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Due to an unfortunate error, an exchange contribution was missing in the computed core-ionization potentials collected in Table III of Ref. 1. The revised values of the ionization potentials are collected in Table I below. Even though the revision does not alter the main conclusions of our previous study, it does deteriorate the agreement between CCSD results and experiment. We note that this is not due to the core-valence separation itself, as we verified by applying the perturbative correction to the ionization potentials. (table presented).

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree–Fock, Kohn–Sham, multiconfigurational self-consistent-field, Møller–Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms. © 2013 John Wiley & Sons, Ltd. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, (CC BY-NC-ND 3.0)

Large differences have been reported in previous SCF calculations of the NMR shielding tensor of the ethylenic carbon atom in tetrachlorocyclopropene. Our calculations show that these differences are due to the use of different molecular geometries, not to differences in the methods applied to obtain gauge-invariance. © 1995 Taylor & Francis Ltd.

We present a novel multiscale approach to study the electronic structure of open shell molecular systems embedded in an external environment. The method is based on the coupling of multilevel Hartree-Fock (MLHF) and Density Functional Theory (MLDFT), suitably extended to the unrestricted formalism, to Molecular Mechanics (MM) force fields (FF). Within the ML region, the system is divided into active and inactive parts, thus describing the most relevant interactions (electrostatic, polarization, and Pauli repulsion) at the quantum level. The surrounding MM part, which is formulated in terms of nonpolarizable or polarizable FFs, permits a physically consistent treatment of long-range electrostatics and polarization effects. The approach is extended to the calculation of hyperfine coupling constants and applied to selected nitroxyl radicals in an aqueous solution.

We introduce the concept of fragment localized molecular orbitals (FLMOs), which are Hartree-Fock molecular orbitals localized in specific fragments constituting a molecular system. In physical terms, we minimize the local electronic energies of the different fragments, at the cost of maximizing the repulsion between them. To showcase the approach, we rationalize the main interactions occurring in large biological systems in terms of interactions between the fragments of the system. In particular, we study an anticancer drug intercalated within DNA and retinal in anabaena sensory rhodopsin as prototypes of molecular systems embedded in biological matrixes. Finally, the FLMOs are exploited to rationalize the formation of two oligomers, prototypes of amyloid diseases, such as Parkinson and Alzheimer.

We introduce a novel density-based multilevel approach in density functional theory. In this multilevel density functional theory (MLDFT), the system is partitioned in an active and an inactive fragment, and all interactions are retained between the two parts. In MLDFT, the Kohn-Sham equations are solved in the MO basis for the active part only, while keeping the inactive density frozen. This results in a reduction of computational cost. We outline the theory and implementation, and discuss applications to aqueous solutions of methyloxirane and glycidol., Comment: 33 pages and 9 figures

In coupled cluster theory, the electronic states are biorthonormal in the sense that the left states are orthonormal to the right states. Here, we present an extension of this formalism to a left and right total molecular wave function. Starting from left and right Born-Huang expansions, we derive projected Schrödinger equations for the left and right nuclear wave functions. Observables may be extracted from the resulting wave function pair using standard expressions. The formalism is shown to be invariant under electronic basis transformations, such as normalization of the electronic states. Consequently, the nonadiabatic coupling elements can be expressed with biorthonormal electronic wave functions. Calculating normalization factors that scale as full configuration interaction is not necessary, contrary to claims in the literature. For nonadiabatic nuclear dynamics, we need expressions for the derivative couplings in the biorthonormal formalism. These are derived in a Lagrangian framework.

We introduce a density-based multilevel Hartree-Fock (HF) method where the electronic density is optimized in a given region of the molecule (the active region). Active molecular orbitals (MOs) are generated by a decomposition of a starting guess atomic orbital (AO) density, whereas the inactive MOs (which constitute the remainder of the density) are never generated or referenced. The MO formulation allows for a significant dimension reduction by transforming from the AO basis to the active MO basis. All interactions between the inactive and active regions of the molecule are retained, and an exponential parametrization of orbital rotations ensures that the active and inactive density matrices separately, and in sum, satisfy the symmetry, trace, and idempotency requirements. Thus, the orbital spaces stay orthogonal, and furthermore, the total density matrix represents a single Slater determinant. In each iteration, the (level-shifted) Newton equations in the active MO basis are solved to obtain the orbital transformation matrix. The approach is equivalent to variationally optimizing only a subset of the MOs of the total system. In this orbital space partitioning, no bonds are broken and no a priori orbital assignments are carried out. In the limit of including all orbitals in the active space, we obtain an MO density-based formulation of full HF.

