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This paper generalizes the recently proposed approaches for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) based on a Slater transition-state density to transitions such as singlet-singlet excitations, where a single-determinant ansatz is insufficient. The proposed approach is based on restricted open-shell Frank et al. [J. Chem. Phys. 108, 4060 (1998)] theory used to describe a spin-adapted Slater transition state. To treat the dependence of electron-electron interactions on the nuclear positions, variational linear-response density-functional perturbation theory is generalized to reference states with an orbital-dependent Kohn-Sham Hamiltonian and nontrivial occupation patterns. The methods proposed in this paper are not limited to the calculation of derivative coupling vectors, but can also be used for the calculation of other transition matrix elements. Moreover, they can be used to calculate the linear response of open-shell systems to arbitrary external perturbations in DFT. [ABSTRACT FROM AUTHOR]

We present the theory and algorithms for computing analytical energy gradients for explicitly correlated second-order Møller-Plesset perturbation theory (MP2-F12). The main difficulty in F12 gradient theory arises from the large number of two-electron integrals for which effective two-body density matrices and integral derivatives need to be calculated. For efficiency, the density fitting approximation is used for evaluating all two-electron integrals and their derivatives. The accuracies of various previously proposed MP2-F12 approximations [3C, 3C(HY1), 3*C(HY1), and 3*A] are demonstrated by computing equilibrium geometries for a set of molecules containing first- and second-row elements, using double-ζ to quintuple-ζ basis sets. Generally, the convergence of the bond lengths and angles with respect to the basis set size is strongly improved by the F12 treatment, and augmented triple-ζ basis sets are sufficient to closely approach the basis set limit. The results obtained with the different approximations differ only very slightly. This paper is the first step towards analytical gradients for coupled-cluster singles and doubles with perturbative treatment of triple excitations, which will be presented in the second part of this series. [ABSTRACT FROM AUTHOR]

The extrapolation method for determining benchmark quality full configuration-interaction energies described in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] is applied to the molecules H2O and N2. As in the neon atom case, discussed in preceding paper [L. Bytautas and K. Ruedenberg, J. Chem. Phys. 121, 10905 (2004)] remarkably accurate scaling relations are found to exist between the correlation energy contributions from various excitation levels of the configuration-interaction approach, considered as functions of the size of the correlating orbital space. The method for extrapolating a sequence of smaller configuration-interaction calculations to the full configuration-interaction energy and for constructing compact accurate configuration-interaction wave functions is also found to be effective for these molecules. The results are compared with accurate ab initio methods, such as many-body perturbation theory, coupled-cluster theory, as well as with variational calculations wherever possible. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The recently proposed universal state-selective (USS) corrections [K. Kowalski, J. Chem. Phys. 134, 194107 (2011)] to approximate multi-reference coupled-cluster (MRCC) energies can be commonly applied to any type of MRCC theory based on the Jeziorski-Monkhorst [B. Jeziorski and H. J. Monkhorst, Phys. Rev. A 24, 1668 (1981)] exponential ansatz. In this paper we report on the performance of a simple USS correction to the Brillouin-Wigner and Mukherjee's MRCC approaches employing single and double excitations (USS-BW-MRCCSD and USS-Mk-MRCCSD). It is shown that the USS-BW-MRCCSD correction, which employs the manifold of single and double excitations, can be related to a posteriori corrections utilized in routine BW-MRCCSD calculations. In several benchmark calculations we compare the USS-BW-MRCCSD and USS-Mk-MRCCSD results with the results obtained with the full configuration interaction method. [ABSTRACT FROM AUTHOR]

In this paper the effect of bias and geometric symmetry breaking on the electronic spectrum of a model molecular system is studied. Geometric symmetry breaking can either enhance the dissipative effect of the bias, where spectral peaks are disabled, or enable new excitations that are absent under zero bias conditions. The spectral analysis is performed on a simple model system by solving for the electronic response to an instantaneously impulsive perturbation in the dipole approximation. The dynamical response is extracted from the electronic equations of motion as expressed by the Keldysh formalism. This expression provides for the accurate treatment of the electronic structure of a bulk-coupled system at the chosen model Hamiltonian electronic structure level. [ABSTRACT FROM AUTHOR]

An analytical energy gradient formula for the density-matrix-based linear-scaling divide-and-conquer (DC) self-consistent field (SCF) method was proposed in a previous paper by Yang and Lee (YL) [J. Chem. Phys. 103, 5674 (1995)]. Since the formula by YL does not correspond to the exact gradient of the DC-SCF energy, we derive the exact formula by direct differentiation, which requires solving the coupled-perturbed equations while including the inter-subsystem coupling terms. Next, we present an alternative formula for approximately evaluating the DC-SCF energy gradient, assuming the variational condition for the subsystem density matrices. Numerical assessments confirmed that the DC-SCF energy gradient values obtained by the present formula are in reasonable agreement with the conventional SCF values when adopting a reliable buffer region. Furthermore, the performance of the present method was found to be better than that of the YL method. [ABSTRACT FROM AUTHOR]

We present molecular applications of a spin free size-extensive state-specific multireference perturbation theory (SS-MRPT), which is valid for model functions of arbitrary spin and generality. In addition to the singlet states, this method is equally capable to handle nonsinglet states. The formulation based on Rayleigh–Schrödinger approach works with a complete active space and treats each of the model space functions democratically. The method is capable of handling varying degrees of quasidegeneracy and of ensuring size consistency as a consequence of size extensivity. In this paper, we illustrate the effectiveness of the Mo\ller–Plesset (MP) partitioning based spin free SS-MRPT [termed as SS-MRPT(MP)] in computations of energetics of the nonsinglet states of several chemically interesting and demanding molecular examples such as LiH, NH2, and CH3. The spectroscopic constants of 3Σ- state of NH and OH+ molecular systems and the ground 1Σg+ as well as excited 3Σu+ states of N2 have been investigated and comparison with experimental and full configuration interaction values (wherever available) has also been provided. We have been able to demonstrate here that the SS-MRPT(MP) method is an intrinsically consistent and promising approach to compute reliable energies of nonsinglet states over different geometries. [ABSTRACT FROM AUTHOR]

