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We present a hierarchy of local coupled cluster (CC) linear response (LR) methods to calculate ionization potentials (IPs), i.e., excited states with one electron annihilated relative to a ground state reference. The time-dependent perturbation operator V(t), as well as the operators related to the first-order (with respect to V(t)) amplitudes and multipliers, thus are not number conserving and have half-integer particle rank m. Apart from calculating IPs of neutral molecules, the method offers also the possibility to study ground and excited states of neutral radicals as ionized states of closed-shell anions. It turns out that for comparable accuracy IPs require a higher-order treatment than excitation energies; an IP-CC LR method corresponding to CC2 LR or the algebraic diagrammatic construction scheme through second order performs rather poorly. We therefore systematically extended the order with respect to the fluctuation potential of the IP-CC2 LR Jacobian up to IP-CCSD LR, keeping the excitation space of the first-order (with respect to V(t)) cluster operator restricted to the m = 1/2 ⊕ 3/2 subspace and the accuracy of the zero-order (ground-state) amplitudes at the level of CC2 or MP2. For the more expensive diagrams beyond the IP-CC2 LR Jacobian, we employ local approximations. The implemented methods are capable of treating large molecular systems with hundred atoms or more. [ABSTRACT FROM AUTHOR]

We introduce orbital specific virtuals (OSVs) to represent the truncated pair-specific virtual space in periodic local Møller-Plesset perturbation theory of second order (LMP2). The OSVs are constructed by diagonalization of the LMP2 amplitude matrices which correspond to diagonal Wannier-function (WF) pairs. Only a subset of these OSVs is adopted for the subsequent OSV-LMP2 calculation, namely, those with largest contribution to the diagonal pair correlation energy and with the accumulated value of these contributions reaching a certain accuracy. The virtual space for a general (non diagonal) pair is spanned by the union of the two OSV sets related to the individual WFs of the pair. In the periodic LMP2 method, the diagonal LMP2 amplitude matrices needed for the construction of the OSVs are calculated in the basis of projected atomic orbitals (PAOs), employing very large PAO domains. It turns out that the OSVs are excellent to describe short range correlation, yet less appropriate for long range van der Waals correlation. In order to compensate for this bias towards short range correlation, we augment the virtual space spanned by the OSVs by the most diffuse PAOs of the corresponding minimal PAO domain. The Fock and overlap matrices in OSV basis are constructed in the reciprocal space. The 4-index electron repulsion integrals are calculated by local density fitting and, for distant pairs, via multipole approximation. New procedures for determining the fit-domains and the distant-pair lists, leading to higher efficiency in the 4-index integral evaluation, have been implemented. Generally, and in contrast to our previous PAO based periodic LMP2 method, the OSV-LMP2 method does not require anymore great care in the specification of the individual domains (to get a balanced description when calculating energy differences) and is in that sense a black box procedure. Discontinuities in potential energy surfaces, which may occur for PAO-based calculations if one is not careful, virtually disappear for OSV-LMP2. Moreover, due to much increased compactness of the pair-specific virtual spaces, the OSV-LMP2 calculations are faster and require much less memory than PAO-LMP2 calculations, despite the noticeable overhead of the initial OSV construction procedure. [ABSTRACT FROM AUTHOR]

We describe theory and implementation of oscillator strengths, orbital-relaxed first-order properties, and nuclear gradients for the local algebraic diagrammatic construction scheme through second order. The formalism is derived via time-dependent linear response theory based on a second-order unitary coupled cluster model. The implementation presented here is a modification of our previously developed algorithms for Laplace transform based local time-dependent coupled cluster linear response (CC2LR); the local approximations thus are state specific and adaptive. The symmetry of the Jacobian leads to considerable simplifications relative to the local CC2LR method; as a result, a gradient evaluation is about four times less expensive. Test calculations show that in geometry optimizations, usually very similar geometries are obtained as with the local CC2LR method (provided that a second-order method is applicable). As an exemplary application, we performed geometry optimizations on the low-lying singlet states of chlorophyllide a. [ABSTRACT FROM AUTHOR]

In order to arrive at linear scaling of the computational cost with molecular size, local coupled cluster methods discriminate pairs of local molecular orbitals according to the spatial separation R of the latter. Only strong pairs are treated at the full coupled cluster level, whereas for weak pairs a lower level of theory (usually Møller-Plesset perturbation theory of second order,MP2) is used. Yet anMP2 treatment of weak pairs is inadequate in certain situations (for example, for describing p-stacking), which calls for an improved but still inexpensive method for dealing with the weak pairs. In a previous contribution, we proposed as a substituent for MP2 the LrCCD3 method, which is based on ring coupled cluster doubles (ring-CCD) and includes all third-order diagrams with energy contributions decaying not quicker than R-6. In the present work, we explore a still more accurate method, which is based on the same principles. It turned out to be essential to abandon the restriction to ring-CCD, i.e., to include further CCD diagrams beyond the ring approximation. The occurring intermediates turn out to be formally very similar to LMP2 density matrices, such that an efficient evaluation of these non-ring CCD diagrams is possible. Furthermore, a computationally cheap a posteriori estimate for the fourth-order singles contribution to the weak pair energy, which also exhibits a decay behavior of R-6, is introduced. The resulting method, denoted as LCCD[S]-R-6, indeed provides a substantial improvement in accuracy over the previous LrCCD3 method at a relatively modest additional computational cost. [ABSTRACT FROM AUTHOR]