We present a novel energy-based localization procedure able to localize molecular orbitals into specific spatial regions. The method is applied to several cases including both conjugated and non-conjugated systems. The obtained localized molecular orbitals are used in a multiscale framework based on the multilevel Hartree-Fock approach. An almost perfect agreement with reference values is achieved for both ground state properties, such as dipole moments, and local excitation energies calculated at the coupled cluster level. The proposed approach is useful to extend the application range of high level electron correlation methods. In fact, the reduced number of molecular orbitals can lead to a large reduction in the computational cost of correlated calculations., 29 pages and 7 figures

We have calculated the optical rotation at λ = 589 nm for 45 fluorinated alcohols, amines, amides, and esters using both time-dependent density functional theory (TDDFT) with the CAM-B3LYP functional and the second-order approximate coupled-cluster singles and doubles (CC2) method, where the aug-cc-pVDZ basis set was adopted in both methods. Comparison of CAM-B3LYP and CC2 results to experiments illustrates that both methods are able to reproduce the experimental optical rotation results for both sign and magnitude. Several conformers for molecules containing the benzyloxy and naphthalene groups needed to be considered to obtain consistent signs with experiments, and these conformers are discussed in detail. We have also used a two-point inverse power extrapolation of the basis set to investigate the optical rotation in the basis set limit at the CC2 level, however, we only found small differences compared to the aug-cc-pVTZ results. Our results demonstrate that the least computationally expensive method investigated here, the CAM-B3LYP functional with the aug-cc-pVDZ basis set, is a reliable method to predict the optical rotation for large molecules and thereby the absolute configuration of chiral molecules.

The high resolution near edge X-ray absorption fine structure spectrum of nitrogen displays the vibrational structure of the core-excited states. This makes nitrogen well suited for assessing the accuracy of different electronic structure methods for core excitations. We report high resolution experimental measurements performed at the SOLEIL synchrotron facility. These are compared with theoretical spectra calculated using coupled cluster theory and algebraic diagrammatic construction theory. The coupled cluster singles and doubles with perturbative triples model known as CC3 is shown to accurately reproduce the experimental excitation energies as well as the spacing of the vibrational transitions. The computational results are also shown to be systematically improved within the coupled cluster hierarchy, with the coupled cluster singles, doubles, triples, and quadruples method faithfully reproducing the experimental vibrational structure. This is the authors’ accepted and refereed manuscript to the article. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Journal of Chemical Physics and may be found at https://doi.org/10.1063/1.5011148

Sodium intercalation and adsorption on graphitic carbon plays an important role in cathode wear during aluminium electrolysis and is relevant for sodium ion battery (NIB) applications. We present a parameter set for the ReaxFF formalism trained to describe sodium interactions with graphitic carbon. The force field developed reproduce the training data with reasonable accuracy and displays qualitatively adequate predictive power. The force field is applied in hybrid grand canonical Monte Carlo-molecular dynamics (GC-MC/MD) simulations of model systems representative of sodium intrusion in graphitic carbon cathodes used in aluminium electrolysis.

We present chemically accurate potential energy curves of CH4, CO2 and H2 moving through hexagonal water rings, calculated by CCSD(T)/aug-cc-pVTZ with counterpoise correction. The barriers are extracted from a potential energy surface obtained by allowing the water ring to expand while the gas molecule diffuses through. State-of-the-art XC-functionals are evaluated against the CCSD(T) potential energy surface.

