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A route to assess non-linear light–matter interactions from the increasingly popular GW-Bethe–Salpeter equation (GW-BSE) method is outlined. In the present work, the necessary analytic expressions within the static-screened exchange approximation of the BSE are derived. This enables a straightforward implementation of the computation of the first hyperpolarizability as well as two-photon absorption processes for molecular systems. Benchmark calculations on small molecular systems reveal that the GW-BSE method is intriguingly accurate for predicting both first hyperpolarizabilities and two-photon absorption strengths. Using state-of-the-art Kohn–Sham references as a starting point, the accuracy of the GW-BSE method rivals that of the coupled-cluster singles-and-doubles method, outperforming both second-order coupled-cluster and time-dependent density-functional theory. [ABSTRACT FROM AUTHOR]

A two-component contour deformation (CD) based GW method that employs frequency sampling to drastically reduce the computational effort when assessing quasiparticle states far away from the Fermi level is outlined. Compared to the canonical CD-GW method, computational scaling is reduced by an order of magnitude without sacrificing accuracy. This allows for an efficient calculation of core ionization energies. The improved computational efficiency is used to provide benchmarks for core ionized states, comparing the performance of 15 density functional approximations as Kohn–Sham starting points for GW calculations on a set of 65 core ionization energies of 32 small molecules. Contrary to valence states, GW calculations on core states prefer functionals with only a moderate amount of Hartree–Fock exchange. Moreover, modern ab initio local hybrid functionals are also shown to provide excellent generalized Kohn–Sham references for core GW calculations. Furthermore, the core–valence separated Bethe–Salpeter equation (CVS-BSE) is outlined. CVS-BSE is a convenient tool to probe core excited states. The latter is tested on a set of 40 core excitations of eight small inorganic molecules. Results from the CVS-BSE method for excitation energies and the corresponding absorption cross sections are found to be in excellent agreement with those of reference damped response BSE calculations. [ABSTRACT FROM AUTHOR]

The increasingly popular GW method is becoming a convenient tool to determine vertical ionization energies in molecular systems. However, depending on the formalism used and the range of orbitals investigated, it may be hampered by a steep computational scaling. To alleviate this issue, correlated natural virtual orbitals (NVOs) based on second-order Møller–Plesset (MP2) and direct MP2 correlation energies are implemented, and the resulting correlated NVOs are tested on GW quasiparticle energies. Test cases include the popular GW variants G0W0 and evGW0 as well as more elaborate vertex corrections. We find that for increasingly larger molecular systems and basis sets, NVOs considerably improve efficiency. Furthermore, we test the performance of the truncated (frozen) NVO ansatz on the GW100 test set. For the latter, it is demonstrated that, using a carefully chosen truncation threshold, NVOs lead to a negligible loss in accuracy while providing speedups of one order of magnitude. Furthermore, we compare the resulting quasiparticle energies to very accurate vertical ionization energies obtained from coupled-cluster theory with singles, doubles, and noniterative triples [CCSD(T)], confirming that the loss in accuracy introduced by truncating the NVOs is negligible compared to the methodical errors in the GW approximation. It is also demonstrated that the choice of basis set impacts results far more than using a suitably truncated NVO space. Therefore, at the same computational expense, more accurate results can be obtained using NVOs. Finally, we provide improved reference CCSD(T) values for the GW100 test set, which have been obtained using the def2-QZVPP basis set. [ABSTRACT FROM AUTHOR]

The direct random-phase approximation (dRPA) is used to calculate and compare atomization energies for the HEAT set and ten selected molecules of the G2-1 set using both plane waves and Gaussian-type orbitals. We describe detailed procedures to obtain highly accurate and well converged results for the projector augmented-wave method as implemented in the Vienna Ab initio Simulation Package as well as the explicitly correlated dRPA-F12 method as implemented in the TURBOMOLE package. The two approaches agree within chemical accuracy (1 kcal/mol) for the atomization energies of all considered molecules, both for the exact exchange as well as for the RPA. The root mean-square deviation is 0.41 kcal/mol for the exact exchange (evaluated using density functional theory orbitals) and 0.33 kcal/mol for exact exchange plus correlation from the RPA. [ABSTRACT FROM AUTHOR]

Molecular rotations and vibrations have been extensively studied by chemists for decades, both experimentally using spectroscopic methods and theoretically with the help of quantum chemistry. However, the theoretical investigation of molecular rotations and vibrations in strong magnetic fields requires computationally more demanding tools. As such, proper calculations of rotational and vibrational spectra were not feasible up until very recently. In this work, we present rotational and vibrational spectra for two small linear molecules, H2 and LiH, in strong magnetic fields. By treating the nuclei as classical particles, trajectories for rotations and vibrations are simulated from ab initio molecular dynamics. Born–Oppenheimer potential energy surfaces are calculated at the Hartree–Fock and MP2 levels of theory using London atomic orbitals to ensure gauge origin invariance. For the calculation of nuclear trajectories, a highly efficient Tajima propagator is introduced, incorporating the Berry curvature tensor accounting for the screening of nuclear charges. [ABSTRACT FROM AUTHOR]

As quantum-chemical calculations of molecules in static external magnetic fields are becoming increasingly popular, the description of molecular symmetry under such conditions is also becoming more and more relevant. Using group theory, a general scheme of identifying the molecular point group in an external magnetic field is constructed. For both point groups that are non-existent in the absence of a field (C∞ and C∞h) and their double groups, the character tables are presented. General properties of all possible point groups are discussed, and it is mathematically proven that they are all Abelian. [ABSTRACT FROM AUTHOR]