In this paper the authors further develop and apply the direct-mapping density functional theory to calculations of the atomization energies and ionization potentials. Single-particle orbitals are determined by solving the Kohn-Sham [Phys. Rev. A. 140, 1133 (1965)] equations with a local effective potential expressed in terms of the external potential. A two-parametric form of the effective potential for molecules is proposed and equations for optimization of the parameters are derived using the exchange-only approximation. Orbital-dependent correlation functional is derived from the second-order perturbation theory in its Mo\ller-Plesset-type zeroth-order approximation based on the Kohn-Sham orbitals and orbital energies. The total atomization energies and ionization potentials computed with the second-order perturbation theory were found to be in agreement with experimental values and benchmark results obtained with ab initio wave mechanics methods. [ABSTRACT FROM AUTHOR]

In this paper, we present a method for constructing simple state-dependent many-body potentials for quantum vibrations in a classical bath. The approach is based on an adiabatic separation between high-frequency quantum vibrational modes of the solute and the lower frequency classical motion of the solvent, and on a first-order perturbation theory description of the dependence of the quantum energies on bath configuration. In the simplest realization of the method, the delocalized quantum probability density of the vibrational mode is approximated by a sum of two δ functions, with positions and weights chosen to represent the lowest three moments of the exact distribution. Thus, in the many-body description of the system, each atom describing the quantum vibration is represented by a pair of particles. These quantum particles are held in rigid relative position and interact with the bath via potentials the magnitudes of which are modified by the δ-function weights. The resulting approach allows the classical molecular dynamics of molecules in arbitrary quantum vibrational states to be simulated with a little more effort than a purely classical description. The applicability of the method is illustrated in many-body simulations of the dephasing of vibrational superposition states of I2 in a cryogenic krypton matrix, yielding results in good agreement with experiment. [ABSTRACT FROM AUTHOR]

We would like to show that what has been presented in the paper by Kim, Kim, and Seong [J. Chem. Phys, 135, 034505 (2011)] is nothing but an unnecessarily complicated version of (optimized) random phase approximation. [ABSTRACT FROM AUTHOR]

In this paper we present a local coupled cluster approach based on a dynamical screening scheme, in which amplitudes are either calculated at the coupled cluster level (in this case CCSD) or at the level of perturbation theory, employing a threshold driven procedure based on MP2 energy increments. This way, controllable accuracy and smooth convergence towards the exact result are obtained in the framework of an a posteriori approximation scheme. For the representation of the occupied space a new set of local orbitals is presented with the size of a minimal basis set. This set is atom centered, is nonorthogonal, and has shapes which are fairly independent of the details of the molecular system of interest. Two slightly different versions of combined local coupled cluster and perturbation theory equations are considered. In the limit both converge to the untruncated CCSD result. Benchmark calculations for four systems (heptane, serine, water hexamer, and oxadiazole-2-oxide) are carried out, and decay of the amplitudes, truncation error, and convergence towards the exact CCSD result are analyzed. [ABSTRACT FROM AUTHOR]

In this work, we present NENCI-2021, a benchmark database of ∼8000 Non-Equilibirum Non-Covalent Interaction energies for a large and diverse selection of intermolecular complexes of biological and chemical relevance. To meet the growing demand for large and high-quality quantum mechanical data in the chemical sciences, NENCI-2021 starts with the 101 molecular dimers in the widely used S66 and S101 databases and extends the scope of these works by (i) including 40 cation–π and anion–π complexes, a fundamentally important class of non-covalent interactions that are found throughout nature and pose a substantial challenge to theory, and (ii) systematically sampling all 141 intermolecular potential energy surfaces (PESs) by simultaneously varying the intermolecular distance and intermolecular angle in each dimer. Designed with an emphasis on close contacts, the complexes in NENCI-2021 were generated by sampling seven intermolecular distances along each PES (ranging from 0.7× to 1.1× the equilibrium separation) and nine intermolecular angles per distance (five for each ion–π complex), yielding an extensive database of 7763 benchmark intermolecular interaction energies (Eint) obtained at the coupled-cluster with singles, doubles, and perturbative triples/complete basis set [CCSD(T)/CBS] level of theory. The Eint values in NENCI-2021 span a total of 225.3 kcal/mol, ranging from −38.5 to +186.8 kcal/mol, with a mean (median) Eint value of −1.06 kcal/mol (−2.39 kcal/mol). In addition, a wide range of intermolecular atom-pair distances are also present in NENCI-2021, where close intermolecular contacts involving atoms that are located within the so-called van der Waals envelope are prevalent—these interactions, in particular, pose an enormous challenge for molecular modeling and are observed in many important chemical and biological systems. A detailed symmetry-adapted perturbation theory (SAPT)-based energy decomposition analysis also confirms the diverse and comprehensive nature of the intermolecular binding motifs present in NENCI-2021, which now includes a significant number of primarily induction-bound dimers (e.g., cation–π complexes). NENCI-2021 thus spans all regions of the SAPT ternary diagram, thereby warranting a new four-category classification scheme that includes complexes primarily bound by electrostatics (3499), induction (700), dispersion (1372), or mixtures thereof (2192). A critical error analysis performed on a representative set of intermolecular complexes in NENCI-2021 demonstrates that the Eint values provided herein have an average error of ±0.1 kcal/mol, even for complexes with strongly repulsive Eint values, and maximum errors of ±0.2–0.3 kcal/mol (i.e., ∼±1.0 kJ/mol) for the most challenging cases. For these reasons, we expect that NENCI-2021 will play an important role in the testing, training, and development of next-generation classical and polarizable force fields, density functional theory approximations, wavefunction theory methods, and machine learning based intra- and inter-molecular potentials. [ABSTRACT FROM AUTHOR]

We recently proposed a linear-scaling evaluation scheme for the second-order Mo\ller-Plesset perturbation (MP2) energy based on the divide-and-conquer (DC) method [M. Kobayashi, Y. Imamura, and H. Nakai, J. Chem. Phys. 127, 074103 (2007)]. In this paper, we propose an approximate but effective expression for the first derivative of the DC-MP2 energy. The present scheme evaluates the one- and two-body density matrices, which appear in the MP2 gradient formula, in the DC manner; that is, the entire matrix is obtained as the sum of subsystem matrices masked by the partition matrix. Therefore, the method requires solving only the local Z-vector equations. Illustrative applications to three types of systems, peptides, Si surface model, and delocalized polyenes, reveal the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