In this work, interactions between carboxylate ions and calcium or sodium ions are investigated via density functional theory (DFT). Despite the ubiquitous presence of these interactions in natural and industrial chemical processes, few DFT studies on these systems exist in the literature. Special focus has been placed on determining the influence of the multibody interactions (with up to 4 carboxylates and one metal ion) on an effective pair-interaction potential, such as those used in molecular mechanics (MM). Specifically, DFT calculations are employed to quantify an effective pair-potential that implicitly includes multibody interactions to construct potential energy curves for carboxylate-metal ion pairs. The DFT calculated potential curves are compared to a widely used molecular mechanics force field (OPLS-AA). The calculations indicate that multibody effects do influence the energetic behavior of these ionic pairs and the extent of this influence is determined by a balance between (a) charge transfer from the carboxylate to the metal ions which stabilizes the complex and (b) repulsion between carboxylates, which destabilizes the complex. Additionally, the potential curves of the complexes with 1 and 2 carboxylates and one counterion have been examined to higher separation distance (20 Å) by the use of relaxed scan optimization and constrained density functional theory (CDFT). The results from the relaxed scan optimization indicate that near the equilibrium distance, the charge transfer between the metal ion and the deprotonated carboxylic acid group is significant and leads to non-negligible differences between the DFT and MM potential curves, especially for calcium. However, at longer separation distances the MM calculated interaction potential functions converge to those calculated with CDFT, effectively indicating the approximate domain of the separation distance coordinate where charge transfer between the ions is occurring.

In this article, we present a black-box approach for the selection of orbital spaces when computing core excitation energies in the multilevel coupled cluster (MLCC) framework. Information available from the lower level of theory is used to generate correlated natural transition orbitals (CNTOs) for the high-level calculation by including both singles and doubles information in the construction of the transition orbitals. The inclusion of the doubles excitation information is essential to obtain a set of orbitals that all contain physical information, in contrast to the natural transition orbitals where only a small subset of the virtual orbitals contains physical information. The CNTOs may be included in an active space based on a cutoff threshold for the eigenvaluescorresponding to the orbitals. We present MLCC results for core excitation energies calculated using coupled cluster singles and doubles (CCSD) in the inactive space and CCSD with perturbative triples (CC3) in the active space. The use of CNTOs results in small errors compared to full CC3. Published by AIP Publishing. Locked until 31.3.2018 due to copyright restrictions. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Journal of Chemical Physics and may be found at https://aip.scitation.org/doi/full/10.1063/1.4979908

Optical rotations of several conformers of four fluorinated molecules containing the 1-naphthalene or 4-(benzyloxy)phenyl group at the stereocenter have been calculated both in the gas phase and in an aqueous environment. For the compounds containing the 4-(benzyloxy)phenyl group, solvent effects on the optical rotations have also been investigated in chloroform as solvent. Optical rotations have been obtained by time-dependent density functional theory (TDDFT) with the CAM-B3LYP functional and the aug-cc-pVDZ basis set at λ = 589 nm. Implicit and explicit solvent effects were investigated through the polarizable continuum model (PCM) and a microsolvation approach in conjunction with PCM, respectively. In the latter model, solvent molecules are considered as an explicit solvent and their positions are obtained by geometry optimizations for different conformers of the chiral molecule. For molecules containing the 1-naphthalene group, this model gives the same optical rotation signs for all conformers as compared to both gas phase and PCM results and reduces absolute deviations between calculations and experiment. Also, the microsolvation model reproduces the sign of the experimental optical rotations for the molecules containing the 4-(benzyloxy)phenyl group using both water and chloroform as solvent. In a microsolvation model, however, the water and chloroform solvent molecules have similar hydrogen bonds but different effects on the conformation and thereby on the optical rotation since one dihedral angle, having a large effect on the optical rotation, is strongly sensitive to hydrogen bonding to water but not to chloroform. Our investigations demonstrate that a microsolvation approach in conjunction with PCM predicts optical rotations in reasonable agreements with experiments for both sign and magnitude. Copyright © 2017 American Chemical Society. This is the authors' accepted and refereed manuscript to the article. Locked until May 31, 2018 due to copyright restrictions

We derive the crossing conditions at conical intersections between electronic states in coupled cluster theory, and show that if the coupled cluster Jacobian matrix is nondefective, two (three) independent conditions are correctly placed on the nuclear degrees of freedom for an inherently real (complex) Hamiltonian. Calculations using coupled cluster theory on an $2 {^{1}}A' / 3 {^{1}}A'$ conical intersection in hypofluorous acid illustrate the nonphysical artifacts associated with defects at accidental same-symmetry intersections. In particular, the observed intersection seam is folded about a space of the correct dimensionality, indicating that minor modifications to the theory are required for it to provide a correct description of conical intersections in general. We find that an accidental symmetry allowed $1 {^{1}}A" / 2 {^{1}}A"$ intersection in hydrogen sulfide is properly described, showing no artifacts as well as linearity of the energy gap to first order in the branching plane., Comment: 9 pages and 4 figures

