings in the computer effort by orders of magnitude.

Assessment of Orbital-Optimized, Spin-Component Scaled Second-Order Many-Body Perturbation Theory for Thermochemistry and Kinetics.

Abstract: An efficient implementation of the orbital-optimized second-order Moller-Plesset perturbation theory (OO-MP2) within the resolution of the identity (RI) approximation is reported. Both conventional MP2 and spin-component scaled (SCS-MP2) variants are considered, and an extensive numerical investigation of the accuracy of these approaches is presented. This work is closely related to earlier work of Lochan, R. C.; Head-Gordon, M. J. Chem. Phys. 2007, 126. Orbital optimization is achieved by making the Hylleraas functional together with the energy of the reference determinant stationary with respect to variations of the double excitation amplitudes and the molecular orbital rotation parameters. A simple iterative scheme is proposed that usually leads to convergence within 5-15 iterations. The applicability of the method to larger molecules (up to ∼1000-2000 basis functions) is demonstrated. The numerical results show that OO-SCS-MP2 is a major improvement in electronically complicated situations, such as represented by radicals or by transition states where spin contamination often greatly deteriorates the quality of the conventional MP2 and SCS-MP2 methods. The OO-(SCS-)MP2 approach reduces the error by a factor of 3-5 relative to the standard (SCS-)MP2. For closed-shell main group elements, no significant improvement in the accuracy relative to the already excellent SCS-MP2 method is observed. In addition, the problems of all MP2 variants with 3d transition-metal complexes are not solved by orbital optimization. The close relationship of the OO-MP2 method to the approximate second-order coupled cluster method (CC2) is pointed out. Both methods have comparable computational requirements. Thus, the OO-MP2 method emerges as a very useful tool for computational quantum chemistry.

A benchmark theoretical study of the electronic ground state and of the singlet-triplet split of benzene and linear acenes

Abstract: A benchmark theoretical study of the electronic ground state and of the vertical and adiabatic singlet-triplet (ST) excitation energies of benzene (n=1) and n-acenes (C4n+2H2n+4) ranging from naphthalene (n=2) to heptacene (n=7) is presented, on the ground of single- and multireference calculations based on restricted or unrestricted zero-order wave functions. High-level and large scale treatments of electronic correlation in the ground state are found to be necessary for compensating giant but unphysical symmetry-breaking effects in unrestricted single-reference treatments. The composition of multiconfigurational wave functions, the topologies of natural orbitals in symmetry-unrestricted CASSCF calculations, the T1 diagnostics of coupled cluster theory, and further energy-based criteria demonstrate that all investigated systems exhibit a A1g singlet closed-shell electronic ground state. Singlet-triplet (S0-T1) energy gaps can therefore be very accurately determined by applying the principles of a focal p...

Long-range-corrected hybrids including random phase approximation correlation

Abstract: We recently demonstrated a connection between the random phase approximation (RPA) and coupled cluster theory [G. E. Scuseria et al., J. Chem. Phys. 129, 231101 (2008)]. Based on this result, we here propose and test a simple scheme for introducing long-range RPA correlation into density functional theory. Our method provides good thermochemical results and models van der Waals interactions accurately.

A variationally computed T = 300 K line list for NH3.

Abstract: Calculations are reported on the rotation-vibration energy levels of ammonia with associated transition intensities. A potential energy surface obtained from coupled cluster CCSD(T) calculations and subsequent fitting against experimental data is further refined by a slight adjustment of the equilibrium geometry, which leads to a significant improvement in the rotational energy level structure. A new accurate ab initio dipole moment surface is determined at the frozen core CCSD(T)/aug-cc-pVQZ level. The calculation of an extensive ammonia line list necessitates a number of algorithmic improvements in the program TROVE that is used for the variational treatment of nuclear motion. Rotation-vibration transitions for (NH3)-N-14 involving states with energies up to 12000 cm(-1) and rotational quantum number J = 20 are calculated. This gives 3.25 million transitions between 184400 energy levels. Comparisons show good agreement with data in the HITRAN database but suggest that HITRAN is missing significant ammonia absorptions, particularly in the near-infrared.

