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Recent years have witnessed an increasing interest in time-dependent coupled-cluster (TDCC) theory for simulating laser-driven electronic dynamics in atoms and molecules, and for simulating molecular vibrational dynamics. Starting from the time-dependent bivariational principle, we review different flavors of single-reference TDCC theory with either orthonormal static, orthonormal time-dependent, or biorthonormal time-dependent spin orbitals. The time-dependent extension of equation-of-motion coupled-cluster theory is also discussed, along with the applications of TDCC methods to the calculation of linear absorption spectra, linear and low-order nonlinear response functions, highly nonlinear high harmonic generation spectra and ionization dynamics. In addition, the role of TDCC theory in finite-temperature many-body quantum mechanics is briefly described along with a few other application areas.

Molecular structure, one of the most central concepts of chemistry, has remained elusive from the perspective of all-particle quantum mechanics despite many efforts. Here, we propose a new definition of molecular structure applicable to arbitrary all-particle wavefunctions and implement a practical method based on Markov Chain Monte Carlo sampling and unsupervised machine learning. Application to the D3+ molecule shows unambiguously that it possesses an equilateral triangular structure. These results provide a major step forward in our understanding of molecular structure from fundamental physical principles.

Machine learning can make a strong contribution to accelerating the discovery of transition metal complexes (TMC). These compounds will play a key role in the development of new technologies for which there is an urgent need, including the production of green hydrogen from renewable sources. Despite the recent developments in machine learning for drug discovery and organic chemistry in general, the application of these methods to TMCs remains challenged by their higher complexity and the limited availability of large datasets. In this work, we report a representation for deep graph learning on TMCs – the natural quantum graph (NatQG), which leverages the electronic structure data available from natural bond orbital (NBO) analysis. This data was used to define both the topology and the information expressed by the NatQG graphs. At the topology level, two different NatQG flavors were developed: u-NatQG, with undirected edges, and d-NatQG, with edges directed along donor → acceptor orbital interactions. At the information level, the node and edge attribute vectors of both graphs contain NBO data, including natural charges and bond orders. The NatQG graphs were used to develop graph neural networks (GNNs) for the prediction of the quantum properties underlying the structure and reactivity of TMCs (e.g. HOMO-LUMO gap and polarizability). These models surpassed baselines based on traditional descriptors and performed at a level similar to, or higher than, state-of-the-art GNNs based on radial cutoffs. The results showed that the electronic structure information encoded by the models has a stronger impact on its accuracy than the geometric information. With the aim of benchmarking the GNNs, we also developed the transition metal quantum mechanics graph dataset (tmQMg), which provides the geometries, properties, and NatQG graphs of 60k TMCs.

Real-time simulations of laser-driven electron dynamics contain information about molecular optical properties through all orders in response theory. These properties can be extracted by assuming convergence of the power series expansion of induced electric and magnetic multipole moments. However, the accuracy relative to analytical results from response theory quickly deteriorates for higher-order responses due to the presence of high-frequency oscillations in the induced multipole moment in the time domain. This problem has been ascribed to missing higher-order corrections. We here demonstrate that the deviations are caused by nonadiabatic effects arising from the finite-time ramping from zero to full strength of the external laser field. Three different approaches, two using a ramped wave and one using a pulsed wave, for extracting electrical properties from real-time time-dependent electronic-structure simulations are investigated. The standard linear ramp is compared to a quadratic ramp, which is found to yield highly accurate results for polarizabilities, and first and second hyperpolarizabilities, at roughly half the computational cost. Results for the third hyperpolarizability are presented along with a simple, computable measure of reliability.

We present a derivation of real-time (RT) time-dependent orbital-optimized Møller–Plesset (TDOMP2) theory and its biorthogonal companion, time-dependent non-orthogonal OMP2 theory, starting from the time-dependent bivariational principle and a parametrization based on the exponential orbital-rotation operator formulation commonly used in the time-independent molecular electronic structure theory. We apply the TDOMP2 method to extract absorption spectra and frequency-dependent polarizabilities and first hyperpolarizabilities from RT simulations, comparing the results with those obtained from conventional time-dependent coupled-cluster singles and doubles (TDCCSD) simulations and from its second-order approximation, TDCC2. We also compare our results with those from CCSD and CC2 linear and quadratic response theories. Our results indicate that while TDOMP2 absorption spectra are of the same quality as TDCC2 spectra, including core excitations where optimized orbitals might be particularly important, frequency-dependent polarizabilities and hyperpolarizabilities from TDOMP2 simulations are significantly closer to TDCCSD results than those from TDCC2 simulations.