The site-specific first microsolvation step of furan and some of its derivatives with methanol is explored to benchmark the ability of quantum-chemical methods to describe the structure, energetics, and vibrational spectrum at low temperature. Infrared and microwave spectra in supersonic jet expansions are used to quantify the docking preference and some relevant quantum states of the model complexes. Microwave spectroscopy strictly rules out in-plane docking of methanol as opposed to the top coordination of the aromatic ring. Contrasting comparison strategies, which emphasize either the experimental or the theoretical input, are explored. Within the harmonic approximation, only a few composite computational approaches are able to achieve a satisfactory performance. Deuteration experiments suggest that the harmonic treatment itself is largely justified for the zero-point energy, likely and by design due to the systematic cancellation of important anharmonic contributions between the docking variants. Therefore, discrepancies between experiment and theory for the isomer abundance are tentatively assigned to electronic structure deficiencies, but uncertainties remain on the nuclear dynamics side. Attempts to include anharmonic contributions indicate that for systems of this size, a uniform treatment of anharmonicity with systematically improved performance is not yet in sight. [ABSTRACT FROM AUTHOR]

Quasiparticle energies of the atoms H–Ne have been computed in the GW approximation in the presence of strong magnetic fields with field strengths varying from 0 to 0.25 atomic units (0.25 B 0 = 0.25 ℏ e − 1 a 0 − 2 ≈ 58 763 T). The GW quasiparticle energies are compared with equation-of-motion ionization-potential (EOM-IP) coupled-cluster singles-and-doubles (CCSD) calculations of the first ionization energies. The best results are obtained with the evGW@PBE0 method, which agrees with the EOM-IP-CCSD model to within about 0.20 eV. Ionization potentials have been calculated for all atoms in the series, representing the first systematic study of ionization potentials for the first-row atoms at field strengths characteristic of magnetic white dwarf stars. Under these conditions, the ionization potentials increase in a near-linear fashion with the field strength, reflecting the linear field dependence of the Landau energy of the ionized electron. The calculated ionization potentials agree well with the best available literature data for He, Li, and Be. [ABSTRACT FROM AUTHOR]

We have implemented and applied the GW method and the static screened Bethe–Salpeter equation (BSE) for calculating linear-response properties for quasirelativistic molecular systems. Our ansatz is based on a two-component (2c) scheme that includes spin–orbit coupling as well as scalar relativistic effects. Efficient, state-of-the-art approaches including the analytic continuation (employing Padé approximants, scaling as N 4 with system size N ) and contour deformation schemes are presented to obtain the required 2c quasirelativistic GW quasiparticle energies. Screened exchange contributions are computed within the resolution-of-the-identity approximation, and working equations for the 2c GW/BSE method are given. The performance of the 2c GW/BSE method is assessed, and results are compared to other methods and experimental data. A robust iterative scheme for solving the eigenvalue problems occurring in the 2c GW/BSE and hybrid time-dependent density functional theories is presented. [ABSTRACT FROM AUTHOR]

We report the extended explicitly correlated approximate coupled-cluster singles and doubles CC2(F12*)-XSP method suitable for response properties. Equations are derived using an automated approach and have subsequently been hand-coded into the computer program KOALA, in which for all two-electron integrals, density fitting is employed. Numerical results are presented for the lowest two vertical singlet excitation energies of a set of selected molecules. The results show that the CC2(F12*)-XSP method provides the correct basis-set limit with no bias to the ground state, and an excellent agreement with reference CC2 values using large basis sets is found. Using Dunning's aug-cc-pVTZ basis, the CC2(F12*)-XSP method yields excitation energies which are converged within 1 mEh to the basis-set limit for valence excitations. [ABSTRACT FROM AUTHOR]

A variety of approaches are presented for the computation of atomic and molecular correlation energies based on the Bethe–Salpeter equation in the framework of the adiabatic-connection fluctuation–dissipation theorem. The performance of the approaches is assessed by computing the total energies of the atoms H—Ne and the atomization energies of the high-accuracy extrapolated ab initio thermochemistry set of small molecules as well as by determining the bond lengths and harmonic vibrational frequencies of the metal monoxides MO with M=Ca—Zn. [ABSTRACT FROM AUTHOR]

Herein we present the results of a blind challenge to quantum chemical methods in the calculation of dimerization preferences in the low temperature gas phase. The target of study was the first step of the microsolvation of furan, 2-methylfuran and 2,5-dimethylfuran with methanol. The dimers were investigated through IR spectroscopy of a supersonic jet expansion. From the measured bands, it was possible to identify a persistent hydrogen bonding OH-O motif in the predominant species. From the presence of another band, which can be attributed to an OH-л interaction, we were able to assert that the energy gap between the two types of dimers should be less than or close to 1 kJ/mol across the series. These values served as a first evaluation ruler for the 12 entries featured in the challenge. A tentative stricter evaluation of the challenge results is also carried out, combining theoretical and experimental results in order to define a smaller error bar. The process was carried out in a double-blind fashion, with both theory and experimental groups unaware of the results on the other side, with the exception of the 2,5-dimethylfuran system which was featured in an earlier publication. [ABSTRACT FROM AUTHOR]