The recently proposed spin-flip symmetry-adapted perturbation theory (SF-SAPT) first-order exchange energy [Patkowski et al., J. Chem. Phys. 148, 164110 (2018)] enables the standard open-shell SAPT approach to treat arbitrary spin states of the weakly interacting complex. Here, we further extend first-order SF-SAPT beyond the single-exchange approximation to a complete treatment of the exchanges of electrons between monomers. This new form of the exchange correction replaces the single-exchange approximation with a more moderate single-spin-flip approximation. The newly developed expressions are applied to a number of small test systems to elucidate the quality of both approximations. They are also applied to the singlet-triplet splittings in pancake bonded dimers. The accuracy of the single-exchange approximation deteriorates at short intermolecular separations, especially for systems with few electrons and for the high-spin state of the complex. In contrast, the single-spin-flip approximation is exact for interactions involving a doublet molecule and remains highly accurate for any number of unpaired electrons. Because the single-exchange approximation affects the high-spin and low-spin states of pancake bonded complexes evenly, the resulting splitting values are of similar accuracy to those produced by the formally more accurate single-spin-flip approximation. [ABSTRACT FROM AUTHOR]

We present a novel spin-component scaled Møller-Plesset second order (MP2) perturbation theory [S. Grimme, J. Chem. Phys. 118, 9095 (2003)] in which the singlet and triplet correlation channels are dressed in a dynamical manner over the entire molecular potential energy surface. In order to strike the right balance between the short and long range correlation, the different correlation channels are scaled by two complementary functions without introducing any external parameter: while the singlet channel contribution to correlation energy is attenuated with increasing strong correlation of the system, the triplet channel contribution is amplified. We have justified our approach from physical reasoning as well as a few numerical examples with some difficult systems, like symmetric stretching of water and nitrogen molecules, which clearly demonstrate the efficacy of this method in describing the molecular potential energy surface, even in the strongly correlated regions where the conventional MP2 and its other variants disastrously fail. [ABSTRACT FROM AUTHOR]

The use of non-orthogonal orbitals allows the construction and use of more compact wave functions than offered by standard methods using orthogonal molecular orbitals; in particular, for molecules containing partly occupied atomic orbitals as present, for example, in transition metal complexes. With the purpose of developing efficient dynamic correlation methods, we discuss several new internal correlation methods employing a reference state containing non-orthogonal active orbitals. The non-orthogonal internally contracted perturbation theory approach is improved in several directions. The major improvements are the use of the Dyall Hamiltonian including two-electron interactions within the active space as the zero-order operator, the calculation of third-order energy-corrections, and the inclusion of excitations in the space of active orbitals. The latter improvement corrects for the use of an incomplete reference state. The improvements are tested for the nitrogen molecule and the challenging chromium dimer. The combined use of the improved zero-order Hamiltonian and the inclusion of active space excitations allow us to obtain potential curves for the chromium dimer that are close to those obtained using the larger complete active space reference wave function. [ABSTRACT FROM AUTHOR]

A benchmark set of relevant geometries of a model protein, the N-acetylphenylalanylamide, is presented to assess the validity of the approximate second-order coupled cluster (CC2) method in studying low-lying excited states of such bio-relevant systems. The studies comprise investigations of basis-set dependence as well as comparison with two multireference methods, the multistate complete active space 2nd order perturbation theory (MS-CASPT2) and the multireference difference dedicated configuration interaction (DDCI) methods. First of all, the applicability and the accuracy of the quasi-linear multireference difference dedicated configuration interaction method have been demonstrated on bio-relevant systems by comparison with the results obtained by the standard MS-CASPT2. Second, both the nature and excitation energy of the first low-lying excited state obtained at the CC2 level are very close to the Davidson corrected CAS+DDCI ones, the mean absolute deviation on the excitation energy being equal to 0.1 eV with a maximum of less than 0.2 eV. Finally, for the following low-lying excited states, if the nature is always well reproduced at the CC2 level, the differences on excitation energies become more important and can depend on the geometry. [ABSTRACT FROM AUTHOR]

We show that the Zwanzig first-order perturbation theory can be obtained directly from a truncated Taylor series expansion of a two-body perturbation theory and that such truncation provides a more accurate prediction of thermodynamic properties than the full two-body perturbation theory. This unexpected result is explained by the quality of the resulting approximation for the fluid radial distribution function. We prove that the first-order and the two-body perturbation theories are based on different approximations for the fluid radial distribution function. To illustrate the calculations, the square-well fluid is adopted. We develop an analytical expression for the two-body perturbed Helmholtz free energy for the square-well fluid. The equation of state obtained using such an expression is compared to the equation of state obtained from the first-order approximation. The vapor-liquid coexistence curve and the supercritical compressibility factor of a square-well fluid are calculated using both equations of state and compared to Monte Carlo simulation data. Finally, we show that the approximation for the fluid radial distribution function given by the first-order perturbation theory provides closer values to the ones calculated via Monte Carlo simulations. This explains why such theory gives a better description of the fluid thermodynamic behavior. [ABSTRACT FROM AUTHOR]

A hybrid stochastic-deterministic approach for computing the second-order perturbative contribution E(2) within multireference perturbation theory (MRPT) is presented. The idea at the heart of our hybrid scheme--based on a reformulation of E(2) as a sum of elementary contributions associated with each determinant of the MR wave function--is to split E(2) into a stochastic and a deterministic part. During the simulation, the stochastic part is gradually reduced by dynamically increasing the deterministic part until one reaches the desired accuracy. In sharp contrast with a purely stochastic Monte Carlo scheme where the error decreases indefinitely as t-1/2 (where t is the computational time), the statistical error in our hybrid algorithm displays a polynomial decay ~t-n with n = 3-4 in the examples considered here. If desired, the calculation can be carried on until the stochastic part entirely vanishes. In that case, the exact result is obtained with no error bar and no noticeable computational overhead compared to the fully deterministic calculation. The method is illustrated on the F2 and Cr2 molecules. Even for the largest case corresponding to the Cr2 molecule treated with the cc-pVQZ basis set, very accurate results are obtained for E(2) for an active space of (28e, 176o) and a MR wave function including up to 2 x 107 determinants. [ABSTRACT FROM AUTHOR]