Local approximations facilitate the application of post-Hartree–Fock methods in the condensed phase, but simultaneously introduce errors leading to discontinuous potential-energy surfaces. In this work, we explore how these discontinuities arise in periodic systems, their implications, and possible ways of controlling them. In addition, we present a fully periodic Divide-Expand-Consolidate second-order Møller–Plesset approach using an attenuated resolution-of-the-identity approximation for the electron repulsion integrals and a convenient class to handle translation-symmetric tensors in block-Toeplitz format.

We demonstrate theoretically and numerically that laser-driven many-electron dynamics, as described by bivariational time-dependent coupled-cluster theory, may be analyzed in terms of stationary-state populations. Projectors heuristically defined from linear response theory and equation-of-motion coupled-cluster theory are proposed for the calculation of stationary-state populations during interaction with laser pulses or other external forces, and conservation laws of the populations are discussed. Numerical tests of the proposed projectors, involving both linear and nonlinear optical processes for the He and Be atoms, and for the LiH, CH$^+$, and LiF molecules, show that the laser-driven evolution of the stationary-state populations at the coupled-cluster singles-and-doubles (CCSD) level is very close to that obtained by full configuration-interaction theory provided all stationary states actively participating in the dynamics are sufficiently well approximated. When double-excited states are important for the dynamics, the quality of the CCSD results deteriorate. Observing that populations computed from the linear-response projector may show spurious small-amplitude, high-frequency oscillations, the equation-of-motion projector emerges as the most promising approach to stationary-state populations., 58 pages, 14 figures

MOLCAS/OpenMolcas is an ab initio electronic structure program providing a large set of computational methods from Hartree-Fock and density functional theory to various implementations of multiconfigurational theory. This article provides a comprehensive overview of the main features of the code, specifically reviewing the use of the code in previously reported chemical applications as well as more recent applications including the calculation of magnetic properties from optimized density matrix renormalization group wave functions. ispartof: JOURNAL OF CHEMICAL PHYSICS vol:152 issue:21 ispartof: location:United States status: published

The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

We present an investigation of the convergence behaviour of the local second-order Møller-Plesset perturbation theory (MP2) correlation energy toward the canonical result for three insulating crystals with either projected atomic orbitals (PAOs) or various orthonormal representations of the virtual orbital space. Echoing recent results for finite molecular systems, we find that significantly fewer PAOs than localised orthonormal virtual orbitals are required to reproduce the canonical correlation energy. We find no clear-cut correlation between conventional measures of orbital locality and the ability of the representation to span the excitation space of local domains. We show that the PAOs of the reference unit cell span parts of the excitation space that can only be reached with distant local orthonormal virtual orbitals.

The definiteness of the Mulliken and Dirac electron repulsion integral (ERI) matrices is examined for different classes of resolution-of-the-identity (RI) ERI approximations with particular focus on local fitting techniques. For global RI, robust local RI, and nonrobust local RI we discuss the definiteness of the approximated ERI matrices as well as the resulting bounds of Hartree, exchange, and total energies. Lower bounds of Hartree and exchange energy contributions are crucial as their absence may lead to variational instabilities, causing severe convergence problems or even convergence to a spurious state in self-consistent-field optimizations. While the global RI approximation guarantees lower bounds of Hartree and exchange energies, local RI approximations are generally unbounded. The robust local RI approximation guarantees a lower bound of the exchange energy but not of the Hartree energy. The nonrobust local RI approximation guarantees a lower bound of the Hartree energy but not of the exchange energy. These issues are demonstrated by sample calculations on carbon dioxide and benzene using the pair atomic RI approximation. © 2017 American Chemical Society