A multistate local CC2 response method for the calculation of analytic energy gradients with respect to nuclear displacements is presented for ground and electronically excited states. The gradient enables the search for equilibrium geometries of extended molecular systems. Laplace transform is used to partition the eigenvalue problem in order to obtain an effective singles eigenvalue problem and adaptive, state-specific local approximations. This leads to an approximation in the energy Lagrangian, which however is shown (by comparison with the corresponding gradient method without Laplace transform) to be of no concern for geometry optimizations. The accuracy of the local approximation is tested and the efficiency of the new code is demonstrated by application calculations devoted to a photocatalytic decarboxylation process of present interest. [ABSTRACT FROM AUTHOR]

A multistate local CC2 response method for the calculation of orbital-relaxed first order properties is presented for ground and electronically excited states. It enables the treatment of excited state properties including orbital relaxation for extended molecular systems and is a major step on the way towards analytic gradients with respect to nuclear displacements. The Laplace transform method is employed to partition the eigenvalue problem and the lambda equations, i.e., the doubles parts of these equations are inverted on-the-fly, leaving only the corresponding effective singles equations to be solved iteratively. Furthermore, the state specific local approximations are adaptive. Density-fitting is utilized to decompose the electron-repulsion integrals. The accuracy of the local approximation is tested and the efficiency of the new code is demonstrated on the example of an organic sensitizer for solar-cell applications, which consists of about 100 atoms. [ABSTRACT FROM AUTHOR]

A local method based on orbital specific virtuals (OSVs) for calculating the perturbative triples correction in local coupled cluster calculations is presented. In contrast to the previous approach based on projected atomic orbitals (PAOs), described by Schütz [J. Chem. Phys. 113, 9986 (2000)], the new scheme works without any ad hoc truncations of the virtual space to domains. A single threshold defines the pair and triple specific virtual spaces completely and automatically. It is demonstrated that the computational cost of the method scales linearly with molecular size. Employing the recommended threshold a similar fraction of the correlation energy is recovered as with the original PAO method at a somewhat lower cost. A benchmark for 52 reactions demonstrates that for reaction energies the intrinsic accuracy of the coupled cluster with singles and doubles excitations and a perturbative treatment of triples excitations method can be reached by OSV-local coupled cluster theory with singles and doubles and perturbative triples, provided a MP2 correction is applied that accounts for basis set incompleteness errors as well as for remaining domain errors. As an application example the interaction energies of the guanine-cytosine dimers in the Watson-Crick and stacked arrangements are investigated at the level of local coupled cluster theory with singles and doubles and perturbative triples. Based on these calculations we propose new complete-basis-set-limit estimates for these interaction energies at this level of theory. [ABSTRACT FROM AUTHOR]

We present a density fitted local configuration interaction singles (CIS) method for calculating optical bandgaps in 3D-periodic systems. We employ an Ewald technique to carry out infinite lattice summations for the exciton-exciton interaction, and robust product-density specific local density fitting in direct space for the electron-hole interaction. Moreover, we propose an alternative to the usual cyclic model with Born-von Karman periodic boundary conditions, the so called Wigner-Seitz supercell truncated infinite model, which exhibits much improved convergence of the CIS excitation energy with respect to the size of the supercell. Test calculations on a series of prototypical systems demonstrate that the method at the present stage can be used to calculate the excitonic bandgaps of 3D periodic systems with up to a dozen atoms in the unit cell, ranging from wide-gap insulators to semiconductors. [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]

We extend the orbital-specific-virtual tensor factorization, introduced for local Mo\ller-Plesset perturbation theory in Ref. [J. Yang, Y. Kurashige, F. R. Manby and G. K. L. Chan, J. Chem. Phys. 134, 044123 (2011)], to local coupled cluster singles and doubles theory (OSV-LCCSD). The method is implemented by modifying an efficient projected-atomic-orbital local coupled cluster program (PAO-LCCSD) described recently, [H.-J. Werner and M. Schütz, J. Chem. Phys. 135, 144116 (2011)]. By comparison of both methods we find that the compact representation of the amplitudes in the OSV approach affords various advantages, including smaller computational time requirements (for comparable accuracy), as well as a more systematic control of the error through a single energy threshold. Overall, the OSV-LCCSD approach together with an MP2 correction yields small domain errors in practical calculations. The applicability of the OSV-LCCSD is demonstrated for molecules with up to 73 atoms and realistic basis sets (up to 2334 basis functions). [ABSTRACT FROM AUTHOR]