A method for calculating intermolecular induction and dispersion energies based on aGW description of the monomers and employing response functions from the Bethe-Salpeter equation is proposed. Calculations on a test set of 10 weakly bound complexes with GW-based symmetry-adapted perturbation theory (GW-SAPT) show an improved performance in comparison with symmetry-adapted perturbation theory based on density-functional theory (DFT-SAPT). [ABSTRACT FROM AUTHOR]

The 1-naphthol·cyclopropane intermolecular complex is formed in a supersonic jet and investigated by resonant two-photon ionization (R2PI) spectroscopy, UV holeburning, and stimulated emission pumping (SEP)-R2PI spectroscopy. Two very different structure types are inferred from the vibronic spectra and calculations. In the "edge" isomer, the OH group of 1-naphthol is directed towards a C--C bond of cyclopropane, the two ring planes are perpendicular. In the "face" isomer, the cyclopropane is adsorbed on one of the π-aromatic faces of the 1-naphthol moiety, the ring planes are nearly parallel. Accurate ground-state intermolecular dissociation energies D0 were measured with the SEP-R2PI technique. The D0(S0) of the edge isomer is bracketed as 15.35 « 0.03 kJ/mol, while that of the face isomer is 16.96 « 0.12 kJ/mol. The corresponding excited-state dissociation energies D0(S1) were evaluated using the respective electronic spectral shifts. Despite the D0(S0) difference of 1.6 kJ/mol, both isomers are observed in the jet in similar concentrations, so they must be separated by substantial potential energy barriers. Intermolecular binding energies, De, and dissociation energies, D0, calculated with correlated wave function methods and two dispersion-corrected density-functional methods are evaluated in the context of these results. The density functional calculations suggest that the face isomer is bound solely by dispersion interactions. Binding of the edge isomer is also dominated by dispersion, which makes up two thirds of the total binding energy. [ABSTRACT FROM AUTHOR]

A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian. [ABSTRACT FROM AUTHOR]

The connection between the random-phase approximation and the ring-coupled-cluster-doubles method bridges the gap between density-functional and wave-function theories and the importance of the random-phase approximation lies in both its broad applicability and this linking role in electronic-structure theory. In this contribution, we present an explicitly correlated approach to the random-phase approximation, based on the direct ring-coupled-cluster-doubles ansatz, which overcomes the problem of slow basis-set convergence, inherent to the random-phase approximation. Benchmark results for a test set of 106 molecules and a selection of 10 organic complexes from the S22 test set demonstrate that convergence to within 99% of the basis-set limit is reached for triple-zeta basis sets for atomisation energies, while quadruple-zeta basis sets are required for interaction energies. Corrections due to single excitations into the complementary auxiliary space reduce the basis-set incompleteness error by one order of magnitude, while contributions due to the coupling of conventional and geminal amplitudes are in general negligible. We find that a non-iterative explicitly correlated correction to first order in perturbation theory exhibits the best ratio of accuracy to computational cost. [ABSTRACT FROM AUTHOR]

A generalization of the approximated coupled-cluster singles and doubles method and the algebraic diagrammatic construction scheme up to second order to two-component spinors obtained from a relativistic Hartree-Fock calculation is reported. Computational results for zero-field splittings of atoms and monoatomic cations, triplet lifetimes of two organic molecules, and the spin-forbidden part of the UV/Vis absorption spectrum of tris(ethylenediamine)cobalt(III) are presented. [ABSTRACT FROM AUTHOR]

Within the framework of density-functional theory, the correlation energy is computed in the random-phase approximation (RPA) using spinors obtained from a two-component relativistic Kohn-Sham calculation accounting for spin-orbit interactions. Ring-coupled-cluster equations are solved to obtain the two-component RPA correlation energy. Results are presented for the hydrides of the halogens Br, I, and At as well as of the coinage metals Cu, Ag, and Au, based on two-component relativistic exact-decoupling Kohn-Sham calculations. [ABSTRACT FROM AUTHOR]

Within the framework of density-functional theory, the basis-set convergence of energies obtained from the random-phase approximation to the correlation energy is equally slow as in wavefunction theory, as for example in coupled-cluster or many-body perturbation theory. Fortunately, the slow basis-set convergence of correlation energies obtained in the random-phase approximation can be accelerated in exactly the same manner as in wavefunction theory, namely by using explicitly correlated two-electron basis functions that are functions of the interelectronic distances. This is demonstrated in the present work. [ABSTRACT FROM AUTHOR]

Combinations of explicitly correlated R12 wave functions with relativistic Douglas–Kroll–Hess (DKH) Hamiltonians are discussed. We considered several ways to incorporate the relativistic terms into the second-order Mo\ller–Plesset R12 method and applied them to the helium isoelectronic series to investigate their accuracy and numerical stability. Among the approaches are the evaluation of the relativistic terms via double resolution-of-the-identity and the explicit evaluation of all terms up to O(c-4) using the Pauli Hamiltonian. Numerical collapse of the latter can be avoided if the R12 amplitudes are determined by Kato’s cusp condition. Closed formulas for new two-electron integrals that include the mass-velocity term have been derived and implemented into the LIBINT2 integral library. The proposed approaches are not restricted to DKH and can be combined with other one- and two-component relativistic Hamiltonians. [ABSTRACT FROM AUTHOR]