Using the GW method within many-body perturbation theory, we investigate the electronic properties of the rutile (011) surfaces with different reconstruction patterns. We find that keeping the Ti:O ratio on the reconstructed surface to 1:2 enlarges the bandgap of the rutile (011) surface to ca. 4.0 eV. Increasing the content of O atoms in the surface can turn rutile into a semi-metal. For some surfaces, it is important to apply self-consistent GW calculation to get the correct charge distributions for the frontier orbitals, which are relevant to the photocatalytic behavior of TiO2. [ABSTRACT FROM AUTHOR]

The Resolution of the Identity second-order Møller-Plesset perturbation theory (RI-MP2) method is implemented within the linear-scaling Divide-Expand-Consolidate (DEC) framework. In a DEC calculation, the full molecular correlated calculation is replaced by a set of independent fragment calculations each using a subset of the total orbital space. The number of independent fragment calculations scales linearly with the system size, rendering the method linear-scaling and massively parallel. The DEC-RI-MP2 method can be viewed as an approximation to the DEC-MP2 method where the RI approximation is utilized in each fragment calculation. The individual fragment calculations scale with the fifth power of the fragment size for both methods. However, the DEC-RI-MP2 method has a reduced prefactor compared to DEC-MP2 and is well-suited for implementation on massively parallel supercomputers, as demonstrated by test calculations on a set of medium-sized molecules. The DEC error control ensures that the standard RI-MP2 energy can be obtained to the predefined precision. The errors associated with the RI and DEC approximations are compared, and it is shown that the DECRI- MP2 method can be applied to systems far beyond the ones that can be treated with a conventional RI-MP2 implementation. [ABSTRACT FROM AUTHOR]

In local coupled cluster treatments the electron pairs can be classified according to the magnitude of their energy contributions or distances into strong, close, weak, and distant pairs. Different approximations are introduced for the latter three classes. In this communication, an improved simplified treatment of close and weak pairs is proposed, which is based on long-range cancellations of individually slowly decaying contributions in the amplitude equations. Benchmark calculations for correlation, reaction, and activation energies demonstrate that these approximations work extremely well, while pair approximations based on local second-order Møller-Plesset theory can lead to errors that are 1-2 orders of magnitude larger. [ABSTRACT FROM AUTHOR]

An explicitly correlated version of the distinguishable-cluster approximation is presented and extensively benchmarked. It is shown that the usual F12-type explicitly correlated approaches are applicable to distinguishable-cluster theory with single and double excitations, and the results show a significant improvement compared to coupled-cluster theory with singles and doubles for closed and open-shell systems. The resulting method can be applied in a black-box manner to systems with single- and multireference character. Most noticeably, optimized geometries are of coupled-cluster singles and doubles with perturbative triples quality or even better. [ABSTRACT FROM AUTHOR]

Perturbation-facilitated two-color resonant four-wave-mixing spectroscopy is realized to access the (dark) triplet manifold of the C3 molecule from the singlet X1Σg+ ground state. The inherent nonlinear signal dependence and coherence of the technique result in a favorable detection of the excited triplet states of interest. The observation of a newly found 3Δu electronic state is achieved by a two-step excitation via 'gate-way' levels (i.e., singlet-triplet mixed levels). Additionally, by fixing the probe laser on a transition exhibiting mainly triplet-triplet character and scanning the pump laser, we demonstrate an effective spin-filtering in a four-wave mixing measurement where only transitions to the perturber 3Σu- state appear exclusively in an otherwise congested spectral range of the Comet band. Ab initio calculations of excited triplet states complement our analysis with the electronic assignment of the observed resonances. [ABSTRACT FROM AUTHOR]

Spin flip equation of motion coupled cluster (EOM-SF-CC) can correctly treat situations involving electronic degeneracies or near degeneracies, e.g., bond breaking, di- and tri-radicals, etc. However, for large systems EOM-SF-CC (even in single and double excitations) is computationally prohibitively expensive. Therefore, earlier approximations to EOM-SF-CC methods such as spin flip configuration interaction singles with perturbative doubles (SF-CIS(D)) have been proposed. In this work, we present a new perturbative approximation to EOM-SF-CC, which has been found to be more accurate than SF-CIS(D). The capabilities, advantages, and timings of the new approach have been demonstrated considering the singlet-triplet gaps in di- and triradicals as well as bond breaking examples. The method is extended to double spin flip EOM-CC and its capabilities have been tested. [ABSTRACT FROM AUTHOR]

An efficient method for the calculation of nuclear magnetic resonance (NMR) shielding tensors is presented, which treats electron correlation at the level of second-order Mo\ller-Plesset perturbation theory. It uses spatially localized functions to span occupied and virtual molecular orbital spaces, respectively, which are expanded in a basis of gauge including atomic orbitals (GIAOs or London atomic orbitals). Doubly excited determinants are restricted to local subsets of the virtual space and pair energies with an interorbital distance beyond a certain threshold are omitted. Furthermore, density fitting is employed to factorize the electron repulsion integrals. Ordinary Gaussians are employed as fitting functions. It is shown that the errors in the resulting NMR shielding constant, introduced (i) by the local approximation and (ii) by density fitting, are very small or even negligible. The capabilities of the new program are demonstrated by calculations on some extended molecular systems, such as the cyclobutane pyrimidine dimer photolesion with adjacent nucleobases in the native intrahelical DNA double strand (ATTA sequence). Systems of that size were not accessible to correlated ab initio calculations of NMR spectra before. The presented method thus opens the door to new and interesting applications in this area. [ABSTRACT FROM AUTHOR]

In the study of open quantum systems, the polaron transformation has recently attracted a renewed interest as it offers the possibility to explore the strong system-bath coupling regime. Despite this interest, a clear and unambiguous analysis of the regimes of validity of the polaron transformation is still lacking. Here we provide such a benchmark, comparing second order perturbation theory results in the original untransformed frame, the polaron frame, and the variational extension with numerically exact path integral calculations of the equilibrium reduced density matrix. Equilibrium quantities allow a direct comparison of the three methods without invoking any further approximations as is usually required in deriving master equations. It is found that the second order results in the original frame are accurate for weak system-bath coupling; the results deteriorate when the bath cut-off frequency decreases. The full polaron results are accurate for the entire range of coupling for a fast bath but only in the strong coupling regime for a slow bath. The variational method is capable of interpolating between these two methods and is valid over a much broader range of parameters. [ABSTRACT FROM AUTHOR]