We investigate the numerical stability of time-dependent coupled-cluster theory for many-electron dynamics in intense laser pulses, comparing two coupled-cluster formulations with full configuration interaction theory. Our numerical experiments show that orbital-adaptive time-dependent coupled-cluster doubles (OATDCCD) theory offers significantly improved stability compared with the conventional Hartree-Fock-based time-dependent coupled-cluster singles-and-doubles (TDCCSD) formulation. The improved stability stems from greatly reduced oscillations in the doubles amplitudes, which, in turn, can be traced to the dynamic biorthonormal reference determinants of OATDCCD theory. As long as these are good approximations to the Brueckner determinant, OATDCCD theory is numerically stable. We propose the reference weight as a diagnostic quantity to identify situations where the TDCCSD and OATDCCD theories become unstable., Comment: 5 pages, 6 figures (supplemental material, 7 pages, 11 figures)

The formulation of the time-dependent Schrodinger equation in terms of coupled-cluster theory is outlined, with emphasis on the bivariational framework and its classical Hamiltonian structure. An indefinite inner product is introduced, inducing physical interpretation of coupled-cluster states in the form of transition probabilities, autocorrelation functions, and explicitly real values for observables, solving interpretation issues which are present in time-dependent coupled-cluster theory and in ground-state calculations of molecular systems under influence of external magnetic fields. The problem of the numerical integration of the equations of motion is considered, and a critial evaluation of the standard fourth-order Runge--Kutta scheme and the symplectic Gauss integrator of variable order is given, including several illustrative numerical experiments. While the Gauss integrator is stable even for laser pulses well above the perturbation limit, our experiments indicate that a system-dependent upper limit exists for the external field strengths. Above this limit, time-dependent coupled-cluster calculations become very challenging numerically, even in the full configuration interaction limit. The source of these numerical instabilities is shown to be rapid increases of the amplitudes as ultrashort high-intensity laser pulses pump the system out of the ground state into states that are virtually orthogonal to the static Hartree-Fock reference determinant., Comment: 14 pages, 13 figures

We compare the performance of three approximate methods for speeding up evaluation of the exchange contribution in Hartree-Fock and hybrid Kohn-Sham calculations: the chain-of-spheres algorithm (COSX; Neese , F. Chem. Phys. 2008 , 356 , 98 - 109 ), the pair-atomic resolution-of-identity method (PARI-K; Merlot , P. J. Comput. Chem. 2013 , 34 , 1486 - 1496 ), and the auxiliary density matrix method (ADMM; Guidon , M. J. Chem. Theory Comput. 2010 , 6 , 2348 - 2364 ). Both the efficiency relative to that of a conventional linear-scaling algorithm and the accuracy of total, atomization, and orbital energies are compared for a subset containing 25 of the 200 molecules in the Rx200 set using double-, triple-, and quadruple-ζ basis sets. The accuracy of relative energies is further compared for small alkane conformers (ACONF test set) and Diels-Alder reactions (DARC test set). Overall, we find that the COSX method provides good accuracy for orbital energies as well as total and relative energies, and the method delivers a satisfactory speedup. The PARI-K and in particular ADMM algorithms require further development and optimization to fully exploit their indisputable potential.

We present a generalization of the divide–expand–consolidate (DEC) framework for local coupled-cluster calculations to periodic systems and test it at the second-order Møller–Plesset (MP2) level of theory. For simple model systems with periodicity in one, two, and three dimensions, comparisons with extrapolated molecular calculations and the local MP2 implementation in the Cryscor program show that the correlation energy errors of the extended DEC (X-DEC) algorithm can be controlled through a single parameter, the fragment optimization threshold. Two computational bottlenecks are identified: the size of the virtual orbital spaces and the number of pair fragments required to achieve a given accuracy of the correlation energy. For the latter, we propose an affordable algorithm based on cubic splines interpolation of a limited number of pair-fragment interaction energies to determine a pair cutoff distance in accordance with the specified fragment optimization threshold.