An automated implementation of the incremental scheme for the computation of MP2-F12 and CCSD(F12) energies is presented. The numerical accuracy of the approach is explored for a set of 15 chemical reactions using the limiting case of single orbital one-site domains as a worst case scenario. The results are analyzed by the maximum absolute deviation, the mean absolute error, and the root mean square error, with respect to the standard MP2-F12 and CCSD(F12) results. It is found that the MP2 reaction energies are within 1 kcal/mol accuracy at third order of the expansion, whereas the F12 corrections are already sufficiently accurate at second order. For the CCSD(F12) method 1 kcal/mol accuracy is obtained at fourth order. [ABSTRACT FROM AUTHOR]

Second-order perturbation theory using explicitly correlated wave functions has been introduced into a quasirelativistic two-component formalism. The convergence of the correlation energy is as much improved as for the nonrelativistic Hamiltonian, achieving basis-set-limit results in a moderate-size basis set. Equilibrium distances and vibrational frequencies of small molecules of the 6th period of the periodic system of the elements have been calculated, demonstrating the improved behavior of the explicitly correlated wave functions. Taking advantage of density-fitting techniques, the explicitly correlated approach is an economical and appealing alternative to conventional two-component second-order perturbation theory in a large one-particle basis. [ABSTRACT FROM AUTHOR]

The gas-phase and in-solvent absorption and emission spectra of pyrene, 1,6-dithiapyrene, and tetrathiafulvalene are studied theoretically in the visible spectral region with the complete active space self-consistent field method, the complete active space second order perturbation theory method, and the resolution-of-identity second order perturbative corrected coupled cluster doubles (RICC2) method, with basis sets up to augmented polarized triple-ζ quality. The time-dependent density functional theory (TDDFT) formalism is also used employing a series of functionals. The nature of the excited states is discussed. With respect to literature theoretical values of the absorption and emission wavelengths of these three molecules, substantial improvements are achieved and comparison with experiment is favorable. Moreover, theoretical absorption and emission spectra of 1,6-dithiapyrene are presented for the first time. It is also exhibited that in most cases, a TDDFT treatment with hybrid functionals combined with a modest basis set (6-31G*) appears to be capable of providing reliable estimates for absorption and emission in all three molecules with relatively low computational cost. Furthermore, the RICC2 method (standalone or in conjunction with TDDFT) provides a satisfactory ab initio alternative, providing a good compromise between accuracy and computational effort. [ABSTRACT FROM AUTHOR]

Films comprising predominantly novel isomers of C60 [=C60(nIPR)] have been generated by low energy ion beam deposition of vibronically excited C60+ onto graphite followed by selective sublimation of C60(Ih) from the deposited isomer mixture. The incident ions were generated by electron impact ionization/fragmentation of sublimed C70. Images of the C60(nIPR) films obtained by applying atomic force microscopy show aggregates, which we attribute to covalently interlinked C60(nIPR) units. The covalent bonds are inferred from the significantly higher thermal stability of the C60(nIPR) films compared to the C60(Ih) van der Waals solid–as measured by thermal desorption with mass spectrometric detection of the C60 mass channel (the only desorbable species). In contrast to the characteristic doublet structure of the occupied valence band in the ultraviolet photoelectron spectrum of pure C60(Ih), the valence band of C60(nIPR) films exhibits a triplet feature with the additional peak occurring at a binding energy of ∼2.6 eV. This is an indicator of the electronic modifications induced by intermolecular bonding. C60(nIPR) films exhibit a narrower band gap than found for C60(Ih). They also have significantly different chemical reactivity toward incorporation of thermal energy deuterium atoms. In order to model the experimental photoelectron spectra, various covalently linked oligomers of #1809C60(C2v), the second most stable conventional 60-atom fullerene cage, were calculated by means of the density functional theory. These spectral predictions together with analogous previous observations on related fullerene solids such as C58 lead us to infer that C60(nIPR) films consist of fullerene cage isomers containing one or more adjacent pentagon pairs, which mediate covalent cage-cage interconnection. [ABSTRACT FROM AUTHOR]

The reaction HOSO2+O2→HO2+SO3 (2) is of crucial importance for sulfuric acid formation in the atmosphere, and reliable thermochemical data are required for an adequate modeling. The currently least well known thermochemical quantity of reaction (2) is the enthalpy of formation of the hydroxysulfonyl radical (HOSO2). We report on high-level quantum chemical calculations to predict the binding energy of the HO–SO2 bond and deduce a value for the enthalpy of formation of HOSO2 using the most reliable thermodynamic data of OH and SO2. On the basis of anharmonic vibrational frequencies from calculations at the fc-CCSD(T)/cc-pV(T+d)Z level of theory, the enthalpy of reaction at 0 K for the reaction OH+SO2→HOSO2 (1) was computed to be ΔRH0 K(1)=-109.4±2.0 kJ/mol and the thermal corrections result in ΔRH298 K(1)=-114.7±3.0 kJ/mol. From these values, we obtain ΔfH0 K(HOSO2)=-366.6±2.5 and ΔfH298 K(HOSO2)=-374.1±3.0 kJ/mol, respectively. Accordingly, ΔRH0 K(2)=-8.5±3.0 and ΔRH298 K(2)=-9.5±3.0 kJ/mol. [ABSTRACT FROM AUTHOR]