Cross sections and photoelectron angular distributions in photodetachment from negative ions using equation-of-motion coupled-cluster Dyson orbitals

Abstract: We report total and differential cross sections for photodetachment from negative ions using Dyson orbitals calculated from equation-of-motion coupled-cluster wave functions and free wave description of the detached electron. The energy dependence of the cross sections is reproduced well, however, the accuracy of absolute values varies. For F−, C−, NH2−, and H−, the calculated cross sections are within the error bars from the experimental values, whereas the errors for Li− and OH− are about 20%. The largest errors are observed for O− and O2− for which the calculated cross sections differ from the experimental ones by factors of 3 and 2, respectively. Calculated anisotropy parameters for atomic anions exhibit too slow decrease, which suggests that the diffuseness of the computed Dyson orbitals is underestimated. Moreover, in the asymptotic region, the orbitals exhibit artifactual oscillations probably due to the limitations of Gaussian basis sets. The analysis of the trends in the experimental anisotropy p...

Accurate theoretical chemistry with coupled pair models.

Abstract: Quantum chemistry has found its way into the everyday work of many experimental chemists. Calculations can predict the outcome of chemical reactions, afford insight into reaction mechanisms, and be used to interpret structure and bonding in molecules. Thus, contemporary theory offers tremendous opportunities in experimental chemical research. However, even with present-day computers and algorithms, we cannot solve the many particle Schrodinger equation exactly; inevitably some error is introduced in approximating the solutions of this equation. Thus, the accuracy of quantum chemical calculations is of critical importance. The affordable accuracy depends on molecular size and particularly on the total number of atoms: for orientation, ethanol has 9 atoms, aspirin 21 atoms, morphine 40 atoms, sildenafil 63 atoms, paclitaxel 113 atoms, insulin nearly 800 atoms, and quaternary hemoglobin almost 12,000 atoms. Currently, molecules with up to ∼10 atoms can be very accurately studied by coupled cluster (CC) theor...

Absorption and fluorescence properties of oligothiophene biomarkers from long-range-corrected time-dependent density functional theory

Abstract: The absorption and fluorescence properties in a class of oligothiophene push–pull biomarkers are investigated with a long-range-corrected (LC) density functional method. Using linear-response time-dependent density functional theory (TDDFT), we calculate excitation energies, fluorescence energies, oscillator strengths, and excited-state dipole moments. To benchmark and assess the quality of the LC-TDDFT formalism, an extensive comparison is made between LC-BLYP excitation energies and approximate coupled cluster singles and doubles (CC2) calculations. When using a properly-optimized value of the range parameter, μ, we find that the LC technique provides an accurate description of charge-transfer excitations as a function of biomarker size and chemical functionalization. In contrast, we find that re-optimizing the fraction of Hartree Fock exchange in conventional hybrid functionals still yields an inconsistent description of excitation energies and oscillator strengths for the two lowest excited states in our series of biomarkers. The results of the present study emphasize the importance of a distance-dependent contribution of exchange in TDDFT for investigating excited-state properties.

Accurate calculations of intermolecular interaction energies using explicitly correlated coupled cluster wave functions and a dispersion-weighted MP2 method.

Abstract: Explicitly correlated coupled-cluster calculations of intermolecular interaction energies for the S22 benchmark set of Jurecka, Sponer, Cerný, and Hobza (Chem. Phys. Phys. Chem. 2006, 8, 1985) are presented. Results obtained with the recently proposed CCSD(T)-F12a method and augmented double-ζ basis sets are found to be in very close agreement with basis set extrapolated conventional CCSD(T) results. Furthermore, we propose a dispersion-weighted MP2 (DW-MP2) approximation that combines the good accuracy of MP2 for complexes with predominately electrostatic bonding and SCS-MP2 for dispersion-dominated ones. The MP2-F12 and SCS-MP2-F12 correlation energies are weighted by a switching function that depends on the relative HF and correlation contributions to the interaction energy. For the S22 set, this yields a mean absolute deviation of 0.2 kcal/mol from the CCSD(T)-F12a results. The method, which allows obtaining accurate results at low cost, is also tested for a number of dimers that are not in the traini...