The vibrational coupled cluster (VCC) equations are analyzed in terms of vibrational Mo\ller-Plesset perturbation theory aiming specifically at the importance of four-mode couplings. Based on this analysis, new VCC methods are derived for the calculation of anharmonic vibrational energies and vibrational spectra using vibrational coupled cluster response theory. It is shown how the effect of four-mode coupling and excitations can be efficiently and accurately described using approximations for their inclusion. Two closely related approaches are suggested. The computational scaling of the so-called VCC[3pt4F] method is not higher than the fifth power in the number of vibrational degrees of freedom when up to four-mode coupling terms are present in the Hamiltonian and only fourth order when only up to three-mode couplings are present. With a further approximation, one obtains the VCC[3pt4] model which is shown to scale with at most the fourth power in the number of vibrational degrees of freedom for Hamiltonians with both three- and four-mode coupling levels, while sharing the most important characteristics with VCC[3pt4F]. Sample calculations reported for selected tetra-atomic molecules as well as the larger dioxirane and ethylene oxide molecules support that the new models are accurate and useful. [ABSTRACT FROM AUTHOR]

Based on the coupled-cluster singles, doubles, and a hybrid treatment of triples (CCSD(T)-h) method developed by us [J. Shen, E. Xu, Z. Kou, and S. Li, J. Chem. Phys. 132, 114115 (2010); and ibid. 133, 234106 (2010); and ibid. 134, 044134 (2011)], we developed and implemented a new hybrid coupled cluster (CC) method, named CCSD(T)q-h, by combining CC singles and doubles, and active triples and quadruples (CCSDtq) with CCSD(T) to deal with the electronic structures of molecules with significant multireference character. These two hybrid CC methods can be solved with non-canonical and canonical MOs. With canonical MOs, the CCSD(T)-like equations in these two methods can be solved directly without iteration so that the storage of all triple excitation amplitudes can be avoided. A practical procedure to divide canonical MOs into active and inactive subsets is proposed. Numerical calculations demonstrated that CCSD(T)-h with canonical MOs can well reproduce the corresponding results obtained with non-canonical MOs. For three atom exchange reactions, we found that CCSD(T)-h can offer a significant improvement over the popular CCSD(T) method in describing the reaction barriers. For the bond-breaking processes in F2 and H2O, our calculations demonstrated that CCSD(T)q-h is a good approximation to CCSDTQ over the entire bond dissociation processes. [ABSTRACT FROM AUTHOR]

We present an orbital-optimized version of our orbital-specific-virtuals second-order Mo\ller-Plesset perturbation theory (OSV-MP2). The OSV model is a local correlation ansatz with a small basis of virtual functions for each occupied orbital. It is related to the Pulay-Saebo\ approach, in which domains of virtual orbitals are drawn from a single set of projected atomic orbitals; but here the virtual functions associated with a particular occupied orbital are specifically tailored to the correlation effects in which that orbital participates. In this study, the shapes of the OSVs are optimized simultaneously with the OSV-MP2 amplitudes by minimizing the Hylleraas functional or approximations to it. It is found that optimized OSVs are considerably more accurate than the OSVs obtained through singular value decomposition of diagonal blocks of MP2 amplitudes, as used in our earlier work. Orbital-optimized OSV-MP2 recovers smooth potential energy surfaces regardless of the number of virtuals. Full optimization is still computationally demanding, but orbital optimization in a diagonal or Kapuy-type MP2 approximation provides an attractive scheme for determining accurate OSVs. [ABSTRACT FROM AUTHOR]

We report high resolution measurements of 372 NaCs 53Π0(v, J) ro-vibrational level energies in the range 0 ≤ v ≤ 22. The data have been used to construct NaCs 53Π0 potential energy curves using the Rydberg-Klein-Rees and inverted perturbation approximation methods. Bound-free 53Π0(v, J) → 1(a)3Σ+ emission has also been measured, and is used to determine the repulsive wall of the 1(a)3Σ+ state and the 53Π0 → 1(a)3Σ+ relative transition dipole moment function. Hyperfine structure in the 53Π0 state has not been observed in this experiment. This null result is explained using a simple vector coupling model. [ABSTRACT FROM AUTHOR]

The dispersion terms are evaluated with the perturbation theory based on the locally projected molecular orbitals. A series of model systems, including some of the S22 set, is examined, and the calculated binding energies are compared with the published results. The basis set dependence is also examined. The dispersion energy correction is evaluated by taking into account the double excitations only of the dispersion type electron configurations and is added to the 3rd order single excitation perturbation energy, which is a good approximation to the counterpoise (CP) corrected Hartree-Fock (HF) binding energy. The procedure is the approximate 'CP corrected HF + D' method. It ensures that the evaluated binding energy is approximately free of the basis set superposition error without the CP procedure. If the augmented basis functions are used, the evaluated binding energies for the predominantly dispersion-bound systems, such as rare gas dimers and halogen bonded clusters, agree with those of the reference calculations within 1 kcal mol-1 (4 kJ mol-1). The limitation of the present method is also discussed. [ABSTRACT FROM AUTHOR]

A non-hard sphere (HS) perturbation scheme, recently advanced by the present author, is elaborated for several technical matters, which are key mathematical details for implementation of the non-HS perturbation scheme in a coupling parameter expansion (CPE) thermodynamic perturbation framework. NVT-Monte Carlo simulation is carried out for a generalized Lennard-Jones (LJ) 2n-n potential to obtain routine thermodynamic quantities such as excess internal energy, pressure, excess chemical potential, excess Helmholtz free energy, and excess constant volume heat capacity. Then, these new simulation data, and available simulation data in literatures about a hard core attractive Yukawa fluid and a Sutherland fluid, are used to test the non-HS CPE 3rd-order thermodynamic perturbation theory (TPT) and give a comparison between the non-HS CPE 3rd-order TPT and other theoretical approaches. It is indicated that the non-HS CPE 3rd-order TPT is superior to other traditional TPT such as van der Waals/HS (vdW/HS), perturbation theory 2 (PT2)/HS, and vdW/Yukawa (vdW/Y) theory or analytical equation of state such as mean spherical approximation (MSA)-equation of state and is at least comparable to several currently the most accurate Ornstein-Zernike integral equation theories. It is discovered that three technical issues, i.e., opening up new bridge function approximation for the reference potential, choosing proper reference potential, and/or using proper thermodynamic route for calculation of fex - ref, chiefly decide the quality of the non-HS CPE TPT. Considering that the non-HS perturbation scheme applies for a wide variety of model fluids, and its implementation in the CPE thermodynamic perturbation framework is amenable to high-order truncation, the non-HS CPE 3rd-order or higher order TPT will be more promising once the above-mentioned three technological advances are established. [ABSTRACT FROM AUTHOR]