An approach for the systematic determination of particularly stable hydride compositions CnH2x of a fullerene Cn is presented. The study is divided into three parts. First, a CCSD(T) benchmark study on benzene and naphthalene hydrogenation is carried out. We show that the TPSS and BP86 functionals give more reliable relative isomer energies and reaction energies than B3LYP, when compared to CCSD(T) calculations. We therefore recommend BP86 for use on fullerenes. In the second part, a scheme for reduction in the immense number of possible fullerene hydride isomers is proposed. The scheme is based on thermodynamic sampling and involves density functional based tight binding as fast preselection method. The testing of the approach for C60 constitutes the last part of the study. A low energy pathway for C60H36 production is determined. Particularly stable structures are identified through analysis of the reaction energies along this pathway. These are C60H2x with 2x=18, 30, and 36. The good agreement of these results with the experimental and previous theoretical data suggests that our method is reliable and can be used to study fullerene hydrogenation. [ABSTRACT FROM AUTHOR]

The photoelectron spectrum (PES) of the uracil anion is reported and discussed from the perspective of quantum chemical calculations of the vertical detachment energies (VDEs) of the anions of various tautomers of uracil. The PES peak maximum is found at an electron binding energy of 2.4 eV, and the width of the main feature suggests that the parent anions are in a valence rather than a dipole-bound state. The canonical tautomer as well as four tautomers that result from proton transfer from an NH group to a C atom were investigated computationally. At the Hartree–Fock and second-order Mo\ller-Plesset perturbation theory levels, the adiabatic electron affinity (AEA) and the VDE have been converged to the limit of a complete basis set to within ±1 meV. Post-MP2 electron-correlation effects have been determined at the coupled-cluster level of theory including single, double, and noniterative triple excitations. The quantum chemical calculations suggest that the most stable valence anion of uracil is the anion of a tautomer that results from a proton transfer from N1H to C5. It is characterized by an AEA of 135 meV and a VDE of 1.38 eV. The peak maximum is as much as 1 eV larger, however, and the photoelectron intensity is only very weak at 1.38 eV. The PES does not lend support either to the valence anion of the canonical tautomer, which is the second most stable anion, and whose VDE is computed at about 0.60 eV. Agreement between the peak maximum and the computed VDE is only found for the third most stable tautomer, which shows an AEA of ≈-0.1 eV and a VDE of 2.58 eV. This tautomer results from a proton transfer from N3H to C5. The results illustrate that the characteristics of biomolecular anions are highly dependent on their tautomeric form. If indeed the third most stable anion is observed in the experiment, then it remains an open question why and how this species is formed under the given conditions. [ABSTRACT FROM AUTHOR]

Recent advances have seen the convergence of the R12 and Gaussian geminal explicitly correlated methods, such that the principal remaining distinction is the way in which the many-electron integrals are handled. Here we examine the weak orthogonality functional and the resolution of the identity and find that the first, although exact in the limit of infinite basis, introduces a conflict between the physical description of the electronic cusp and the satisfaction of the strong orthogonality constraint. This leads us to propose an improved weak orthogonality functional where the explicitly correlated pair functions are almost orthogonal to the occupied orbitals by construction. For applications where 95%-98% accuracy in the total correlation energy is sufficient, we recommend use of the strong orthogonality functional in combination with the resolution of the identity for three- and four-electron integral evaluations. [ABSTRACT FROM AUTHOR]

A valence-type anion of the canonical tautomer of uracil has been characterized using explicitly correlated second-order Mo\ller-Plesset perturbation theory (RI-MP2-R12) in conjunction with conventional coupled-cluster theory with single, double, and perturbative triple excitations. At this level of electron-correlation treatment and after inclusion of a zero-point vibrational energy correction, determined in the harmonic approximation at the RI-MP2 level of theory, the valence anion is adiabatically stable with respect to the neutral molecule by 40 meV. The anion is characterized by a vertical detachment energy of 0.60 eV. To obtain accurate estimates of the vertical and adiabatic electron binding energies, a scheme was applied in which electronic energy contributions from various levels of theory were added, each of them extrapolated to the corresponding basis-set limit. The MP2 basis-set limits were also evaluated using an explicitly correlated approach, and the results of these calculations are in agreement with the extrapolated values. A remarkable feature of the valence anionic state is that the adiabatic electron binding energy is positive but smaller than the adiabatic electron binding energy of the dipole-bound state. [ABSTRACT FROM AUTHOR]

The basis set limit Møller-Plesset second-order equilibrium bond lengths of He2, Be2, and Ne2, accurate to 0.01a0, are computed to be 5.785a0, 5.11a0, and 6.05a0. The corresponding binding energies are 22.4±0.1, 2180±20, and 86±2 μEh, respectively. An accuracy of 95% in the binding energy requires an aug-cc-pV6Z basis or larger for conventional Møller-Plesset theory. This accuracy is obtained using an aug-cc-pV5Z basis if geminal basis functions with a linear correlation factor are included and with an aug-cc-pVQZ basis if the linear correlation factor is replaced by exp(-γr12) with γ=1. The correlation factor r12 exp(-γr12) does not perform as well, describing the atom more efficiently than the dimer. The geminal functions supplement the orbital basis in the description of both the short-range correlation, at electron coalescence, and the long-range dispersion correlation and the values of γ that give the best binding energies are smaller than those that are optimum for the atom or the dimer. It is important to sufficiently reduce the error due to the resolution of the identity approximation for the three- and four-electron integrals and we recommend the complementary auxiliary basis set method. The effect of both orbital and geminal basis set superposition error must be considered to obtain accurate binding energies with small orbital basis sets. In this respect, we recommend using exp(-γr12) with localized orbitals and the original orbital-variant formalism. [ABSTRACT FROM AUTHOR]