The atomic orbital basis set limit is approached in periodic correlated calculations for solid LiH. The valence correlation energy is evaluated at the level of the local periodic second order Mo\ller-Plesset perturbation theory (MP2), using basis sets of progressively increasing size, and also employing 'bond'-centered basis functions in addition to the standard atom-centered ones. Extended basis sets, which contain linear dependencies, are processed only at the MP2 stage via a dual basis set scheme. The local approximation (domain) error has been consistently eliminated by expanding the orbital excitation domains. As a final result, it is demonstrated that the complete basis set limit can be reached for both HF and local MP2 periodic calculations, and a general scheme is outlined for the definition of high-quality atomic-orbital basis sets for solids. [ABSTRACT FROM AUTHOR]

We present a density fitted local configuration interaction singles (CIS) method for calculating optical band gaps in 1D-periodic systems. The method is based on the Davidson diagonalization procedure, carried out in the reciprocal space. The one-electron part of the matrix-vector products is also evaluated in the reciprocal space, where the diagonality of the Fock matrix can be exploited. The contraction of the CIS vectors with the two electron integrals is performed in the direct space in the basis of localized occupied (Wannier) and virtual (projected atomic) orbitals. The direct space approach allows to utilize the sparsity of the integrals due to the local representation and locality of the exciton. The density fitting approximation employed for the two electron integrals reduces the nominal scaling with unit cell size to O(N4). Test calculations on a series of prototypical systems demonstrate that the method in its present stage can be used to calculate the excitonic band gaps of polymers with up to a few dozens of atoms in the cell. The computational cost depends on the locality of the exciton, but even relatively delocalized excitons occurring in the polybiphenyl in the parallel orientation, can be routinely treated with this method. [ABSTRACT FROM AUTHOR]

A new multistate local CC2 response method for calculating excitation energies and first-order properties of excited triplet states in extended molecular systems is presented. The Laplace transform technique is employed to partition the left/right local CC2 eigenvalue problems as well as the linear equations determining the Lagrange multipliers needed for the properties. The doubles part in the equations can then be inverted on-the-fly and only effective equations for the singles part must be solved iteratively. The local approximation presented here is adaptive and state-specific. The density-fitting method is utilized to approximate the electron-repulsion integrals. The accuracy of the new method is tested by comparison to canonical reference values for a set of 12 test molecules and 62 excited triplet states. As an illustrative application example, the lowest four triplet states of 3-(5-(5-(4-(bis(4-(hexyloxy)phenyl)amino)phenyl)thiophene-2-yl)thiophene-2-yl)-2-cyanoacrylic acid, an organic sensitizer for solar-cell applications, are computed in the present work. No triplet charge-transfer states are detected among these states. This situation contrasts with the singlet states of this molecule, where the lowest singlet state has been recently found to correspond to an excited state with a pronounced charge-transfer character having a large transition strength. [ABSTRACT FROM AUTHOR]

The lowest electronically excited states of the aniline dimer and trimer related to the lowest π*←π transition of the monomer are investigated by applying time-dependent coupled cluster theory, primarily at the level of the (spin-component-scaled) CC2 model. Minimum energy structures in the vicinity of the Franck-Condon points were determined on the individual potential energy surfaces. For the dimer we find an excimer and a head-to-tail configuration (with the monomers substantially displaced relative to the ground state minimum) for the lowest (dark) and second lowest (bright) states, respectively. The excitation is delocalized on both chromophores for both of these states. For the trimer three distinct minima with quite different hydrogen-bonding arrangements are found for the three lowest states. In strong contrast to the dimer the excitation here is clearly localized on the individual aniline chromophores for each of these three states. One of the three geometries is rather similar to the ground state minimum, while the two others are rather different and thus have presumably quite small Franck-Condon factors. It can be expected that only the electronic origin of the first conformer can eventually be detected in the absorption spectrum of the trimer, provided that it is separated by high-enough barriers from other, energetically lower configurations. [ABSTRACT FROM AUTHOR]

The aniline dimer and trimer are investigated in their electronic ground state. The potential energy surface was thoroughly searched for low lying minima by applying global optimizations on a model potential, which is recalibrated on-the-fly by ab initio calculations (spin-component-scaled LMP2) at relevant configurations. The most stable structure of the dimer corresponds to a head-to-tail arrangement with both aniline monomers being nearly equivalent. DFT-SAPT calculations reveal that the interaction energy is dominated by van der Waals dispersion, which is of comparable size as for the benzene dimer, but with a much larger total interaction energy than for the latter. The global minimum of the aniline trimer corresponds to a hydrogen bonding arrangement involving three directional NH–N hydrogen bonds, with the individual monomers being clearly distinguishable. Nonadditive three-body dispersion contributions appear to play a minor role for the trimer. [ABSTRACT FROM AUTHOR]