The motion of electrons and nuclei in photochemical events often involve conical intersections, degeneracies between electronic states. They serve as funnels for nuclear relaxation - on the femtosecond scale - in processes where the electrons and nuclei couple nonadiabatically. Accurate ab initio quantum chemical models are essential for interpreting experimental measurements of such phenomena. In this paper we resolve a long-standing problem in coupled cluster theory, presenting the first formulation of the theory that correctly describes conical intersections between excited electronic states of the same symmetry. This new development demonstrates that the highly accurate coupled cluster theory can be applied to describe dynamics on excited electronic states involving conical intersections., Comment: 8 pages and 3 figures and including supporting information (with corrections and improved notation)

Optical rotation of 14 molecules containing the pyrrole group is calculated by employing both time-dependent density functional theory (TDDFT) with the CAM-B3LYP functional and the second-order approximate coupled-cluster singles and doubles (CC2) method. All optical rotations have been provided using the aug-cc-pVDZ basis set at λ = 589 nm. The two methods predict similar results for both sign and magnitude for the optical rotation of all molecules. The obtained signs are consistent with experiments as well, although several conformers for four molecules needed to be studied to reproduce the experimental sign. We have also calculated excitation energies and rotatory strengths for the six lowest lying electronic transitions for several conformers of the two smallest molecules and found that each rotatory strength has various contributions for each conformer which can cause different optical rotations for different conformers of a molecule. Our results illustrate that both methods are able to reproduce the experimental optical rotations, and that the CAM-B3LYP functional, the least computationally expensive method used here, is an applicable and reliable method to predict the optical rotation for these molecules in line with previous studies.

A new implementation of the coupled cluster singles and doubles with approximate triples correction method [CCSD(T)] using Cholesky decomposition of the orbital energy denominators is described. The new algorithm reduces the scaling of CCSD(T) from N-7 to N-6, where N is the number of orbitals. The Cholesky decomposition is carried out using simple analytical expressions that allow us to evaluate a priori the order in which the decomposition should be carried out and to obtain the relevant parts of the vectors whenever needed in the calculation. Several benchmarks have been carried out comparing the performance of the conventional and Cholesky CCSD(T) implementations. The Cholesky implementation shows a speed-up factor larger than O-2/V, where O is the number of occupied and V the number of virtual orbitals, and in general at most 5 vectors are needed to get a precision of mu E-h. We demonstrate that the Cholesky algorithm is better suited for studying large systems. (c) 2010 Wiley Periodicals, Inc. Int J Quantum Chem 111: 349-355, 2011 (Less)

To further the understanding of the role of sodium in carbon cathode degradation in Hall-Heroult cells, we present potential energy surfaces and charge transfer curves for finite-size complexes of sodium intercalated between various polycyclic aromatic hydrocarbons. Calculations for lithium and potassium are included to highlight the disparate intercalation behaviour of the alkali metals in graphite intercalation compounds. Static energy barriers from density functional theory are used to compute macroscopic diffusion coefficients according to transition state theory. Comparing the calculated diffusion coefficient to experimental values from literature shed light on the role of lattice diffusion of sodium graphite intercalation compounds in sodium intrusion in graphitic carbon cathodes.

We have calculated the electronic optical rotation of seven molecules using coupled cluster singles-doubles (CCSD) and the second-order approximation (CC2) employing the aug-cc-pVXZ (X = D, T, or Q) basis sets. We have also compared to time-dependent density functional theory (TDDFT) by utilizing two functionals B3LYP and CAM-B3LYP and the same basis sets. Using relative and absolute error schemes, our calculations demonstrate that the CAM-B3LYP functional predicts optical rotation with the minimum deviations compared to CCSD at λ = 355 and 589.3 nm. Furthermore, our results illustrate that the aug-cc-pVDZ basis set provides the optical rotation in good agreement with the larger basis sets for molecules not possessing small-angle optical rotation at λ = 589.3 nm. We have also performed several two-point inverse power extrapolations for the basis set convergence, i.e., OR(∞) + AX(-n), using the CC2 model at λ = 355 and 589.3 nm. Our results reveal that a two-point inverse power extrapolation with the aug-cc-pVTZ and aug-cc-pVQZ basis sets at n = 5 provides optical rotation deviations similar to those of aug-cc-pV5Z with respect to the basis limit.