The combination of the coupled cluster (CC) method with the polarizable continuum model (PCM) of solvation requires a much larger computational effort than gas phase CC calculations, since the PCM contribution depends nonlinearly on the CC reduced density: perturbation theory energy and density (PTED) scheme. An approximation can be introduced that neglects the 'correlation' PCM contribution and only considers the 'reference' PCM contribution to the free energy: PTE scheme. The PTE scheme is a computationally efficient strategy, since the cost is comparable to gas phase CC, but the difference in the free energy with respect to the PTED scheme can be significant. In this work, two intermediate approximations are presented, PTE(S) and PTES (where S stands for singles), which retain the computational efficiency of the PTE scheme while reducing the energy gap with the PTED scheme. PTE(S) only introduces an energy correction to the PTE free energy, while PTES introduces explicit PCM terms in the iterative solution of the CC equations. PTE(S) improves the PTE free energy, although such correction is small. PTES recovers 50%-80% of the PTE-PTED difference and represents a promising approach to perform calculations in solution of CC quality at a cost comparable to gas phase CC. The expressions for the CC-PTE(S) and -PTES wave functions, free energy, and free energy analytical gradients are presented, and the methods are tested with numerical examples. [ABSTRACT FROM AUTHOR]

The formalism for developing perturbation theory by using an arbitrary fixed (external) set of amplitudes as an initial approximation is presented in a compact form: external coupled-cluster perturbation theory (xCCPT). Nonperturbative approaches also fit into the formalism. As an illustration, the weakly interacting dimers Ne2 and Ar2 have been studied in the various ring-coupled-cluster doubles (CCD) approximations; ring, direct-ring, antisymmetrized ring, and antisymmetrized direct ring, and a second-order correction in the xCCPT approach is added. The direct approaches include the summation of just Coulomb terms with the intention of selectively summing the largest terms in the perturbation first. 'Coulomb attenuation' is effected by taking the random phase approximation to define such amplitudes, whose results are then improved upon using perturbation theory. Interaction energies at the ring-CCD level are poor but the xCCPT correction employed predicts binding energies which are only a few percent from the coupled-cluster single double (triple) values for the direct ring-CCD variants. Using the MP2 amplitudes which neglect exchange, the initial Coulomb-only term, leads to very accurate Ne2 and Ar2 potentials. However, to accurately compute the Na2 potential required a different initial wavefunction, and hence perturbation. The potential energy surfaces of Ne2 and Ar2 are much too shallow using linear coupled-cluster doubles. Using xCCPT(2) with these amplitudes as the initial wavefunction led to slightly worse results. These observations suggest that an optimal external set of amplitudes exists which minimizes perturbational effects and hence improve the predictability of methods. [ABSTRACT FROM AUTHOR]

Efficient periodic boundary condition (PBC) calculations by the second-order Mo\ller-Plesset perturbation (MP2) method based on crystal orbital formalism are developed by introducing the resolution-of-identity (RI) approximation of four-center two-electron repulsion integrals (ERIs). The formulation and implementation of the PBC RI-MP2 method are presented. In this method, the mixed auxiliary basis functions of the combination of Poisson and Gaussian type functions are used to circumvent the slow convergence of the lattice sum of the long-range ERIs. Test calculations of one-dimensional periodic trans-polyacetylene show that the PBC RI-MP2 method greatly reduces the computational times as well as memory and disk sizes, without the loss of accuracy, compared to the conventional PBC MP2 method. [ABSTRACT FROM AUTHOR]

Careful spin-orbit multireference studies were carried out for the late p-block elements Tl, Pb, Bi, Po, At, and Rn and their hydrides using the model core potentials developed in the present work. The model core potentials were designed to treat the scalar-relativistic and spin-orbit coupling effects at the Douglas–Kroll level. The variational stability of the spin-orbit coupling operator was discussed in terms of the relativistic kinematic operators and depicted graphically. A detailed analysis of the spin-orbit multireference dissociation curves of the 6p element hydrides as well as of their atomic spectra allowed to establish the accuracy of the model core potentials with respect to all-electron calculations to be within several mÅ for re, meV (ceV) for De at the correlation level of configuration interaction (multireference perturbation theory), 30 cm-1 for ωe, and about 350 cm-1 for the low-lying atomic and molecular term and level energies. These values are expected to be the maximum error limits for the model core potentials of all the np-block elements (n=2–6). Furthermore, a good agreement with experiment requires that many terms be coupled in the spin-orbit coupling calculations. A timing study of Tl and TlH computations indicates that the model core potentials lead to 20-fold (6-fold) speedup at the level of configuration interaction (multireference perturbation theory) calculations. [ABSTRACT FROM AUTHOR]

The study of the minimum Born–Oppenheimer structures of the protonated water clusters, (H2O)nH+, is performed for n=20 and 21. The structures belonging to four basic morphologies are optimized at the Hartree–Fock, second-order many-body perturbation theory and coupled cluster level, with the 6–31G, 6-31G*, and 6-311G** basis sets, using the parallel ACES III program. The lowest energy structure for each n is found to be the cagelike form filled with H2O, with the proton located on the surface. The cage is the distorted dodecahedron for the 21-mer case, and partially rearranged dodecahedral structure for the 20-mer. The results confirm that the lowest energy structure of the magic number n=21 clusters corresponds to a more stable form than that of the 20-mer clusters. [ABSTRACT FROM AUTHOR]