We have calculated the equilibrium geometry, formation energy, and bulk modulus of two molecular bulk crystals, NH3 and CO2, at the periodic post-Hartree–Fock correlated level. The dependence of the results on the basis set has been analyzed, by employing basis sets up to aug-cc-pVQZ quality. In the calculations, we used the periodic local Mo\ller–Plesset second order perturbation theory (LMP2), implemented in the CRYSCOR program. Multipolar expansion techniques, as well as density fitting, are employed in this code to reduce the number of and to factorize the required electron repulsion integrals; as a consequence of that, the computational cost for the correlation part of the calculations is comparable to that of the Hartree–Fock. Auxiliary calculations performed on molecular dimers are also reported to verify the accuracy of the LMP2 approach and of the basis sets used. Furthermore, the effect of spin-component scaling has been investigated for the two crystals. One intention of the present paper is also to lay out and specify the computational setup, which is generally applicable for accurate CRYSCOR calculations on molecular crystals. [ABSTRACT FROM AUTHOR]

A new Laplace transform based multistate local CC2 response method for calculating excitation energies of extended molecular systems is presented. By virtue of the Laplace transform trick, the eigenvalue problem involving the local CC2 Jacobian is partitioned along the doubles-doubles block (which is diagonal in the parental canonical method) without losing the sparsity in the integral, amplitude, and amplitude response supermatrices. Hence, only an effective eigenvalue problem involving singles vectors has to be solved, while the doubles part can be computed on-the-fly. Within this framework, a multistate treatment of excited states with state specific and adaptive local approximations imposed on the doubles part is straightforwardly possible. Furthermore, in the context of the density fitting approximation of the two-electron integrals, a procedure to specify the local approximation, i.e., the restricted pair lists and domains, on the basis of an analysis of the object to be approximated itself is proposed. Performance and accuracy of the new Laplace transformed density fitted local CC2 (LT-DF-LCC2) response method are tested for set of different test molecules and states. It turns out that LT-DF-LCC2 response is much more robust than the earlier local CC2 response method proposed before, which failed to find some excited states in difficult cases. [ABSTRACT FROM AUTHOR]

The potential energy surfaces of the S0 and S1(π*←π) states of the 2-naphthol(H2O)n, n∈{1,2} clusters were explored at the level of coupled cluster (CC2) response theory. In the electronic ground state two different types of hydrogen-bonding networks coexist for n=2, (i) a cyclic one [similar to those of the water trimer and phenol(H2O)2] where the hydroxy group of the aryl alcohol acts simultaneously as H donor for the first, and as H acceptor for the second water molecule, and (ii) a hydrogen-bonding arrangement where the aromatic π system is taking over the role as H acceptor. In the S1 state, on the other hand, the cyclic conformers are unstable. Consequently, the first group of cyclic ground state conformers gives rise to broad unstructured band shapes in the absorption spectrum, whereas the second group of conformers involving the aromatic π system gives rise to nicely structured band shapes. Based on these results the puzzling absorption spectrum of the n=2 cluster can properly be interpreted. [ABSTRACT FROM AUTHOR]

A hybrid scheme for the computation of reaction energies in large molecular systems is proposed. The approach is based on localized orbitals and allows for the treatment of different parts of a molecule at different computational levels. The localized orbitals are assigned to regions, and then different local correlation methods, such as local MP2 or local CCSD(T), can be applied to different regions. In contrast to previous hybrid schemes, the molecule does not have to be split into parts and, therefore, it is not necessary to saturate dangling bonds using link atoms. For fixed region sizes, the cost of the high-level calculation becomes independent of the molecular size, and it is demonstrated that O(1) scaling can be achieved. Illustrative applications are presented and the convergence of the results with respect to the size of the regions is investigated for reaction energies, barrier heights, and weakly bound complexes. [ABSTRACT FROM AUTHOR]

The S1(π*←π) state surfaces of the phenol-water1<=n<=3 clusters are reexplored at the level of coupled cluster response theory. The global minima for n=2 and n=3 so obtained are qualitatively different from those reported so far, which were obtained with methods such as configuration interaction singles or complete active space self-consistent field lacking dynamical electron correlation effects. Furthermore, the minimum-energy points on the conical intersection seams were located in this work. The results of these calculations offer a qualitative explanation for the anomalous photophysical behavior (broad congested absorption band structure, low quantum yield, short lifetime) of n=2 and the observed predissociation of n=3 at excess energies beyond ≈100 cm-1, resolving a disagreement between theory and experiment which persisted for almost a decade [ABSTRACT FROM AUTHOR]

A new ab initio method for calculating transition strengths and orbital-unrelaxed first-order properties of singlet ground and excited states of extended molecular systems is presented. It is based on coupled cluster response theory at the level of the CC2 model with local approximations introduced to the doubles-excitation part of the wave function. Density fitting is employed for the calculation of the electron repulsion integrals, so that—with the exception of doubles amplitudes—only three-indexed objects do occur in the formalism. The new method was tested by performing calculations for a set of various molecules and excited states and by comparing the results with corresponding canonical (nonlocal) calculations. It turned out that for calculating transition strengths and properties of excited states the ordinary Boughton-Pulay domains are insufficient in numerous cases. To circumvent this problem a new scheme for extending domains is proposed, which is based on the solution of the coupled perturbed localization and Hartree-Fock equations. When such extended domains are used, a satisfactory agreement between canonical and local results is achieved. [ABSTRACT FROM AUTHOR]