Multiconfigurational wavefunction analysis and entanglement measures based on von Neumann entropy shed light on the electronic structure of a Ru nitrosyl complex, in particular on the Ru–NO bond., Complete active space self-consistent field (CASSCF) wavefunctions and an orbital entanglement analysis obtained from a density-matrix renormalisation group (DMRG) calculation are used to understand the electronic structure, and, in particular, the Ru–NO bond of a Ru nitrosyl complex. Based on the configurations and orbital occupation numbers obtained for the CASSCF wavefunction and on the orbital entropy measurements evaluated for the DMRG wavefunction, we unravel electron correlation effects in the Ru coordination sphere of the complex. It is shown that Ru–NO π bonds show static and dynamic correlation, while other Ru–ligand bonds feature predominantly dynamic correlation. The presence of static correlation requires the use of multiconfigurational methods to describe the Ru–NO bond. Subsequently, the CASSCF wavefunction is analysed in terms of configuration state functions based on localised orbitals. The analysis of the wavefunctions in the electronic singlet ground state and the first triplet state provides a picture of the Ru–NO moiety beyond the standard representation based on formal oxidation states. A distinct description of the Ru and NO fragments is advocated. The electron configuration of Ru is an equally weighted superposition of RuII and RuIII configurations, with the RuIII configuration originating from charge donation mostly from Cl ligands. However, and contrary to what is typically assumed, the electronic configuration of the NO ligand is best described as electroneutral.

We extend the local exchange (LK) algorithm [Aquilante, F.; Pedersen, T. B.; Lindh, R. J. Chem. Phys.2007, 126, 194106] to the calculation of analytical gradients with density fitting. We discuss the features of the screening procedure and demonstrate the possible advantages of using this formulation, which is easily interfaced to a standard integral-direct gradient code. With auxiliary basis sets obtained from Cholesky decomposition of atomic or molecular integral blocks with a decomposition threshold of 10(-4)Eh, typical errors due to the density fitting in bond lengths, bond angles, and dihedral angles are 0.1 pm, 0.1°, and 0.5°, respectively. The overall speedup of geometry optimizations is about 1 order of magnitude for atomic natural-orbital-type basis sets but much less pronounced for correlation-consistent basis sets.

Chemical and electrochemical oxidation or reduction of our recently reported Ir(IV,IV) mono-μ-oxo dimers results in the formation of fully characterized Ir(IV,V) and Ir(III,III) complexes. The Ir(IV,V) dimers are unprecedented and exhibit remarkable stability under ambient conditions. This stability and modest reduction potential of 0.99 V vs NHE is in part attributed to complete charge delocalization across both Ir centers. Trends in crystallographic bond lengths and angles shed light on the structural changes accompanying oxidation and reduction. The similarity of these mono-μ-oxo dimers to our Ir "blue solution" water-oxidation catalyst gives insight into potential reactive intermediates of this structurally elusive catalyst. Additionally, a highly reactive material, proposed to be a Ir(V,V) μ-oxo species, is formed on electrochemical oxidation of the Ir(IV,V) complex in organic solvents at 1.9 V vs NHE. Spectroelectrochemistry shows reversible conversion between the Ir(IV,V) and proposed Ir(V,V) species without any degradation, highlighting the exceptional oxidation resistance of the 2-(2-pyridinyl)-2-propanolate (pyalk) ligand and robustness of these dimers. The Ir(III,III), Ir(IV,IV) and Ir(IV,V) redox states have been computationally studied both with DFT and multiconfigurational calculations. The calculations support the stability of these complexes and provide further insight into their electronic structures.