Core excited states are challenging to calculate, mainly because they are embedded in a manifold of high energy valence-excited states. However, their-locality makes their determination ideal for local correlation methods. In this paper, we demonstrate the performance of multilevel coupled cluster theory in computing core spectra both within the core valence separated and the asymmetric Lanczos implementations of coupled cluster linear response theory. We also propose a visualization-tool to analyze the excitations using the difference between the-ground-state and excited-state electron densities.

We present an efficient implementation of the closed shell multilevel coupled cluster method where coupled cluster singles and doubles (CCSD) is used for the inactive orbital space and CCSD with perturbative triples (CC3) is employed for the smaller active orbital space. Using Cholesky orbitals, the active space can be spatially localized and the computational cost is greatly reduced compared to full CC3 while retaining the accuracy of CC3 excitation energies. For the small organic molecules considered we achieve up to two orders of magnitude reduction in the computational requirements.

Benzene-fluorobenzene complexes are used as model systems to simulate the interactions of the SBB-HCAII protein-ligand complex. Using the second-order Moller-Plesset [MP2] and the coupled cluster singles and doubles including connected triple excitations models recently implemented with Cholesky decompositions we evaluate accurate interaction energies for several benzene-fluorobenzene van der Waals complexes. We consider edge-to-face interactions and compare the results to those from a recent MP2 study and to experimental findings. In contrast to experimental trends, we find that the interaction tends to decrease with increasing fluorination and conclude that benzene-fluorobenzene complexes are too simple to simulate the full SBB-HCAII protein-ligand system. (c) 2007 Elsevier B.V. All rights reserved. (Less)

We present a simple scheme to compute X-ray absorption spectra (e.g., near-edge absorption fine structure) and core ionisation energies within coupled cluster linear response theory. The approach exploits the so-called core-valence separation to effectively reduce the excitation space to processes involving at least one core orbital, and it can be easily implemented within any pre-existing coupled cluster code for low energy states. We further develop a perturbation correction that incorporates the effect of the excluded part of the excitation space. The correction is shown to be highly accurate. Test results are presented for a set of molecular systems for which well converged results in full space could be generated at the coupled cluster singles and doubles level of theory only, but the scheme is straightforwardly generalizable to all members of the coupled cluster hierarchy of approximations, including CC3.

The benzene–Ar lowest energy triplet state T1 intermolecular potential energy surface is evaluated using coupled cluster methods and the aug-cc-pVDZ basis set extended with a set of 3s3p2d1f1g midbond functions. This surface is characterized by an absolute minimum of −392.5 cm−1, where the argon atom is located on the benzene C6 axis at a distance of 3.5153 A, and has a general shape very close to the ground state S0 and the first singlet S1 excited state surfaces. Using the T1 potential, the intermolecular vibrational energy levels were evaluated and the results compared to those for the ground S0 and the excited S1 states. The calculated fundamental frequencies for the bending and the stretching modes are lower than those in the S1 state. The calculated data for the T1 state is expected to have the same accuracy as previously calculated data for the S1 state.

The second dielectric virial coefficients of helium and argon are investigated using a fully quantum statistical approach and recent accurate ab initio results for the interatomic potentials and the interaction-induced polarizabilities. We thereby extend a preceding investigation based on a semiclassical approach to include quantum effects. For helium the results support the findings of a previous study by Moszynski et al. [J. Chem. Phys. 247, 440 (1995)] that quantum effects are substantial for temperatures below 10 K, while they are practically negligible above 70 K. For argon special care is needed in the numerical integrations carried out in the quantum statistical calculation of the virial coefficients, due to the presence of quasibound states in the continuum and a slow convergence of the summation over the angular momentum. Here quantum effects are practically negligible in the range of temperatures experimentally investigated, i.e., between 243 and 408 K. As far as comparison with experimental data is concerned, large discrepancies are found for some of the low-temperature experimental measurements of helium. Agreement is also unsatisfactory for high temperatures for argon and experimental redetermination is suggested.

Using the coupled cluster singles and doubles including connected triples model and the augmented correlation consistent polarized valence double zeta basis set extended with a set of 3s3p2d1f1g midbond functions, ab initio helium–, neon–, and argon–cyclopropane ground state intermolecular potential energies are evaluated and fitted to an analytic function including up to four-body interactions. These are the first ab initio potential energy surfaces available for these complexes and are characterized by an absolute minimum of −73.3 cm−1 at a distance on the cyclopropane C3-axis of 3.291 A, −125.3 cm−1 at 3.435 A, and −301.1 cm−1 at 3.696 A for helium, neon, and argon, respectively. The bound van der Waals states are calculated. Two types of tunneling motion cause splittings of these levels: a C3 tunneling between the three equivalent local minima placed in the cyclopropane plane, and a C2 tunneling motion of the rare gas atom between the global minima above and below the cyclopropane plane.