A new local method for the computation of electronic excitation energies of singlet states in extended molecular systems is presented. It is based on the CC2 model and local approximations to the wave functions. In the proposed method the singles excitations are treated nonlocally and local restrictions are imposed on doubles amplitudes only. The accuracy of the new method was tested by calculating several lowest excited states for 14 molecules and comparing them with canonical CC2 values. Deviations of the local excitation energies from the canonical reference values do not exceed 0.05 eV for all test molecules and all states in the lower energy range investigated in this work. The method uses the density-fitting approximation for all two-electron integrals, which considerably simplifies the computational complexity of the individual diagrams. A combination of the local approximations and the powerful density-fitting technique leads to a low-scaling method, capable to treat molecular systems comprised of 100 atoms and more in a basis of a polarized double zeta quality. A test calculation for a system consisting of 127 atoms and 370 active electrons without symmetry is presented to show the efficiency of the new method. [ABSTRACT FROM AUTHOR]

An efficient method to compute analytical energy derivatives for local second-order Møller–Plesset perturbation energy is presented. Density fitting approximations are employed for all 4-index integrals and their derivatives. Using local fitting approximations, quadratic scaling with molecular size and cubic scaling with basis set size for a given molecule is achieved. The density fitting approximations have a negligible effect on the accuracy of optimized equilibrium structures or computed energy differences. The method can be applied to much larger molecules and basis sets than any previous second-order Møller–Plesset gradient program. The efficiency and accuracy of the method is demonstrated for a number of organic molecules as well as for molecular clusters. Examples of geometry optimizations for molecules with 100 atoms and over 2000 basis functions without symmetry are presented. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The ground- and first excited state of s-tetrazine arising from a π*←n excitation (1Ag,1B3u) have been studied using the complete active space (CASSCF) and the second order multiconfiguration perturbation theory (CASPT2) ab initio methods. The focus of this study is on the effect of the electronic excitation on the molecular structure and on those electronic properties which are important to model the solvatochromatic behavior of the molecule in polymer matrices as used in permanent hole burning experiments. Since the accurate computation of excited state molecular properties represents a major challenge for today’s numerical quantum chemistry, some technical aspects are also considered. The present study shows that the change in geometry upon electronic excitation is small. This is in partial contradiction with the experimental studies which however disagree among themselves [see K. K. Innes, I. G. Ross, and W. R. Moomaw, J. Mol. Spectrosc. 132, 492 (1988), and R. E. Smalley, L. Wharton, and D. H. Levi, ibid. 66, 375 (1977)]. This study also confirms that the first excited state equilibrium structure is of D2h symmetry. In an earlier theoretical study it was found that the D2h symmetry structure may represent a saddle point rather than a minimum on the excited state potential surface [see A. C. Scheiner and H. F. Schaefer III, J. Chem. Phys. 87, 3539 (1987)]. In the first excited state, we observe an increase of the mean polarizability of s-tetrazine along with an enhanced anisotropy. The change in the polarizability is almost exclusively in the ‘‘in-plane’’ components of the tensor; the polarizability in the vertical direction is nearly unchanged. This observation questions recent experimental results reported for this molecule [see S. Heitz, D. Weidnauer, and A. Hese, J. Chem. Phys. 95, 7952 (1991)]. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We report a combined spectroscopic and theoretical investigation of the intermolecular vibrations of supersonic jet-cooled phenol·(H2O)3 and d1-phenol·(D2O)3 in the S0 and S1 electronic states. Two-color resonant two-photon ionization combined with time-of-flight mass spectrometry and dispersed fluorescence emission spectroscopy provided mass-selective vibronic spectra of both isotopomers in both electronic states. In the S0 state, eleven low-frequency intermolecular modes were observed for phenol·(H2O)3, and seven for the D isotopomer. For the S1 state, several intermolecular vibrational excitations were observed in addition to those previously reported. Ab initio calculations of the cyclic homodromic isomer of phenol·(H2O)3 were performed at the Hartree–Fock level. Calculations for the eight possible conformers differing in the position of the ‘‘free’’ O–H bonds with respect to the almost planar H-bonded ring predict that the ‘‘up–down–up–down’’ conformer is differentially most stable. The calculated structure, rotational constants, normal-mode eigenvectors, and harmonic frequencies are reported. Combination of theory and experiment allowed an analysis and interpretation of the experimental S0 state vibrational frequencies and isotope shifts. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The global and local minima, stationary points, and torsional rearrangement processes of cyclic homodromic (H2O)4 were studied on its four-dimensional torsional intermolecular potential energy surface. Eight different energetically low-lying torsional stationary point structures were found by ab initio theory, and fully structure-optimized at the second-order Mo\ller–Plesset level, using large basis sets. Second-order energies close to the one-particle basis set limit were obtained at these geometries using the explicitly correlated Mo\ller–Plesset method. The effects of higher-order correlation energy terms were investigated by coupled cluster theory, and terms beyond second order were found to cancel in good approximation. The S4 symmetric global minimum has a square and almost planar O...O...O...O arrangement with free O–H bonds alternating ‘‘up’’ and ‘‘down’’ relative to this plane, with two isometric versions of this structure. Another torsional conformer with two neighboring up O–H bonds followed by two neighboring down O–H bonds is a local minimum, 0.93 kcal/mol above the global minimum. The four versions of this structure are connected to the global minima via two distinct but almost degenerate first-order torsional saddle points, which occur as two sets of eight isometric versions each, both about 1.24 kcal/mol above the global minimum. Yet another set of eight second-order saddle points lies at 1.38 kcal/mol. The structure with three O–H bonds up and one down is not a stationary point, while the structure with all four O–H bonds on the same side of the plane is a first-order saddle point.The fully planar C4h symmetric structure is a fourth-order stationary point 2.8 kcal/mol above the minimum. The torsional interconversion paths between this multitude of points are complex, and are discussed in three-dimensional spaces of symmetry-adapted... [ABSTRACT FROM AUTHOR]