A hard sphere+triangle-well potential is employed to test a recently proposed thermodynamic perturbation theory (TPT) based on a coupling parameter expansion. It is found that the second-order term of the coupling parameter expansion surpasses by far that of a high temperature series expansion under a macroscopic compressibility approximation and several varieties. It is also found that the fifth-order version displays best among all of the numerically accessible versions with dissimilar truncation orders. Particularly, the superiority of the fifth-order TPT from other available liquid state theories is exhibited the most incisively when the temperature of interest obviously falls. We investigate the modification of the phase behavior of the hard sphere+triangle-well fluid resulting from a density dependence imposed on the original potential function. It is shown that (1) the density dependence induces polymorphism of fluid phase, particularly liquid-liquid transition in metastable supercooled region, and (2) along with enhanced decaying of the potential function as a function of bulk density, both the liquid-liquid transition and vapor-liquid transition tend to be situated at the domain of lower temperature, somewhat similar to a previously disclosed thumb rule that the fluid phase transition tends to metastable with respect to the fluid-solid transition as the range of the attraction part of a density-independence potential is sufficiently short compared to the range of the repulsion part of the same density-independence potential. [ABSTRACT FROM AUTHOR]

A new explicitly correlated local MP2-F12 method is proposed in which the error caused by truncating the virtual orbital space to pair-specific local domains is almost entirely removed. This is achieved by a simple modification of the ansatz for the explicitly correlated wave function, which makes it possible that the explicitly correlated terms correct both for the basis set incompleteness error as well as for the domain error in the LMP2. Benchmark calculations are presented for 21 molecules and 16 chemical reactions. The results demonstrate that the local approximations have hardly any effect on the accuracy of the computed correlation energies and reaction energies, and the LMP2-F12 reaction energies agree within 0.1–0.2 kcal/mol with estimated MP2 basis set limits. [ABSTRACT FROM AUTHOR]

The interaction between two dielectric plates immersed in an electrolyte solution is examined by using a variational perturbation approximation for the grand partition function. This approach differs from previous treatments in that the screening length between the plates is treated as a variational parameter. A key finding is that adjacent to each plate is a layer of ion depletion with thickness given by about one-half of a Bjerrum length. Consequently, for plate-plate separations less than the Bjerrum length, nearly all the electrolyte is excluded from between the plates, and the interaction is given by the sum of a van der Waals interaction and an attractive osmotic depletion force. In contrast to the predictions of previous theories, the interaction between the plates at short range increases with increasing electrolyte concentration and may provide an important contribution to the salt-induced attraction, commonly referred to as salting out. Because the range of the osmotic depletion force is roughly equal to the Bjerrum length, it increases with the square of the valency of the electrolyte. At larger plate-plate separations, the van der Waals interaction is screened as electrolyte enters the space between the plates, leading to an exponential decay of the interactions, as has been previously observed. However, this interaction is slightly stronger than that previously predicted, due to ion depletion from the surface of the interface, also this effect increases with increasing electrolyte concentration. [ABSTRACT FROM AUTHOR]

The application of the frozen-core approximation (FCA) and effective core potentials (ECPs) within symmetry-adapted perturbation theory (SAPT) has been investigated and implemented. Unlike in the case of conventional electronic-structure theories, the development of a frozen-core version of SAPT is not straightforward. In particular, the FCA realizations neglecting excitations from core orbitals and restricting all summation indices to valence orbitals only are no longer equivalent. It is shown that it is necessary in SAPT to keep some terms containing products of the valence orbitals of one monomer and the core orbitals of the other one in the exchange-energy components. When these terms are included or, equivalently, the “infinite-excitation-energy” approximation omitting only the excitations from the core orbitals is used, the accuracy of the frozen-core approximation in SAPT matches that obtained in supermolecular perturbational and coupled-cluster methods. If these terms are neglected, i.e., within the “index-range-restriction” approximation, several exchange corrections are significantly underestimated. When ECPs are used in SAPT, the accuracy of the interaction energies is as good as in conventional supermolecular methods, provided that the residual supermolecular Hartree-Fock term is included. We have found that only some types of ECPs can be reliably used for calculations of interaction energies both in SAPT and in supermolecular approaches. For systems containing heavy atoms, both FCA and the use of ECPs lead to very significant savings of computer time. [ABSTRACT FROM AUTHOR]

The zero-field splitting (ZFS) (expressed in terms of the D tensor) is the leading spin-Hamiltonian parameter for systems with a ground state spin S>1/2. To first order in perturbation theory, the ZFS arises from the direct spin-spin dipole-dipole interaction. To second order, contributions arise from spin-orbit coupling (SOC). The latter contributions are difficult to treat since the SOC mixes states of different multiplicities. This is an aspect of dominant importance for the correct prediction of the D tensor. In this work, the theory of the D tensor is discussed from the point of view of analytic derivative theory. Starting from a general earlier perturbation treatment [F. Neese and E. I. Soloman, Inorg. Chem. 37, 6568 (1998)], straightforward response equations are derived that are readily transferred to the self-consistent field (SCF) Hartree-Fock (HF) or density functional theory (DFT) framework. The main additional effort in such calculations arises from the solution of nine sets of nonstandard coupled-perturbed SCF equations. These equations have been implemented together with the spin-orbit mean-field representation of the SOC operator and a mean-field treatment of the direct spin-spin interaction into the ORCA electronic structure program. A series of test calculations on diatomic molecules with accurately known zero-field splittings shows that the new approach corrects most of the shortcomings of previous DFT based methods and, on average, leads to predictions within 10% of the experimental values. The slope of the correlation line is essentially unity for the B3LYP and BLYP functionals compared to ∼0.5 in previous treatments. [ABSTRACT FROM AUTHOR]