Using the time-dependent Lagrangian response approach, the recently revived orbital optimized coupled cluster (OCC) model is reformulated using nonorthogonal orbital rotations in a manner that conserves the commutativity of the cluster excitation operators. The gauge invariance and the simple pole structure of the OCC linear response function are retained, while the dimension of the eigenvalue problem is reduced by a factor of 2. Restricting the cluster operator to double excitations, we have carried out the first implementation of gauge invariant coupled cluster response theory. Test calculations of the excitation energy, and length and velocity gauge oscillator strengths are presented for the lowest electric dipole allowed transitions of the CH + molecular ion and the Ne atom. Additionally, the excitation energies to the four lowest-lying states of water are calculated.

Using the random phase approximation and coupled cluster singles and doubles linear response theory in conjunction with two basis sets of augmented double-zeta quality and two nuclear geometries, we have calculated electronic absorption and natural circular dichroism spectra of (-)-trans-cyclooctene. We present a density functional theory optimized nuclear geometry whose ground state electric dipole moment and harmonic vibrational spectrum compare well with experimental data. The coupled cluster results obtained with this nuclear geometry are in good agreement with experimental electronic spectra, although the original interpretation of the most intense low-lying band as a π→π* transition is contradicted. © 2000 American Institute of Physics.

A highly accurate ab initio intermolecular potential energy surface for the benzene-argon van der Waals complex is evaluated using the coupled cluster singles and doubles model including connected triple excitations [CCSD(T)] model with an augmented correlation consistent polarized valence double zeta basis set extended with midbond functions. The vibrational energy levels obtained by full three-dimensional dynamical calculations are in excellent agreement with the available experimental data. © 1999 American Institute of Physics.

We present the first coupled cluster singles and doubles calculations of the scalar rotatory strength and the rotatory strength tensor, which determine the intensity of isotropic and oriented electronic circular dichroismspectra, respectively, for the ethylene chromophore of (−)-trans-cyclo-octene. Results for the oscillator strength of the ordinary electronic absorption spectra are also reported. The results are presented in pictorial form for seven different basis sets and two formally equivalent formulations of the intensity quantities. The theoretical results are compared with the experimental absorption and isotropic circular dichroismspectra of (+)-trans-cyclo-octene.

We formulate the time-dependent variational principle in the form of the Euler-Lagrange equations, and demonstrate that standard variational as well as nonvariational wave functions may be obtained from these. We also demonstrate how inherently real expectation values of Hermitian operators can be constructed for nonvariational wave functions by using the time-dependent Hellmann-Feynman theorem which, in turn, is a simple consequence of the Euler-Lagrange equations. The procedure is illustrated by derivation of time-dependent Hartree-Fock and of time-dependent coupled cluster theory. Finally we give the fundamental equations for molecular dynamics within semiclassical electron nuclear dynamics (END) with a classical description of the nuclei and coupled cluster description of the electrons. © 1998 American Institute of Physics.

Using London atomic orbitals and a recent parallel implementation of our second-order ab initio property code, we have determined the Hartree–Fock limit for the magnetizability of C60 to be −359±5 ppm cgs, in excellent agreement with earlier basis-set limit extrapolations. Using diamagnetic exaltation as a criterion for aromaticity, our calculations show that C60 is an aromatic molecule with a relative diamagnetic exaltation greater than that of benzene.

We present gauge-origin independent calculations of the Cotton‐Mouton effect of liquid water. The liquid is represented by a semi-continuum model such that the central molecule is surrounded by its first solvation shell, which explicitly accounts for the strong interaction between the water molecule of interest and its closest neighbors. The long-range interactions with the solvent are modeled by a dielectric continuum surrounding the water molecule and the first solvation shell. We employ large basis sets, using London atomic orbitals in order to obtain gauge-origin independent results close to the Hartree‐Fock limit. It is demonstrated that the direct interaction between neighboring molecules leads to a large effect on the calculated Cotton‐Mouton constant, which undergoes a sign change from the gas to liquid phase, as observed previously for the linear electro-optical effect @K. V. Mikkelsen et al., J. Chem. Phys 102, 9362 ~1995!#. Our best estimate for the molar Cotton‐Mouton constant, 238.1i10 220 G 22 cm 3 mol 21 ~corrected for local field effects!, is in reasonable agreement with the experimental value of 2118(15)i10 220 G 22 cm 3 mol 21 . We expect that the remaining discrepancy is mainly due to an inadequate treatment of electron correlation. © 1998 American Institute of Physics.@S0021-9606~98!50102-X#