Undefined mesophilic mixed (DL-type) starter cultures are composed of predominantly Lactococcus lactis subspecies and 1 to 10 % Leuconostoc spp. The composition of the Leuconostoc population in the starter culture ultimately affects the characteristics and the quality of the final product. The scientific basis for the taxonomy of dairy relevant leuconostocs can be traced back fifty years, and no documentation on the genomic diversity of leuconostocs in starter cultures exists. We present data on the Leuconostoc population in five DL-type starter cultures commonly used by the dairy industry. The analyses were performed using traditional cultivation methods, and further augmented by next-generation DNA sequencing methods. Bacterial counts for starter cultures cultivated on two different media, MRS and MPCA, revealed large differences in the relative abundance of leuconostocs. Most of the leuconostocs in two of the starter cultures were unable to grow on MRS, emphasizing the limitations of culture-based methods and the importance of careful media selection or use of culture independent methods. Pan-genomic analysis of 59 Leuconostoc genomes enabled differentiation into twelve robust lineages. The genomic analyses show that the diary-associated leuconostocs are highly adapted to their environment, characterized by the acquisition of genotype traits such as the ability to metabolize citrate. In particular, Leuconostoc mesenteroides subsp. cremoris display telltale signs of a degenerative evolution, likely resulting from a long period of growth in milk in association with lactococci. Great differences in the metabolic potential between Leuconostoc species and subspecies were revealed. Using targeted amplicon sequencing, the composition of the Leuconostoc population in the five commercial starter cultures was shown to be significantly different. Three of the cultures were dominated by Ln. mesenteroides subspecies cremoris. Leuconostoc pseudomesenteroides dominated in two of the cultures while Leuconostoc lactis, reported to be a major constituent in fermented dairy products, was only present in low amounts in one of the cultures. This is the first in-depth study of Leuconostoc genomics and diversity in dairy starter cultures. The results and the techniques presented may be of great value for the dairy industry.

The density-fitting technique for approximating electron-repulsion integrals relies on the quality of auxiliary basis sets. These are commonly obtained through data fitting, an approach that presents some shortcomings. On the other hand, it is possible to derive auxiliary basis sets by removing elements from the product space of both contracted and primitive orbitals by means of a particular form of inner projection technique that has come to be known as Cholesky decomposition (CD). This procedure allows for on-the-fly construction of auxiliary basis sets that may be used in conjunction with any quantum chemical method, i.e. unbiased auxiliary basis sets. One key feature of these sets is that they represent the electron-repulsion integral matrix in atomic orbital basis with an accuracy that can be systematically improved. Another key feature is represented by the fact that locality of fitting coefficients is obtained even with the long-ranged Coulomb metric, as result of integral accuracy. Here we report on recent advances in the development of the CD-based density fitting technology. In particular, the implementation of analytical gradients algorithms is reviewed and the present status of local formulations – potentially linear scaling – is analysed in detail. © 2017 Taylor & Francis

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, MOller-Plesset, confi ...

An algorithm for computing analytical gradients of the second-order MOller-Plesset (MP2) energy using density fitting (DF) is presented. The algorithm assumes that the underlying canonical Hartree-Fock reference is obtained with the same auxiliary basis set, which we obtain by Cholesky decomposition (CD) of atomic electron repulsion integrals. CD is also used for the negative semidefinite MP2 amplitude matrix. Test calculations on the weakly interacting dimers of the S22 test set (Jureka et al., Phys. Chem. Chem. Phys. 2006, 8, 1985) show that the geometry errors due to the auxiliary basis set are negligible. With double-zeta basis sets, the error due to the DF approximation in intermolecular bond lengths is better than 0.1 pm. The computational time is typically reduced by a factor of 6-7. (c) 2013 Wiley Periodicals, Inc. (Less)

In this report, we summarize and describe the recent unique updates and additions to the Molcas quantum chemistry program suite as contained in release version 8. These updates include natural and spin orbitals for studies of magnetic properties, local and linear scaling methods for the Douglas-Kroll-Hess transformation, the generalized active space concept in MCSCF methods, a combination of multiconfigurational wave functions with density functional theory in the MC-PDFT method, additional methods for computation of magnetic properties, methods for diabatization, analytical gradients of state average complete active space SCF in association with density fitting, methods for constrained fragment optimization, large-scale parallel multireference configuration interaction including analytic gradients via the interface to the Columbus package, and approximations of the CASPT2 method to be used for computations of large systems. In addition, the report includes the description of a computational machinery for nonlinear optical spectroscopy through an interface to the QM/MM package Cobramm. Further, a module to run molecular dynamics simulations is added, two surface hopping algorithms are included to enable nonadiabatic calculations, and the DQ method for diabatization is added. Finally, we report on the subject of improvements with respects to alternative file options and parallelization. QC 20210506