The basis set limit Møller-Plesset second-order equilibrium bond lengths of He2, Be2, and Ne2, accurate to 0.01a0, are computed to be 5.785a0, 5.11a0, and 6.05a0. The corresponding binding energies are 22.4±0.1, 2180±20, and 86±2 μEh, respectively. An accuracy of 95% in the binding energy requires an aug-cc-pV6Z basis or larger for conventional Møller-Plesset theory. This accuracy is obtained using an aug-cc-pV5Z basis if geminal basis functions with a linear correlation factor are included and with an aug-cc-pVQZ basis if the linear correlation factor is replaced by exp(-γr12) with γ=1. The correlation factor r12 exp(-γr12) does not perform as well, describing the atom more efficiently than the dimer. The geminal functions supplement the orbital basis in the description of both the short-range correlation, at electron coalescence, and the long-range dispersion correlation and the values of γ that give the best binding energies are smaller than those that are optimum for the atom or the dimer. It is important to sufficiently reduce the error due to the resolution of the identity approximation for the three- and four-electron integrals and we recommend the complementary auxiliary basis set method. The effect of both orbital and geminal basis set superposition error must be considered to obtain accurate binding energies with small orbital basis sets. In this respect, we recommend using exp(-γr12) with localized orbitals and the original orbital-variant formalism. [ABSTRACT FROM AUTHOR]

As known since about two decades, R12 methods, which include terms linear in the interelectronic distance r12 in the wave function, improve substantially the basis set convergence of the ground state correlation energy. In a previous study, however, it was found that the same approach does not give a similar systematic improvement if applied to excited states in the framework of coupled cluster response theory. In the present work, we examine the reason for this behavior and show that the inclusion of additional orbitals in the construction of the r12 pair functions leads to an enhanced basis set convergence (and thus a balanced description) also for the excited states. [ABSTRACT FROM AUTHOR]

Reliable thermochemical data for the reaction SO3+H2O⇔SO3·H2O (1a) are of crucial importance for an adequate modeling of the homogeneous H2SO4 formation in the atmosphere. We report on high-level quantum chemical calculations to predict the binding energy of the SO3·H2O complex. The electronic binding energy is accurately computed to De=40.9±1.0 kJ/mol=9.8±0.2 kcal/mol. By using harmonic frequencies from density functional theory calculations (B3LYP/cc-pVTZ and TPSS/def2-TZVP), zero-point and thermal energies were calculated. From these data, we estimate D0=-ΔH1a0(0 K)=7.7±0.5 kcal/mol and ΔH1a0(298 K)=-8.3±1.0 kcal/mol. [ABSTRACT FROM AUTHOR]

To reduce remaining basis-set errors in the determination of molecular equilibrium geometries, a basis-set extrapolation (BSE) scheme is suggested for the forces used in geometry optimizations. The proposed BSE scheme is based on separating the Hartree-Fock and electron-correlation contributions and uses expressions obtained by straightforward differentiation of well established extrapolation formulas for energies when using basis sets from Dunning’s hierarchy of correlation-consistent basis sets. Comparison with reference data obtained at the R12 coupled-cluster level [CCSD(T)-R12] demonstrates that BSE significantly accelerates the convergence to the basis-set limit, thus leading to improvements comparable to or even better than those obtained by increasing the cardinal number in the used basis set by one. However, BSE alone is insufficient to improve agreement with experiment, even after additional consideration of inner-shell correlation and quadruple-excitation effects (mean error and standard deviation with extrapolation are -0.014 and 0.047 pm in comparison with mean error and standard deviation of -0.002 and 0.036 pm without extrapolation). Improvement is obtained only when other contributions of similar magnitude as the BSE contributions (e.g., pentuple-excitation effects and relativistic effects) are also considered. A rather large discrepancy (of the order of a few tenths of a picometer) is observed for the F2 molecule indicating an enhanced basis-set requirement for the various contributions in this case. [ABSTRACT FROM AUTHOR]

A formalism is presented for the calculation of relativistic corrections to molecular electronic energies and properties. After a discussion of the Dirac and Breit equations and their first-order Foldy-Wouthuysen [Phys. Rev. 78, 29 (1950)] transformation, we construct a second-quantization electronic Hamiltonian, valid for all values of the fine-structure constant α. The resulting α-dependent Hamiltonian is then used to set up a perturbation theory in orders of α2, using the general framework of time-independent response theory, in the same manner as for geometrical and magnetic perturbations. Explicit expressions are given to second order in α2 for the Hartree-Fock model. However, since all relativistic considerations are contained in the α-dependent Hamiltonian operator rather than in the wave function, the same approach may be used for other wave-function models, following the general procedure of response theory. In particular, by constructing a variational Lagrangian using the α-dependent electronic Hamiltonian, relativistic corrections can be calculated for nonvariational methods as well. [ABSTRACT FROM AUTHOR]

Coupled-cluster response theory for vertical excitation energies within the second-order approximate coupled-cluster singles-and-doubles model CC2, including linear-r12 corrections, is derived and implemented for Ansätze 1 and 2 of R12 theory. An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation in order to calculate the three- and four-electron integrals needed in R12 theory. The basis set convergence is investigated for a selected set of atoms and small molecules and it is found that in many cases the convergence is not improved. An analysis of the different contributions to excitation energies shows that the present scheme for the construction of the R12 pair functions leads in response theory to an unbalanced description of ground- and excited-state wave functions and needs to be generalized to carry the high accuracy of R12 methods over to response theory. [ABSTRACT FROM AUTHOR]