Using a valence double-zeta polarization basis, full configuration-interaction (FCI) calculations are carried out on water at its equilibrium geometry and at geometries where the OH bond lengths are stretched until dissociation. At the same geometries and with the same basis set configuration interaction calculations at excitation levels up to hextuples, multireference singles doubles configuration interaction calculations, coupled cluster calculations at excitation levels up to quadruples, Møller-Plesset perturbation theory calculations through order fifteen, and complete active space second-order perturbation theory calculations are also carried out. The static correlation contribution increase with increasing bond length. The calculations show that the coupled cluster approach has a remarkable ability to describe even relatively large static correlation contributions. The single reference perturbation expansion breaks down for larger OH bond length, while the multireference approach preserves the accuracy for the whole potential curve. At the equilibrium geometry, FCI calculations have also been carried out for the lowest state of2A1,2B1, and2B2symmetry of H2O+, and the results compared with state of the art correlation results for total energies and ionization potentials (IP's). Differential energies (IP's) are obtained more accurately than absolute (total) energies in the size extensive coupled cluster and perturbation approaches. For the nonsize extensive configuration interaction method errors are obtained of the same size for differential and absolute energies. © 1996 American Institute of Physics.

An efficient and highly vectorized implementation of the coupled cluster singles and doubles (CCSD) model using a direct atomic integral technique is presented. The minimal number of n6processes has been implemented for the most time consuming terms and point group symmetry is used to further reduce operation counts and memory requirements. The significantly increased application range of the CCSD method is illustrated with sample calculations on several systems with more than 500 basis functions. Furthermore, we present the basic trends of an open ended algorithm and discuss the use of integral prescreening. © 1996 American Institute of Physics.

We present a size-extensive extension to the CC2 model that avoids the complications with quasi-degeneracies that are present in the CC2 model and related perturbation theory-based approaches. The formulation also provides a consistent model for treating different parts of a molecular system at different levels of electron correlation. Such a subsystem approach leads to large reductions in the computational requirements without compromising the accuracy. In this initial study, we focus on static molecular properties. © 2013 Copyright Taylor and Francis Group, LLC.

We present a detailed assessment of state-of-the-art exchange-correlation functionals. The assessment is carried out by comparing potential energy curves of van der Waals complexes of sodium and benzene calculated with density functional theory to extrapolated CCSD(T)/aug-cc-pVQZ values. According to the presented results, the Perdew-Burke-Ernzerhof functional (PBE) displays the best performance among the tested density functionals. PBE is the most accurate functional for the complexes studied, both in terms of absolute and relative accuracy. © 2013 Copyright Taylor and Francis Group, LLC.

The implementation of two simple ideas concerning the optimization of a many-electron ground state wavefunction is reported. Firstly, the wavefunction is written as a sum of non-orthogonal Slater determinants. Secondly, the optimization is carried out by adding one determinant at a time and determining the best possible orbitals to be used in that determinant. Technical details of gradient-optimization methods are included. Calculations on the electronic ground state of Be, BH and H2O indicate that near full-CI accuracy can be attained using a comparatively small number of determinants. Finally, it is conjectured that a geminal approach might provide an effective solution to the problem of initiating the optimization sequence for each successively added determinant. © 1993.

Decomposing the Hartree-Fock one-electron density matrix and a virtual pseudodensity matrix, we obtain an orthogonal set of normalized molecular orbitals with local character to be used in post-Hartree-Fock calculations. The applicability of the procedure is illustrated by calculating CCSD(T) energies and CCSD molecular properties in reduced active spaces. © 2010 American Institute of Physics.