Analytical state-average complete-active-space self-consistent field derivative (nonadiabatic) coupling vectors are implemented. Existing formulations are modified such that the implementation is compatible with Cholesky-based density fitting of two-electron integrals, which results in efficient calculations especially with large basis sets. Using analytical nonadiabatic coupling vectors, the optimization of conical intersections is implemented within the projected constrained optimization method. The standard description and characterization of conical intersections is reviewed and clarified, and a practical and unambiguous system for their classification and interpretation is put forward. These new tools are subsequently tested and benchmarked for 19 different conical intersections. The accuracy of the derivative coupling vectors is validated, and the information that can be drawn from the proposed characterization is discussed, demonstrating its usefulness.

At variance, with most of the quantum chemistry software presently available, MOLCAS is a package that is specialized in multiconfigurational wave function theory (MC-WFT) rather than density functional theory (DFT). Given the much higher algorithmic complexity of MC-WFT versus DFT, an extraordinary effort needs to be made from the programming point of view to achieve state-of-the-art performance for large-scale calculations. In particular, a robust and efficient implementation of the Cholesky decomposition techniques for handling two-electron integrals has been developed which is unique to MOLCAS. Together with this 'Cholesky infrastructure', a powerful and multilayer graphical and scripting user interface is available, which is an essential ingredient for the setup of MC-WFT calculations. These two aspects of the MOLCAS software constitute the focus of the present report. (C) 2012 John Wiley & Sons, Ltd. (Less)

The electronic structure and low-lying electronic states of a Co(III)(diiminato)(NPh) complex have been studied using multiconfigurational wave function theory (CASSCF/CASPT2). The results have been compared to those obtained with density functional theory. The best agreement with ab initio results is obtained with a modified B3LYP functional containing a reduced amount (15%) of Hartree-Fock exchange. A relativistic basis set with 869 functions has been employed in the most extensive ab initio calculations, where a Cholesky decomposition technique was used to overcome problems arising from the large size of the two-electron integral matrix. It is shown that this approximation reproduces results obtained with the full integral set to a high accuracy, thus opening the possibility to use this approach to perform multiconfigurational wave-function-based quantum chemistry on much larger systems relative to what has been possible until now.

The accuracy of auxiliary basis sets derived by Cholesky decompositions of the electron repulsion integrals is assessed in a series of benchmarks on total ground state energies and dipole moments of a large test set of molecules. The test set includes molecules composed of atoms from the first three rows of the periodic table as well as transition metals. The accuracy of the auxiliary basis sets are tested for the 6-31 G**, correlation consistent, and atomic natural orbital basis sets at the Hartree-Fock, density functional theory, and second-order Moller-Plesset levels of theory. By decreasing the decomposition threshold, a hierarchy of auxiliary basis sets is obtained with accuracies ranging from that of standard auxiliary basis sets to that of conventional integral treatments.

We compute noncovalent intermolecular interaction energies for the S22 test set [Phys. Chem. Chem. Phys. 2006, 8, 1985-1993] of molecules at the Moller-Plesset and coupled cluster levels of supermolecular theory using density fitting (DF) to approximate all two-electron integrals. The error due to the DF approximation is analyzed for a range of auxiliary basis sets derived from Cholesky decomposition (CD) in conjunction with correlation consistent and atomic natural orbital valence basis sets. A Cholesky decomposition threshold of 10(-4)E(h) for full molecular CD and its one-center approximation (1C-CD) generally yields errors below 0.03 kcal/mol, whereas 10(-3)E(h) is sufficient to obtain the same level of accuracy or better with the atomic CD (aCD) and atomic compact CD (acCD) auxiliary basis sets. Comparing to commonly used predefined auxiliary basis sets, we find that while the aCD and acCD sets are larger by a factor of 2-4 with triple-zeta AO basis sets, they provide results 1-2 orders of magnitude more accurate.