The frequency-dependent electric field-induced second harmonic generation (ESHG) second hyperpolarizabilities γ of neon, argon, and krypton are calculated using the approximate coupled cluster triples model CC3. Systematic basis set investigations are carried out to establish basis set limits, and scalar relativistic effects are accounted for by direct perturbation theory. To estimate higher-order correlation effects, full configuration-interaction results are used to benchmark the accuracy of CC3. The best theoretical estimates obtained thereby for the static second hyperpolarizabilities γ0 are 107.4, 1159, and 2589 a.u. for neon, argon, and krypton, respectively. These values as well as the results for the dispersion curve of the parallel component γ∥ agree well with the latest experimental values from electric field-induced second harmonic generation. In addition, the dispersion of the perpendicular component γ⊥ and the hyperpolarizability ratios γ∥/γ⊥ has been studied for the first time on a consistently correlated ab initio level. The analysis of the results indicates that, in particular for neon and krypton, the presently available experimental values are flawed. [ABSTRACT FROM AUTHOR]

We have investigated the correlation factors exp(-ζr12), r12 exp(-ζr12), erfc(ζr12), and r12 erfc(ζr12) in place of the linear-r12 term for use in explicitly correlated electronic-structure methods. The accuracy obtained with all of these correlation factors is significantly greater than that obtained with the plain correlation factor r12. Polarization functions that are more diffuse than those of standard basis sets give even better results. The correlation factor exp(-ζr12) is very close to the optimum correlation factor for helium and outperforms the others. [ABSTRACT FROM AUTHOR]

The analytic calculation of first-order properties has been implemented in the DALTON program at the level of explicitly correlated second-order Mo\ller-Plesset perturbation theory (MP2-R12). The implementation has been accomplished for MP2-R12 theory based on standard approximations A, A′, and B, using an auxiliary basis for the resolution-of-the-identity approximation, with and without a frozen core. MP2-R12 first-order molecular properties have been calculated analytically for a few small test molecules. For BH and HF, the MP2-R12 results were supplemented with explicitly correlated coupled-cluster calculations (but at this level from numerical derivatives) including vibrational and relativistic corrections. [ABSTRACT FROM AUTHOR]

A simplified singles-and-doubles linear-r12 corrected coupled-cluster model, denoted CCSD(R12), is proposed and compared with the complete singles-and-doubles linear-r12 coupled-cluster method CCSD-R12. An orthonormal auxiliary basis set is used for the resolution-of-the-identity approximation to calculate three-electron integrals needed in the linear-r12 Ansatz. Basis-set convergence is investigated for a selected set of atoms and small molecules. In a large basis, the CCSD(R12) model provides an excellent approximation to the full linear-r12 energy contribution, whereas the magnitude of this contribution is significantly overestimated at the level of second-order perturbation theory. [ABSTRACT FROM AUTHOR]

First-order relativistic corrections to the energy of closed-shell molecular systems are calculated, using all terms in the two-component Breit–Pauli Hamiltonian. In particular, we present the first implementation of the two-electron Breit orbit–orbit integrals, thus completing the first-order relativistic corrections within the two-component Pauli approximation. Calculations of these corrections are presented for a series of small and light molecules, at the Hartree–Fock and coupled-cluster levels of theory. Comparisons with four-component Dirac–Coulomb–Breit calculations demonstrate that the full Breit–Pauli energy corrections represent an accurate approximation to a fully relativistic treatment of such systems. The Breit interaction is dominated by the spin–spin interaction, the orbit–orbit interaction contributing only about 10% to the total two-electron relativistic correction in molecules consisting of light atoms. However, the relative importance of the orbit–orbit interaction increases with increasing nuclear charge, contributing more than 20% in H2S. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In the framework of second-order Møller—Plesset linear-r12 MP2-R12 perturbation theory, a method is developed and implemented that uses an auxiliary basis set for the resolution-of-the-identity RI approximation for the three- and four-electron integrals. In contrast to previous work, the two-electron integrals that must be evaluated never involve more than one auxiliary basis function. The new method therefore scales linearly with the number of auxiliary basis functions and is much more efficient than the previous one, which scaled quadratically. A general formulation of MP2-R12 theory is presented for various ansätze, approximations, and orbitals (canonical or localized). The new method is assessed by computations of the valence-shell second-order Møller—Plesset correlation energy of a few small closed-shell systems. The preliminary calculations indicate that the difference between the new and previous methods is about one order of magnitude smaller than the errors that occur due to basis-set truncations and RI approximations and under the assumptions of generalized and extended Brillouin conditions. [ABSTRACT FROM AUTHOR]

The basis-set convergence of cc-pVXZ basis sets is investigated for the MP2 and CCSD equilibrium bond distances and harmonic frequencies of BH, HF, CO, N[sub 2], and F[sub 2] by comparing with explicitly correlated R12 results. The convergence is, in general, smooth but slow—for example, for harmonic frequencies at the quadruple-zeta level, the basis-set error is typically 7 cm[sup -1]; at the sixtuple-zeta level, it is about 2 cm[sup -1]. For most constants, the convergence can be accelerated by using a two-point linear extrapolation procedure. Equilibrium bond distances, harmonic frequencies, anharmonic contributions, vibration-rotation interaction constants, and rotational constants for the vibrational ground state have been calculated for the same set of molecules using standard wave function and basis-set levels of ab initio theory. The accuracy of the calculated constants has been established by carrying out a statistical analysis of the deviations with respect to experiment. The largest errors for bond distances and harmonic frequencies calculated at the core-corrected CCSD(T)/cc-pV6Z level are 0.4 pm and 13.4 cm[sup -1], respectively. Much smaller errors occur for the anharmonic contributions. [ABSTRACT FROM AUTHOR]