Long-range-corrected hybrids including RPA correlation

Abstract: We recently demonstrated a connection between the random phase approximation (RPA) and coupled cluster theory [J. Chem. Phys. 129, 231101 (2008)]. Based on this result, we here propose and test a simple scheme for introducing long-range RPA correlation into density functional theory. Our method provides good thermochemical results and models van derWaals interactions accurately.

Local explicitly correlated coupled-cluster methods: Efficient removal of the basis set incompleteness and domain errors

Abstract: We propose an explicitly correlated local LCCSD-F12 method in which the basis set incompleteness error as well as the error caused by truncating the virtual orbital space to pair-specific local domains are strongly reduced. This is made possible by including explicitly correlated terms that are orthogonalized only to the pair-specific configuration space. Thus, the contributions of excitations outside the domains are implicitly accounted for by the explicitly correlated terms. It is demonstrated for a set of 54 reactions that the reaction energies computed with the new LCCSD-F12 method and triple-zeta basis sets deviate by at most 2.5 kJ/mol from conventional CCSD complete basis set results (RMS: 0.6 kJ/mol). The local approximations should make it possible to achieve linear scaling of the computational cost with molecular size.

Absorption Spectrum of the Green Fluorescent Protein Chromophore: A Difficult Case for ab Initio Methods?

Abstract: We perform a thorough comparative investigation of the excitation energies of the anionic and neutral forms of the green fluorescent protein (GFP) chromophore in the gas phase using a variety of first-principle theoretical approaches commonly used to access excited state properties of photoactive molecules. These include time-dependent density functional theory (TDDFT), complete-active-space second-order perturbation theory (CASPT2), equation-of-motion coupled cluster (EOM-CC), and quantum Monte Carlo (QMC) methods. We find that all approaches give roughly the same vertical excitation for the anionic form, while TDDFT predicts an excitation for the neutral chromophore significantly lower than the highly correlated methods. Our findings support the picture emerging from the extrapolation of the Kamlet-Taft fit of absorption experimental data in solution and indicate that the protein gives rise to a considerable bathochromic shift with respect to vacuum. These results also open some questions on the interpretation of photodestruction spectroscopy experiments in the gas phase as well as on the accuracy of previous theoretical calculations in the more complex protein environment

A coupled-cluster approach to the many-body perturbation theory for open-shell systems

Abstract: A new approach to the diagrammatic formulation of many-body perturbation theory for open-shell systems is presented. The formalism is based on a generalized form of the Bloch equation that also generates the Rayleigh-Schrodinger perturbation expansion for a system with several open shells. Second quantization in the particle-hole formulation is used together with Wick's theorem in order to derive graphical rules in the usual way. The linked-diagram property of the wave operator and of the effective interaction is shown by expanding the wave operator in terms of normal products of connected diagram clusters, in analogy with the exp(S) formalism of Coester and Kummel for closed-shell systems. Self-consistent “coupled-cluster” equations are derived for the open-shell case from the generalized Bloch equation by a straightforward extension of the procedure of Cižek and Paldus. The application of such equations for investigating different properties of open-shell atoms is discussed.