A torsional potential energy surface for the cyclic water trimer was calculated at the level of second-order Mo\ller–Plesset perturbation theory. For the construction of this ab initio surface, the first-order wave function was expanded in a many-electron basis which linearly depends on the interelectronic coordinates r12. The one-electron basis of Gaussian orbitals was calibrated on the water monomer and dimer to ensure that the ab initio surface computed represents the (near- ) basis set limit for the level of theory applied. The positions of the free O—H bonds are described by three torsional angles. The respective three-dimensional torsional space was investigated by 70 counterpoise corrected single-point calculations for various values of these angles, providing a grid to fit an analytical representation of the potential energy surface. The four symmetry unique stationary points previously found at the Hartree–Fock and conventional Mo\ller–Plesset levels [Schütz et al., J. Chem. Phys. 99, 5228 (1993)] were studied in detail: Relative energies of the structures were calculated by applying second-order Mo\ller–Plesset and coupled cluster methods; harmonic vibrational frequencies were calculated at the second-order Mo\ller–Plesset level with a 6-311++G(d,p) basis set at these stationary points. It is expected that the present torsional potential energy surface for the water trimer will play an important role in the understanding of the vibrational transitions observed by far-infrared vibration–rotation–tunneling spectroscopy in terms of a nearly free pseudorotational interconversion on a cyclic vibrational–tunneling path. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The minimum energy structure of the cyclic water trimer, its stationary points, and rearrangement processes at energies <1 kcal/mol above the global minimum are examined by ab initio molecular orbital theory. Structures corresponding to stationary points are fully optimized at the Hartree–Fock and second-order Mo\ller–Plesset levels, using the 6-311++G(d,p) basis; each stationary point is characterized by harmonic vibrational analyses. The lowest energy conformation has two free O–H bonds on one and the third O–H bond on the other side of an approximately equilateral hydrogen-bonded O...O...O (O3) triangle. The lowest energy rearrangement pathway corresponds to the flipping of one of the two free O–H bonds which are on the same side of the plane across this plane via a transition structure with this O–H bond almost within the O3 plane. Six distinguishable, but isometric transition structures of this type connect six isometric minimum energy structures along a cyclic vibrational-tunneling path; neighboring minima correspond to enantiomers. The potential energy along this path has C6 symmetry and a very low barrier V6=0.1±0.1 kcal/mol. This implies nearly free pseudorotational interconversion of the six equilibrium structures. The corresponding anharmonic level structure was modeled using an internal rotation Hamiltonian. Two further low-energy saddle points on the surface are of second and third order; they correspond to crown-type and planar geometries with C3 and C3h symmetries, respectively. Interconversion tunneling vibrations via these stationary points are also important for the water trimer dynamics. A unified and symmetry-adapted description of the intermolecular potential energy surface is given in terms of the three flipping coordinates of the O–H bonds. Implications of these results for the interpretation of spectroscopic data are discussed. [ABSTRACT FROM AUTHOR]