In explicitly correlated Møller–Plesset (MP2-R12) methods, the first-order wave function is expanded not only in terms of products of one-electron functions—that is, orbitals—but also in terms of two-electron functions that depend linearly on the interelectronic coordinates r[sub ij]. With these functions, three- and four-electron integrals occur, but these integrals can be avoided by inserting a resolution of the identity (RI) in terms of the one-electron basis. In previous work, only one single basis was used for both the electronic wave function and the RI approximation. In the present work, a new computational approach is developed that uses an auxiliary basis set to represent the RI. This auxiliary basis makes it possible to employ standard basis sets in explicitly correlated MP2-R12 calculations.© 2002 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Starting from the Le´vy-Leblond equation, which is the four-component nonrelativistic limit of the Dirac equation, a direct perturbation theory of magnetic properties and relativistic corrections is developed and implemented for point-charge and finite nuclei. The perturbed small components are regularized by projecting them onto an auxiliary small-component basis of Gaussian functions. The relevant operators and matrix elements are derived for the point-nuclear and Gaussian nuclear models. It is demonstrated how the usual paramagnetic spin-orbit, Fermi-contact, and spin-dipole integrals of Ramsey’s theory can be evaluated in the same manner as field and field-gradient integrals—that is, as derivatives of potential-energy integrals. A few illustrative calculations are performed. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The accuracy of atomization energies obtained from explicitly correlated coupled-cluster R12 calculations (CC-R12)—including single and double excitation operators (CCSD-R12) and a posteriori perturbative corrections for triple excitations [CCSD[T]-R12 and CCSD(T)-R12]—is studied for CH[sub 2]([sup 1]A[sub 1]), NH[sub 3], H[sub 2]O, HF, N[sub 2], CO, and F[sub 2]. The basis-set convergence with functions of high angular momentum is demonstrated. Unlike for conventional calculations, already the spdf saturation on nonhydrogen atoms and spd saturation on hydrogen are sufficient for CC-R12 calculations to provide results accurate to within 1 kJ/mol of the limit of a complete basis. Remaining small uncertainties at the CCSD[T]-R12 or CCSD(T)-R12 levels are attributed to the insufficient convergence within the coupled-cluster hierarchy towards the limit of full configuration interaction. It is shown that near the basis-set limit (as provided by CC-R12 calculations) the CCSD[T] variant of the triples correction gives, on average, results closer to the experimental data than its CCSD(T) counterpart. Approximate error bars are estimated by one single CC-R12 calculation from the difference between the CCSD[T] and CCSD(T) methods and from the second-order electronic cusp correction in standard approximation B. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The accuracy of standard ab initio wave-function calculations of atomization energies and reaction enthalpies has been assessed by comparing with experimental data for 16 small closed-shell molecules and 13 isogyric reactions. The investigated wave-function models are Hartree-Fock (HF), Møller-Plesset second-order perturbation theory (MP2), coupled-cluster theory with singles and doubles excitations (CCSD) and CCSD with perturbative triple-excitation corrections [CCSD(T)]; the one-electron basis sets used are the correlation-consistent cc-pVxZ and cc-pCVxZ basis sets with cardinal numbers x=D, T, Q, 5, and 6. Results close to the basis-set limit have been obtained by using two-point extrapolations. In agreement with previous studies, it is found that the intrinsic error of the CCSD(T) method is less than chemical accuracy (≈4 kJ/mol) for both atomization energies and reaction enthalpies. The mean and maximum absolute errors of the best CCSD(T) calculations are 0.8 and 2.3 kJ/mol for the atomization energies and 1.0 and 2.3 kJ/mol for the reaction enthalpies. Chemical accuracy is obtained already from the extrapolations based on the cc-pCVTZ and cc-pCVQZ basis sets—with mean and maximum absolute errors of 1.7 and 4.0 kJ/mol for atomization energies and 1.3 and 3.1 kJ/mol for reaction enthalpies. The intrinsic errors of the Hartree-Fock, MP2, and CCSD wave-function models are significantly larger than for CCSD(T). For CCSD and MP2, the mean absolute errors in the basis set limit are about 32 kJ/mol for the atomization energies and about 10 and 15 kJ/mol, respectively, for the reaction enthalpies. For the Hartree-Fock model, the mean absolute errors are 405 and 29 kJ/mol for atomization energies and reaction enthalpies, respectively. Correlation of the core electrons is important in order to obtain accurate results with CCSD(T). Without compromising the accuracy, the core contribution may be calculated with a basis set that has one cardinal... [ABSTRACT FROM AUTHOR]

Computes the Hartree-Fock approximation and correlation contributions to the interaction energy of hydrogen-bonded complexes in conventional calculations employing the aug-cc-pVXZ series of basis sets. Examination of the basis set convergence of the interaction energy; Findings indicating that Hartree-Fock interaction energies converge very unsystematically.

Studies the high-level ab initio computations of structures and relative energies of two isomers of the carbon dioxide trimer. Computational details; Slipped parallel and T-shaped dimmers; Interaction energies of the cyclic trimer.

Examines the interaction between two harmonic function (HF) molecules as a function of all six internal coordinates. Details on ab initio approach; Representation of HF monomer properties; Characterization of hypersurfaces through stationary point analysis.