Divide-and-conquer-based linear-scaling approach for traditional and renormalized coupled cluster methods with single, double, and noniterative triple excitations

Abstract: We have reported the divide-and-conquer (DC)-based linear-scaling correlation treatment of coupled-cluster method with single and double excitations (CCSD) [Kobayashi and Nakai, J. Chem. Phys. 129, 044103 (2009)]. In the DC-CCSD method, the CCSD equations derived from subsystem orbitals are solved for each subsystem in order to obtain the total correlation energy by summing up subsystem contributions using energy density analysis. In this study, we extend the DC-CCSD method for treating noniterative perturbative triple excitations using CCSD T(1) and T(2) amplitudes, namely, CCSD(T). In the DC-CCSD(T) method, the so-called (T) corrections are also computed for each subsystem. Numerical assessments indicate that DC-CCSD(T) reproduces the CCSD(T) results with high accuracy and significantly less computational cost. We further extend the DC-based correlation method to renormalized CCSD(T) [Kowalski and Piecuch, J. Chem. Phys. 113, 18 (2000)] for avoiding the divergence that occurs in multireference problems such as bond dissociation.

Benchmarks for Electronically Excited States: A Comparison of Noniterative and Iterative Triples Corrections in Linear Response Coupled Cluster Methods: CCSDR(3) versus CC3.

Abstract: CCSDR(3) calculations of vertical excitation energies are reported for a set of 24 molecules and 121 excited valence singlet states from a recently published benchmark of organic molecules. The same geometries (MP2/6−31G*) and basis set (TZVP) were employed as in our previous linear response CC2, CCSD, and CC3 calculations. The CCSDR(3) results are compared against the CCSD and CC3 results. Statistical evaluation of all CCSDR(3) excitation energies gives mean absolute deviations of 0.09 eV from CC3 and 0.30 eV from CCSD. For excited states, which are dominated by single excitations, the absolute mean deviation from CC3 is reduced to 0.02 eV and the maximum deviation is 0.09 eV. CCSDR(3) is thus a very cost-effective accurate alternative to CC3.

Left‐eigenstate completely renormalized equation‐of‐motion coupled‐cluster methods: Review of key concepts, extension to excited states of open‐shell systems, and comparison with electron‐attached and ionized approaches

Abstract: The recently proposed left-eigenstate completely renormalized (CR) coupled-cluster (CC) method with singles, doubles, and noniterative triples, termed CR-CC(2,3) Piecuch and Wloch, J Chem Phys, 2005, 123, 224105; Piecuch et al Chem Phys Lett, 2006, 418, 467 and the companion CR-EOMCC(2,3) methodology, which has been previously applied to singlet excited states of closed-shell molecular systems Wloch et al Mol Phys, 2006, 104, 2149 and in which relatively inexpensive noniterative corrections due to triple excitations derived from the biorthogonal method of moments of CC equations (MMCC) are added to the CC singles and doubles (CCSD) or equation-of-motion (EOM) CCSD energies, have been extended to excited states of open-shell species The resulting highly efficient computer codes for the open-shell CR-EOMCC(2,3) approach exploiting the recursively generated intermediates and fast matrix multiplication routines have been developed and interfaced with the GAMESS package, enabling CR-EOMCC(2,3) calculations for singlet as well as nonsinglet ground and excited states of closed- and open-shell systems using the restricted Hartree–Fock or restricted open-shell Hartree–Fock references A number of important mathematical and algorithmic details related to formal aspects and computer implementation of the CR-EOMCC(2,3) method have been discussed, in addition to overviewing the key concepts behind the CR-EOMCC(2,3) and biorthogonal MMCC methodologies for ground and excited states, and the numerical results involving low-lying states of the CH, CNC, C2N, N3, and NCO species, including states dominated by two-electron transitions, have been presented The results of the CR-EOMCC(2,3) calculations have been compared with other CC/EOMCC approaches, including the EOMCCSD and EOMCC singles, doubles, and triples methods, and their full and active-space valence counterparts based on the electron-attached and ionized EOMCC methodologies, and the predecessor of CR-EOMCC(2,3) termed CR-EOMCCSD(T) Kowalski and Piecuch, J Chem Phys, 2004, 120, 1715 © 2009 Wiley Periodicals, Inc Int J Quantum Chem, 2009

RESEARCH ARTICLE Basis set effects on coupled cluster benchmarks of electronically excited states: CC3, CCSDR(3) and CC2