Double-hybrid density functionals are based on a mixing of standard generalized gradient approximations (GGAs) for exchange and correlation with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional (dubbed B2PLYP) contains only two empirical parameters that describe the mixture of HF and GGA exchange (ax) and of the PT2 and GGA correlation (ac), respectively. Extensive testing has recently demonstrated the outstanding accuracy of this approach for various ground state problems in general chemistry applications. The method is extended here without any further empirical adjustments to electronically excited states in the framework of time-dependent density functional theory (TD-DFT) or the closely related Tamm-Dancoff approximation (TDA-DFT). In complete analogy to the ground state treatment, a scaled second-order perturbation correction to configuration interaction with singles (CIS(D)) wave functions developed some years ago by Head-Gordon et al. [Chem. Phys. Lett. 219, 21 (1994)] is computed on the basis of density functional data and added to the TD(A)-DFT/GGA excitation energy. The method is implemented by applying the resolution of the identity approximation and the efficiency of the code is discussed. Extensive tests for a wide variety of molecules and excited states (of singlet, triplet, and doublet multiplicities) including electronic spectra are presented. In general, rather accurate excitation energies (deviations from reference data typically <0.2 eV) are obtained that are mostly better than those from standard functionals. Still, systematic errors are obtained for Rydberg (too low on average by about 0.3 eV) and charge-transfer transitions but due to the relatively large ax parameter (0.53), B2PLYP outperforms most other functionals in this respect. Compared to conventional HF-based CIS(D), the method is more robust in electronically complex situations due to the implicit account of static correlation effects by the GGA parts. The (D) correction often works in the right direction and compensates for the overestimation of the transition energy at the TD level due to the elevated fraction of HF exchange in the hybrid GGA part. Finally, the limitations of the method are discussed for challenging systems such as transition metal complexes, cyanine dyes, and multireference cases. [ABSTRACT FROM AUTHOR]

A systematic method for approximating the ab initio electronic energy of molecules from the energies of molecular fragments has been adapted to estimate the total electronic energy of crystal lattices. The fragmentation method can be employed with any ab initio electronic structure method and allows optimization of the crystal structure based on ab initio gradients. The method is demonstrated on SiO2 polymorphs using the Hartree-Fock approximation, second order Möller-Plesset perturbation theory, and the quadratic configuration interaction method with single and double excitations and triple excitations added perturbatively . [ABSTRACT FROM AUTHOR]

129Xe nuclear shielding tensor is calculated at the leading-order, one-electron Breit-Pauli perturbation theory (BPPT) level for the xenon fluorides XeF+, XeF2, XeF3+, and XeF4 that cover the large nuclear magnetic resonance chemical shift range of this nucleus. BPPT is found to improve the shift range and relative shifts as compared to the nonrelativistic (NR) theory. While the full BPPT expansion consists of 16 relativistic terms, 5 of them are responsible for the entire chemical shift and shielding anisotropy. The remaining terms are practically isotropic, corelike contributions that are significant for the absolute shielding constant but cancel for the relative chemical shifts. The five principal terms are due to the spin-orbit-modified wave function allowing the Fermi contact and spin-dipole hyperfine interactions to be coupled to the orbital Zeeman interaction, as well as three distinct scalar relativistic modifications of the NR paramagnetic shielding: wave function change due to mass-velocity and Darwin interactions and the relativistic modification of the orbital hyperfine interaction. A very good agreement with the experimental shifts is obtained for XeF2 and the particularly challenging XeF+ species when both the NR and the five main relativistic terms are calculated at electron-correlated ab initio levels of theory. The performance of density-functional theory (DFT) with different pure and hybrid exchange-correlation functionals (with increasing exact exchange admixture) is tested against the ab initio data for each individual contribution. It is shown that DFT has difficulties in the description of paramagnetic shielding, already and especially in the NR contribution, which causes a large discrepancy of DFT results with experiment for xenon fluorides. In contrast, the DFT errors for the relativistic terms cancel out to the extent that a fairly good approximation of the total relativistic shift and anisotropy contributions may be obtained. A combination of high-level ab initio NR calculation with hybrid DFT estimates of the five main BPPT terms is proposed for reasonable estimates of xenon chemical shift in molecules. For the difficult cases such as the present XeF+ and XeF3+ cations, correlated ab initio calculations are unavoidable throughout. None of the other currently available relativistic methods, either at the fully relativistic or a variationally stable quasirelativistic levels of theory, surpasses the quality of the present approach for Xe shifts in these systems. [ABSTRACT FROM AUTHOR]

A simple procedure for the determination of hard sphere (HS) solid phase radial distribution function (rdf) is proposed, which, thanks to its physical foundation, allows for extension to other crystal structures besides the fcc structure. The validity of the procedure is confirmed by comparing (1) the predicted HS solid phase rdf’s with corresponding simulation data and (2) the predicted non-HS solid phase Helmholtz free energy by the present solid phase first-order thermodynamic perturbation theory (TPT) whose numerical implementation depends on the HS solid phase rdf’s as input, with the corresponding predictions also by the first-order TPT but the required HS solid phase rdf is given by an “exact” empirical simulation-fitted formula. The present solid phase first-order TPT predicts isostructural fcc-fcc transition of a hard core attractive Yukawa fluid, in very satisfactory agreement with the corresponding simulation data and is far more accurate than a recent thermodynamically consistent density functional perturbation theory. The present solid phase first-order TPT is employed to investigate multiple solid phases. It is found that a short-ranged potential, even if it is continuous and differentiable or is superimposed over a long-ranged potential, is sufficient to induce the multiple solid phases. When the potential range is short enough, not only isostructural fcc-fcc transition but also isostructural bcc-bcc transition, simple cubic (sc)-sc transition, or even fcc-bcc, fcc-sc, and bcc-sc transitions can be induced. Even triple point involving three solid phases becomes possible. The multiple solid phases can be stable or metastable depending on the potential parameters. [ABSTRACT FROM AUTHOR]

Theoretical foundation of rate kernel equation approaches for diffusion-influenced chemical reactions is presented and applied to explain the kinetics of fluorescence quenching reactions. A many-body master equation is constructed by introducing stochastic terms, which characterize the rates of chemical reactions, into the many-body Smoluchowski equation. A Langevin-type of memory equation for the density fields of reactants evolving under the influence of time-independent perturbation is derived. This equation should be useful in predicting the time evolution of reactant concentrations approaching the steady state attained by the perturbation as well as the steady-state concentrations. The dynamics of fluctuation occurring in equilibrium state can be predicted by the memory equation by turning the perturbation off and consequently may be useful in obtaining the linear response to a time-dependent perturbation. It is found that unimolecular decay processes including the time-independent perturbation can be incorporated into bimolecular reaction kinetics as a Laplace transform variable. As a result, a theory for bimolecular reactions along with the unimolecular process turned off is sufficient to predict overall reaction kinetics including the effects of unimolecular reactions and perturbation. As the present formulation is applied to steady-state kinetics of fluorescence quenching reactions, the exact relation between fluorophore concentrations and the intensity of excitation light is derived. [ABSTRACT FROM AUTHOR]