A matrix decomposition method for the determination of the lowest eigenvalue of a Hermitian matrix is formulated as an approach to full configuration-interaction calculations on the ground state of many-electron systems. For a wavefunction of the form | ψ 〉 = ∑ | α,β 〉 C αβ the expansion coefficients are written as a separable sum of product terms, P α Q β The elements P a and Q β are then determined from the variation principle for each term. The corresponding Hermitian eigenvalue problem has a dimension which is essentially the square root of the dimension of the original problem. Preliminary calculations on the ground state of the beryllium atom indicate that nearly full configuration-interaction results can be obtained using a comparatively small number of product terms.

We introduce a response function formalism that enables smaller number of parameters than that defined in standard coupled cluster response theory. This is essential in the development of reduced scaling methods. The formalism is general and it applies to all parameterizations at all levels of the coupled cluster hierarchy. We show that to achieve physically reasonable results the parameterization must fulfill certain criteria. The linear response functions are derived and discussed in the context of optimized virtual orbitals and Cholesky decomposition of the cluster amplitudes. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

The computation of the frequency dependent linear and quadratic response functions is formulated at the full configuration interaction (FCI) level of theory. It is demonstrated that the frequency dependent polarizability (for real and imaginary frequencies) may be obtained with quadratic dependence on the error in the solution of the response equations. An efficient solution of the FCI response equations for large imaginary frequencies is developed. Initial application is to the Be atom in the standard 9s9p5d basis. Reported results include transition energies and dipole moments for the first few singlet and triplet S, P, and D states, the first polarizability at real and imaginary frequencies, the C6coefficient, and the static second hyperpolarizability. Comparison to prior theoretical results in this basis, and to experiment, is made where possible. It is the first time that many of these properties have been computed at the FCI level of theory for any system. © 1991 American Institute of Physics.

Using correlated ab initio methods, the polarizability of large [4n + 2]-annulenes is determined, showing that there exists an almost linear relation between the exaltation of magnetic susceptibility (a measure of aromaticity) and an equivalent enlargement of polarizability.

Using Cholesky decomposition and density fitting to approximate the electron repulsion integrals, an implementation of the complete active space self-consistent field (CASSCF) method suitable for large-scale applications is presented. Sample calculations on benzene, diaquo-tetra- μ -acetato-dicopper(II), and diuraniumendofullerene demonstrate that the Cholesky and density fitting approximations allow larger basis sets and larger systems to be treated at the CASSCF level of theory with controllable accuracy. While strict error control is an inherent property of the Cholesky approximation, errors arising from the density fitting approach are managed by using a recently proposed class of auxiliary basis sets constructed from Cholesky decomposition of the atomic electron repulsion integrals. © 2008 American Institute of Physics.

We present a novel approach to the calculation of the Coulomb and exchange contributions to the total electronic energy in self consistent field and density functional theory. The numerical procedure is based on the Cholesky decomposition and involves decomposition of specific Hadamard product matrices that enter the energy expression. In this way, we determine an auxiliary basis and obtain a dramatic reduction in size as compared to the resolution of identity (RI) method. Although the auxiliary basis is determined from the energy expression, we have complete control of the errors in the gradient or Fock matrix. Another important advantage of this method specific Cholesky decomposition is that the exchange energy and Fock matrix can be evaluated with a linear scaling effort contrary to the RI method or standard Cholesky decomposition of the two-electron integral matrix. The methods presented show the same scaling properties as the so-called local density fitting methods, but with full error control. © 2008 American Institute of Physics.

In this work we present a theoretical and experimental study of the i 3Π−g→b 3∑+u transition dipole moment in molecular hydrogen. By means of translational spectroscopy the functional dependence on internuclear distance of the transition dipole moment was directly probed. Selective excitation of the i 3Π−g, N=1 level, being unaffected by rotational couplings with other 3d singly excited states, allows for straightforward comparison with ab initio calculations. Excellent agreement is found.

We report second order Møller-Plesset (MP2) and MP2-F12 total energies on He, Ne, Ar, H2 O, C H4, C2 H2, C2 H4, and C6 H6, using the correlation consistent basis sets, aug-cc-pVXZ (X=D-7). Basis set extrapolation techniques are applied to the MP2 and MP2-F12/B methods. The performance of the methods is tested in the calculations of the atoms, He, Ne, and Ar. It is indicated that the two-point extrapolation of MP2-F12/B with the basis sets (X=5,6) is the most reliable. Similar accuracy is obtained using two-point extrapolated conventional MP2 with the basis sets (X=6,7). For the molecules investigated the valence MP2 correlation energy is estimated within 1 m Eh. © 2007 American Institute of Physics.