Abstract: Vertical electronic excitation energies and one-electron properties of 28 medium-size molecules from a previously proposed benchmark set are revisited using the augmented correlationconsistent triple-zeta aug-cc-pVTZ basis set in CC2, CCSDR(3), and CC3 calculations. The results are compared to those obtained previously with the smaller TZVP basis set. For each of the three coupled cluster methods, a correlation coefficien t greater than 0.994 is found between the vertical excitation energies computed with the two basis sets. The deviations of the CC2 and CCSDR(3) results from the CC3 reference values are very similar for both basis sets, thus confirming previous conclusions on the intrinsic accuracy of CC2 and CCSDR(3). This similarity justifies the use of CC2- or CCSDR(3)-based corrections to account for basis set incompleteness in CC3 studies of vertical excitation energies. For oscillator strengths and excited-state dipole moments, CC2 calculations with the aug-cc-pVTZ and TZVP basis sets give correlation coefficients of 0.966 and 0.833, respectively, implying that basis set convergence is slower for these one-electron properties.

Large-scale parallel uncontracted multireference-averaged quadratic coupled cluster: the ground state of the chromium dimer revisited.

Abstract: The accurate prediction of the potential energy function of the X1Sigmag+ state of Cr2 is a remarkable challenge; large differential electron correlation effects, significant scalar relativistic contributions, the need for large flexible basis sets containing g functions, the importance of semicore valence electron correlation, and its multireference nature pose considerable obstacles. So far, the only reasonable successful approaches were based on multireference perturbation theory (MRPT). Recently, there was some controversy in the literature about the role of error compensation and systematic defects of various MRPT implementations that cannot be easily overcome. A detailed basis set study of the potential energy function is presented, adopting a variational method. The method of choice for this electron-rich target with up to 28 correlated electrons is fully uncontracted multireference-averaged quadratic coupled cluster (MR-AQCC), which shares the flexibility of the multireference configuration interaction (MRCI) approach and is, in addition, approximately size-extensive (0.02 eV in error as compared to the MRCI value of 1.37 eV for two noninteracting chromium atoms). The best estimate for De arrives at 1.48 eV and agrees well with the experimental data of 1.47 +/- 0.056 eV. At the estimated CBS limit, the equilibrium bond distance (1.685 A) and vibrational frequency (459 cm-1) are in agreement with experiment (1.679 A, 481 cm-1). Large basis sets and reference configuration spaces invariably result in huge wave function expansions (here, up to 2.8 billion configuration state functions), and efficient parallel implementations of the method are crucial. Hence, relevant details on implementation and general performance of the parallel program code are discussed as well.

Water-benzene interactions: an effective fragment potential and correlated quantum chemistry study.

Abstract: Structures and binding in small water−benzene complexes (1−8 water molecules and 1−2 benzene molecules) are studied using the general effective fragment potential (EFP) method The lowest energy conformers of the clusters were found using a Monte Carlo technique The binding energies in the smallest clusters (dimers, trimers, and tetramers) were also evaluated with second order perturbation theory (MP2) and coupled cluster theory (CCSD(T)) The EFP method accurately predicts structures and binding energies in the water−benzene complexes Benzene is polarizable and consequently participates in hydrogen bond networking of water Since the water−benzene interactions are only slightly weaker than water−water interactions, structures with different numbers of water−water, benzene−water, and benzene−benzene bonds often have very similar binding energies This is a challenge for computational methods

Damping functions in the effective fragment potential method

Abstract: This work presents the implementation and analysis of several damping functions for Coulomb, induction, and dispersion interactions within the framework of the general effective fragment potential (EFP) method. Damping is necessary to obtain the correct asymptotic short-range behavior of these interactions. Correctly chosen damping functions allow a balanced description of different parts of intermolecular potential energy surfaces and improve the accuracy of predicted intermolecular distances and binding energies. The performance of different damping functions is tested by comparing the EFP energy terms with the symmetry adapted perturbation theory (SAPT) energy terms in a range of intermolecular separations for ten molecular dimers. The total EFP binding energies in these dimers were compared with the binding energies obtained from SAPT and coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. A formula for electrostatic damping that was derived from first principles...