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)

The accuracy of auxiliary basis sets derived from Cholesky decomposition of two-electron integrals is assessed for excitation energies calculated at the state-average complete active space self-consistent field (CASSCF) and multiconfigurational second order perturbation theory (CASPT2) levels of theory using segmented as well as generally contracted atomic orbital basis sets. Based on 196 valence excitations in 26 organic molecules and 72 Rydberg excitations in 3 organic molecules, the results show that Cholesky auxiliary basis sets can be used without compromising the accuracy of the multiconfigurational methods. Specifically, with a decomposition threshold of 10(-4) au, the mean error due to the Cholesky auxiliary basis set is 0.001 eV, or smaller, decreasing with increasing atomic orbital basis set quality.

Some of the new unique features of the MOLCAS quantum chemistry package version 7 are presented inthis report. In particular, the Cholesky decomposition method applied to some quantum chemical methods is described. This approach is used both in the context of a straight forward approximation of the two-electron integrals and in the generation of so-called auxiliary basis sets. The article describes how the method is implemented for most known wave functions models: self-consistent field, density functional theory, 2nd order perturbation theory, complete-active space self-consistent field multiconfigurational reference 2nd order perturbation theory, and coupled-cluster methods. The report further elaborates on the implementation of a restricted-active space self-consistent field reference function in conjunction with 2nd order perturbation theory. The average atomic natural orbital basis for relativistic calculations, covering the whole periodic table, are described and associated unique properties are demonstrated. Furthermore, the use of the arbitrary order Douglas-Kroll-Hess transformation for one-component relativistic calculations and its implementation are discussed. This section especially focuses on the implementation of the so-called picture-change-free atomic orbital property integrals. Moreover, the ElectroStatic Potential Fitted scheme, a version of a quantum mechanics/molecular mechanics hybrid method implemented in MOLCAS, is described and discussed. Finally, the report discusses the use of the MOLCAS package for advanced studies of photo chemical phenomena and the usefulness of the algorithms for constrained geometry optimization in MOLCAS in association with such studies. (c) 2009 Wiley Periodicals, Inc. J Corn put Chem 31: 224-247, 2010

Recent progress in the use of Cholesky decomposition techniques within the density fitting approximation of two-electron integrals is reviewed with emphasis on the theoretical background. Special attention is paid to the fact that errors due to the density fitting approximation can be controlled by constructing auxiliary basis sets by means of Cholesky decomposition of either the entire or certain subblocks of the molecular two-electron integral matrix. Finally, the prospects of trivial linear-scaling calculation of fitting coefficients in the Cholesky decomposition-based density fitting scheme are outlined.

Molecular vibrations can have a significant influence on gas phase specific optical rotations. Mainly due to the large number of nuclear degrees of freedom in most chiral molecules, theoretical predictions of vibrational corrections quickly become prohibitively expensive. Here, we investigate an approach in which the purely electronic contribution is calculated at the coupled cluster singles and doubles level, while the zero-point vibrational correction is computed using the less demanding density functional theory (B3LYP functional). By comparing to experimental gas phase results for seven molecules and two wavelengths, we find that the mixed coupled cluster/B3LYP approach performs significantly better than pure B3LYP predictions. In fact, we find that it is more important to use high-level electron correlation for the electronic contribution than to include zero-point vibrational corrections. Chirality 21:E68–E75, 2009. © 2009 Wiley-Liss, Inc.

Using coupled cluster singles and doubles linear response theory and the d-aug-cc-pVTZ basis set extended with a 3s3p2d1f1g set of midbond functions, the interaction induced electric dipole polarisability surface of the CO–Ar van der Waals complex is computed. Combining this surface with accurate intermolecular potential energy and electric dipole surfaces, the pressure and dielectric second virial coefficients of the complex are calculated by a classical statistical approach. Excellent agreement with experimental results (to within the experimental error bars) is obtained for the pressure second virial coefficient over a range of temperatures. No previous experimental or theoretical investigations have been carried out for the dielectric second virial coefficient, B e(T), which is estimated to be about 1.9 cm6 mol− 1 at room temperature. This value results from a balance of terms due to the interaction induced electric dipole polarisability (predominant at high temperatures) and orientational electric di...

The scaled opposite spin second-order Moller-Plesset (SOS-MP2) energy expression is reformulated using Cholesky decomposition of the amplitude matrix. The resulting algorithm requires an auxiliary ...