A combined experimental and theoretical study of the 2-naphthol·H2O/D2O system was performed. Two different rotamers of 2-naphthol (2-hydroxynaphthalene, 2HN) exist with the O–H bond in cis- and trans-position relative to the naphthalene frame. Using Hartree–Fock (HF) calculations with the 6-31G(d,p) basis set, fully energy-minimized geometries were computed for both cis- and trans-2HN·H2O of (a) the equilibrium structures with trans-linear H-bond arrangement and Cs symmetry and (b) the lowest-energy transition states for H atom exchange on the H2O subunit, which have a nonplanar C1 symmetry. Both equilibrium and transition state structures are similar to the corresponding phenol·H2O geometries. The H-bond stabilization energies with zero point energy corrections included are ≊5.7 kcal/mol for both rotamers, ≊2.3 kcal/mol stronger than for the water dimer, and correspond closely to the binding energy calculated for phenol·H2O at the same level of theory. Extension of the aromatic π-system therefore hardly affects the H-bonding conditions. The barrier height to internal rotation around the H-bond only amounts to 0.5 kcal/mol. Harmonic vibrational analysis was carried out at these stationary points on the HF/6-31G(d,p) potential energy surface with focus on the six intermolecular modes. The potential energy distributions and M-matrices reflect considerable mode scrambling for the deuterated isotopomers. For the a’ intermolecular modes anharmonic corrections to the harmonic frequencies were evaluated. The β2 wag mode shows the largest anharmonic contributions. For the torsional mode τ (H2O H-atom exchange coordinate) the vibrational level structure in an appropriate periodic potential was calculated. On the experimental side resonant-two-photon ionization and dispersed fluorescence emission spectra of 2HN·H2O and d-2HN·D2O were measured. A detailed assignment of the bands in... [ABSTRACT FROM AUTHOR]

Extensive ab initio calculations of the phenol·H2O complex were performed at the Hartree–Fock level, using the 6-31G(d,p) and 6-311++G(d,p) basis sets. Fully energy-minimized geometries were obtained for (a) the equilibrium structure, which has a translinear H bond and the H2O plane orthogonal to the phenol plane, similar to (H2O)2; (b) the lowest-energy transition state structure, which is nonplanar (C1 symmetry) and has the H2O moiety rotated by ±90°. The calculated MP2/6-311G++(d,p) binding energy including basis set superposition error corrections is 6.08 kcal/mol; the barrier for internal rotation around the H bond is only 0.4 kcal/mol. Intra- and intermolecular harmonic vibrational frequencies were calculated for a number of different isotopomers of phenol·H2O. Anharmonic intermolecular vibrational frequencies were computed for several intermolecular vibrations; anharmonic corrections are very large for the β2 intermolecular wag. Furthermore, the H2O torsion τ around the H-bond axis, and the β2 mode are strongly anharmonically coupled, and a two-dimensional τ/β2 potential energy surface was explored. The role of tunneling splitting due to the torsional mode is discussed and tunnel splittings are estimated for the calculated range of barriers. The theoretical studies were complemented by a detailed spectroscopic study of h-phenol·H2O and d-phenol·D2O employing two-color resonance-two-photon ionization and dispersed fluorescence emission techniques, which extends earlier spectroscopic studies of this system. The β1 and β2 wags of both isotopomers in the S0 and S1 electronic states are newly assigned, as well as several other weaker transitions. Tunneling splittings due to the torsional mode may be important in the S0 state in conjunction with the excitation of the intermolecular σ and β2 modes. [ABSTRACT FROM AUTHOR]

The recently proposed minimax quadrature for Laplace-transformed energy denominators in second order Mo\ller–Plesset perturbation theory is compared to the conventionally used least-squares quadrature. Our test calculations show that the quality of the least-squares quadrature is not inferior compared to minimax. Its computational overhead (required to determine points and weights of the quadrature) is clearly insignificant relative to the subsequent MP2 calculation. For high accuracy and all-electron calculations (correlated core) good starting guesses for the roots are essential. [ABSTRACT FROM AUTHOR]

Local coupled cluster theory is based on (i) a restriction of the list of pairs (or triples) of occupied molecular orbitals, and (ii) a truncation of the virtual space to orbital pair (or triple) specific subspaces. The latter is motivated by an exponential decay of the contributions to the pair energy with respect to the distance between related local occupied and virtual orbitals; the former only by a polynomial R-6 decay with respect to the distance R between the two occupied orbitals of the pair. Consequently, the restriction of the pair list is more critical, and contributions of pairs should not be neglected unless the corresponding interorbital distance is really large. In local coupled cluster theory pairs are usually discriminated on the basis of the interorbital distance, or the size of the 2nd order Mo\ller-Plesset perturbation theory (MP2) estimate of the pair energy. Only strong pairs are treated at the full coupled cluster level, while weak pairs are treated just at the level of MP2. Yet MP2 might be problematic in certain cases, for example, π-stacking is badly described by MP2, etc. We propose to substitute the MP2 treatment of weak pairs by an approach based on ring-CCD by including third-order diagrams with R-6 decay behavior. Such an approach is clearly superior; it provides higher accuracy, while the computational cost is not significantly higher than that of a MP2 based treatment of weak pairs. [ABSTRACT FROM AUTHOR]

Presents a correction to an article published in the 1993 issue of the 'Journal of Chemical Physics,' which deals with fluxionality.