Atomization energies from coupled-cluster calculations augmented with explicitly-correlated perturbation theory

Abstract: The atomization energies of the 105 molecules in the test set of Bakowies [D. Bakowies, J. Chem. Phys. 127 (2007) 084105] have been computed with an estimated standard deviation (from the values compiled in the Active Thermochemical Tables) of {+-}0.1 kJ/mol per valence electron in the molecule. Equilibrium geometries and harmonic vibrational frequencies were calculated at the all-electron CCSD(T)/cc-pCVTZ level, that is, at the level of coupled-cluster theory with singles, doubles and non-iterative triples in a correlation-consistent polarized core-valence triple-zeta basis. Single-point energy calculations were performed at the all-electron CCSD(T) level in a correlation-consistent polarized core-valence quadruple-zeta basis (cc-pCVQZ), and several corrections were added: (i) a correction for the basis-set truncation error, obtained from second-order perturbation theory using Slater-type geminals (MP2-F12 theory), (ii) a correction for the effect of anharmonicity on the zero-point vibrational energy, (iii) a relativistic correction, (iv) a correction for the difference between the full CCSDT model (coupled-cluster theory with singles, doubles and triples) and the CCSD(T) approximation, and (v) a correction for connected quadruple excitations obtained from CCSDT(Q) calculations. The correction for the basis-set truncation error was obtained from MP2-F12 calculations by scaling the MP2 basis-set truncation error by an empirically optimized 'interference factor' of f{submore » int} = 0.78. The reference values from the Active Thermochemical Tables for 73 molecules in the test set, the equilibrium geometries, the harmonic vibrational frequencies, and all of the energy corrections represent valuable data for performance assessments of additivity schemes that will be developed in the future, in which the basis-set truncation error will be calculated at the level of coupled-cluster theory using Slater-type geminals (CC-F12 theory). Such a scheme will be free of empirical corrections and scaling factors.« less

Quadratic canonical transformation theory and higher order density matrices

Abstract: Canonical transformation (CT) theory provides a rigorously size-extensive description of dynamic correlation in multireference systems, with an accuracy superior to and cost scaling lower than complete active space second order perturbation theory. Here we expand our previous theory by investigating (i) a commutator approximation that is applied at quadratic, as opposed to linear, order in the effective Hamiltonian, and (ii) incorporation of the three-body reduced density matrix in the operator and density matrix decompositions. The quadratic commutator approximation improves CT’s accuracy when used with a single-determinant reference, repairing the previous formal disadvantage of the single-reference linear CT theory relative to singles and doubles coupled cluster theory. Calculations on the BH and HF binding curves confirm this improvement. In multireference systems, the three-body reduced density matrix increases the overall accuracy of the CT theory. Tests on the H2OH2O and N2N2 binding curves yield results highly competitive with expensive state-of-the-art multireference methods, such as the multireference Davidson-corrected configuration interaction (MRCI+Q), averaged coupled pair functional, and averaged quadratic coupled cluster theories.

Accurate dipole polarizabilities for water clusters n=2-12 at the coupled-cluster level of theory and benchmarking of various density functionals.

Abstract: The static dipole polarizabilities of water clusters (2≤N≤12) are determined at the coupled-cluster level of theory (CCSD). For the dipole polarizability of the water monomer it was determined that the role of the basis set is more important than that of electron correlation and that the basis set augmentation converges with two sets of diffuse functions. The CCSD results are used to benchmark a variety of density functionals while the performance of several families of basis sets (Dunning, Pople, and Sadlej) in producing accurate values for the polarizabilities was also examined. The Sadlej family of basis sets was found to produce accurate results when compared to the ones obtained with the much larger Dunning basis sets. It was furthermore determined that the PBE0 density functional with the aug-cc-pVDZ basis set produces overall remarkably accurate polarizabilities at a moderate computational cost.