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)

An analysis of Dunlap’s robust fitting approach reveals that the resulting two-electron integral matrix is not manifestly positive semidefinite when local fitting domains or non-Coulomb fitting metrics are used. We present a highly local approximate method for evaluating four-center two-electron integrals based on the resolution-of-the-identity (RI) approximation and apply it to the construction of the Coulomb and exchange contributions to the Fock matrix. In this pair-atomic resolutionof-the-identity (PARI) approach, atomic-orbital (AO) products are expanded in auxiliary functions centered on the two atoms associated with each product. Numerical tests indicate that in 1% or less of all Hartree‐Fock and Kohn‐Sham calculations, the indefinite integral matrix causes nonconvergence in the self-consistent-field iterations. In these cases, the two-electron contribution to the total energy becomes negative, meaning that the electronic interaction is effectively attractive, and the total energy is dramatically lower than that obtained with exact integrals. In the vast majority of our test cases, however, the indefiniteness does not interfere with convergence. The total energy accuracy is comparable to that of the standard Coulomb-metric RI method. The speed-up compared with conventional algorithms is similar to the RI method for Coulomb contributions; exchange contributions are accelerated by a factor of up to eight with a triple-zeta quality basis set. A positive semidefinite integral matrix is recovered within PARI by introducing local auxiliary basis functions spanning the full AO product space, as may be achieved by using Cholesky-decomposition techniques. Local completion, however, slows down the algorithm to a level comparable with or below conventional calculations. V C 2013

We present calculations of ground state and excitation energies for ethene between metal electrodes. The model determines the effects of the electrodes by incorporating a heterogeneous and structured solvation model with the quantum mechanical description of the molecular system. The effects of the electrodes are of electrostatic origin and an external bias can be applied enabling a close connection to the actual physical process related to the measurements of charge transport in molecules located between electrodes.

We present an ab initio study of the n --> pi(*) electronic excitation energy together with the corresponding oscillator strength and rotatory strength tensor for two optically active cyclopropanone related structures: S,S-dimethylcyclopropanone and R,R-t-butylcyclopropanone. We discuss and compare the available experimental data for the n --> pi(*) electronic excitation energy and rotatory strength with the theoretical calculations. (C) 2004 Elsevier B.V. All rights reserved.

In this article we present the first theoretical study of solvent effects on the rotatory strength tensor. The system chosen is solvated formaldehyde for which only one tensor element is nonvanishing, and the solvent is modeled as a linear, homogeneous, and isotropic dielectric continuum. We present results using both an equilibrium and a nonequilibrium description of the solvent. Four illustrative solvents (ethyl ether, acetone, methanol, and water) are considered together with the corresponding results for formaldehyde in vacuum. We utilize the following ab initio methods: the coupled cluster model including singles and doubles (CCSD) and the coupled cluster second-order approximate singles and doubles (M). Furthermore, we compare the coupled cluster results with the corresponding uncorrelated self-consistent-field (SCF) results. In addition to the rotatory strength tensor we also present solvent effects on the low-lying electronic excitation energies and corresponding ordinary intensities using both the length and velocity gauges. We find that both correlation and solvent effects have a significant influence on the transition properties. The introduction of the solvent is, in some cases, found to result in a sign change of the rotatory strength tensor elements which clearly demonstrates the importance of a proper description of the solvent influence on this property. (Less)

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.

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.

The theory of the rotatory strength tensor describing circular dichroism (CD) of electronic excitations in oriented molecules is summarized in length and velocity formulations, and we outline an ab initio implementation of the calculation of this tensor and its electric dipole — magnetic dipole and electric dipole — electric quadrupole components in the random phase approximation. Results are presented for the predominantly π → π ∗ and σ → π ∗ type transitions in an ethylene molecule twisted into chiral D2 conformations demonstrating the origin-sensitivity of the electric dipole-magnetic dipole and electric dipole-electric quadrupole contributions to the tensor, and demonstrating origin-invariance of the total tensor in the velocity formulation. The electric dipole-electric quadrupole contribution is small, but not insignificant for both transitions. We present a pictorial representation of the CD response, and its application to the total tensor and its components for the π → π ∗ excitation.