We present a comprehensive benchmark study of the adsorption energy of a single water molecule on the (001) LiH surface using periodic coupled cluster and quantum Monte Carlo theories. We benchmark and compare different implementations of quantum chemical wave function based theories in order to verify the reliability of the predicted adsorption energies and the employed approximations. Furthermore we compare the predicted adsorption energies to those obtained employing widely used van der Waals density-functionals. Our findings show that quantum chemical approaches are becoming a robust and reliable tool for condensed phase electronic structure calculations, providing an additional tool that can also help in potentially improving currently available van der Waals density-functionals.

In this paper, we present theory and implementation of an efficient program for calculating magnetizabilities and rotational g tensors of closed-shell molecules at the level of local second-order Møller-Plesset perturbation theory (MP2) using London orbitals. Density fitting is employed to factorize the electron repulsion integrals with ordinary Gaussians as fitting functions. The presented program for the calculation of magnetizabilities and rotational g tensors is based on a previous implementation of NMR shielding tensors reported by S. Loibl and M. Schütz [J. Chem. Phys. 137, 084107 (2012)]. Extensive test calculations show (i) that the errors introduced by density fitting are negligible, and (ii) that the errors of the local approximation are still rather small, although larger than for nuclear magnetic resonance (NMR) shielding tensors. Electron correlation effects for magnetizabilities are tiny for most of the molecules considered here. MP2 appears to overestimate the correlation contribution of magnetizabilities such that it does not constitute an improvement over Hartree-Fock (when comparing to higher-order methods like CCSD(T)). For rotational g tensors the situation is different and MP2 provides a significant improvement in accuracy over Hartree-Fock. The computational performance of the new program was tested for two extended systems, the larger comprising about 2200 basis functions. It turns out that a magnetizability (or rotational g tensor) calculation takes about 1.5 times longer than a corresponding NMR shielding tensor calculation.

An efficient local coupled cluster method with single and double excitation operators and perturbative treatment of triple excitations [DF-LCCSD(T)] is described. All required two-electron integrals are evaluated using density fitting approximations. These have a negligible effect on the accuracy but reduce the computational effort by 1-2 orders of magnitude, as compared to standard integral-direct methods. Excitations are restricted to local subsets of non-orthogonal virtual orbitals (domain approximation). Depending on distance criteria, the correlated electron pairs are classified into strong, close, weak, and very distant pairs. Only strong pairs, which typically account for more than 90% of the correlation energy, are optimized in the LCCSD treatment. The remaining close and weak pairs are approximated by LMP2 (local second-order Mo̸ller-Plesset perturbation theory); very distant pairs are neglected. It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations. Using this ansatz for the wavefunction, the evaluation and transformation of the two-electron integrals scale cubically with molecular size. If local density fitting approximations are activated, this is reduced to linear scaling. The LCCSD iterations scale quadratically, but linear scaling can be achieved by neglecting some terms involving contractions of single excitations. The accuracy and efficiency of the method is systematically tested using various approximations, and calculations for molecules with up to 90 atoms and 2636 basis functions are presented., (© 2011 American Institute of Physics)

We have calculated the equilibrium geometry, formation energy, and bulk modulus of two molecular bulk crystals, NH(3) and CO(2), at the periodic post-Hartree-Fock correlated level. The dependence of the results on the basis set has been analyzed, by employing basis sets up to aug-cc-pVQZ quality. In the calculations, we used the periodic local Møller-Plesset second order perturbation theory (LMP2), implemented in the CRYSCOR program. Multipolar expansion techniques, as well as density fitting, are employed in this code to reduce the number of and to factorize the required electron repulsion integrals; as a consequence of that, the computational cost for the correlation part of the calculations is comparable to that of the Hartree-Fock. Auxiliary calculations performed on molecular dimers are also reported to verify the accuracy of the LMP2 approach and of the basis sets used. Furthermore, the effect of spin-component scaling has been investigated for the two crystals. One intention of the present paper is also to lay out and specify the computational setup, which is generally applicable for accurate CRYSCOR calculations on molecular crystals.

The potential energy surfaces of the S(0) and S(1)(pi(*)<--pi) states of the 2-naphthol(H(2)O)(n), n is an element of {1,2} clusters were explored at the level of coupled cluster (CC2) response theory. In the electronic ground state two different types of hydrogen-bonding networks coexist for n=2, (i) a cyclic one [similar to those of the water trimer and phenol(H(2)O)(2)] where the hydroxy group of the aryl alcohol acts simultaneously as H donor for the first, and as H acceptor for the second water molecule, and (ii) a hydrogen-bonding arrangement where the aromatic pi system is taking over the role as H acceptor. In the S(1) state, on the other hand, the cyclic conformers are unstable. Consequently, the first group of cyclic ground state conformers gives rise to broad unstructured band shapes in the absorption spectrum, whereas the second group of conformers involving the aromatic pi system gives rise to nicely structured band shapes. Based on these results the puzzling absorption spectrum of the n=2 cluster can properly be interpreted.

The S1(pi*<--pi) state surfaces of the phenol-water(1