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A systematic study is made of the accuracy and efficiency of a number of existing quadrature schemes for molecular Kohn–Sham Density-Functional Theory (DFT) using 408 molecules and 254 chemical reactions. Included are the fixed SG-x (x = 0–3) grids of Gill et al., Dasgupta, and Herbert, the 3-zone grids of Treutler and Ahlrichs, a fixed five-zone grid implemented in Molpro, and a new adaptive grid scheme. While all methods provide a systematic reduction of errors upon extension of the grid sizes, significant differences are observed in the accuracies for similar grid sizes with various approaches. For the tests in this work, the SG-x fixed grids are less suitable to achieve high accuracies in the DFT integration, while our new adaptive grid performed best among the schemes studied in this work. The extra computational time to generate the adaptive grid scales linearly with molecular size and is negligible compared with the time needed for the self-consistent field iterations for large molecules. A comparison of the grid accuracies using various density functionals shows that meta-GGA functionals need larger integration grids than GGA functionals to reach the same degree of accuracy, confirming previous investigations of the numerical stability of meta-GGA functionals. On the other hand, the grid integration errors are almost independent of the basis set, and the basis set errors are mostly much larger than the errors caused by the numerical integrations, even when using the smallest grids tested in this work. [ABSTRACT FROM AUTHOR]

We present a new computational framework to describe polaritons, which treats photons and electrons on the same footing using coupled-cluster theory. As a proof of concept, we study the coupling between the first electronically excited state of carbon monoxide and an optical cavity. In particular, we focus on how the interaction with the photonic mode changes the vibrational spectroscopic signature of the electronic state and how this is affected when tuning the cavity frequency and the light–matter coupling strength. For this purpose, we consider different methodologies and investigate the validity of the Born–Oppenheimer approximation in such situations. [ABSTRACT FROM AUTHOR]

A new general approach is introduced for defining an optimum zero-order Hamiltonian for Rayleigh–Schrödinger perturbation theory. Instead of taking the operator directly from a model problem, it is constructed to be a best fit to the exact Hamiltonian within any desired functional form. When applied to many-body perturbation theory for electrons, strongly improved convergence is observed in cases where the conventional Fock Hamiltonian leads to divergence or slow convergence. [ABSTRACT FROM AUTHOR]

We derive an electron–vibration model Hamiltonian in a quantum chemical framework and explore the extent to which such a Hamiltonian can capture key effects of nonadiabatic dynamics. The model Hamiltonian is a simple two-body operator, and we make preliminary steps at applying standard quantum chemical methods to evaluate its properties, including mean-field theory, linear response, and a primitive correlated model. The Hamiltonian can be compared to standard vibronic Hamiltonians, but it is constructed without reference to potential energy surfaces through direct differentiation of the one- and two-electron integrals at a single reference geometry. The nature of the model Hamiltonian in the harmonic and linear-coupling regime is investigated for pyrazine, where a simple time-dependent calculation including electron–vibration correlation is demonstrated to exhibit the well-studied population transfer between the S2 and S1 excited states. [ABSTRACT FROM AUTHOR]

We introduce a new theoretical and computational framework for treating molecular quantum mechanics without the Born–Oppenheimer approximation. The molecular wavefunction is represented in a tensor-product space of electronic and vibrational basis functions, with electronic basis chosen to reproduce the mean-field electronic structure at all geometries. We show how to transform the Hamiltonian to a fully second-quantized form with creation/annihilation operators for electronic and vibrational quantum particles, paving the way for polynomial-scaling approximations to the tensor-product space formalism. In addition, we make a proof-of-principle application of the new Ansatz to the vibronic spectrum of C2. [ABSTRACT FROM AUTHOR]

Molpro is a general purpose quantum chemistry software package with a long development history. It was originally focused on accurate wavefunction calculations for small molecules but now has many additional distinctive capabilities that include, inter alia, local correlation approximations combined with explicit correlation, highly efficient implementations of single-reference correlation methods, robust and efficient multireference methods for large molecules, projection embedding, and anharmonic vibrational spectra. In addition to conventional input-file specification of calculations, Molpro calculations can now be specified and analyzed via a new graphical user interface and through a Python framework. [ABSTRACT FROM AUTHOR]

A new orbital optimization for the multiconfiguration self-consistent field method is presented. This method combines a second-order (SO) algorithm for the optimization of the active orbitals with the first-order super configuration interaction (SCI) optimization of the remaining closed-virtual rotations and is denoted as the SO–SCI method. The SO–SCI method significantly improves the convergence as compared to the conventional SCI method. In combination with density fitting, the intermediates from the gradient calculation can be reused to evaluate the two-electron integrals required for the active Hessian without introducing a large computational overhead. The orbitals and CI coefficients are optimized alternately, but the CI-orbital coupling is accounted for by the limited memory Broyden–Fletcher–Goldfarb–Shanno quasi-Newton method. This further improves the speed of convergence. The method is applicable to large molecules. The efficiency and robustness of the presented method is demonstrated in benchmark calculations for 21 aromatic molecules as well as for various transition metal complexes with up to 826 electrons and 5154 basis functions. [ABSTRACT FROM AUTHOR]

A new improved implementation of the second-order multiconfiguration self-consistent field optimization method of Werner and Knowles [J. Chem. Phys. 82, 5053 (1985)] is presented. It differs from the original method by more stable and efficient algorithms for minimizing the second-order energy approximation in the so-called microiterations. Conventionally, this proceeds by alternating optimizations of the orbitals and configuration (CI) coefficients and is linearly convergent. The most difficult part is the orbital optimization, which requires solving a system of nonlinear equations that are often strongly coupled. We present a much improved algorithm for solving this problem, using an iterative subspace method that includes part of the orbital Hessian explicitly, and discuss different strategies for performing the uncoupled optimization in a most efficient manner. Second, we present a new solver in which the orbital-CI coupling is treated explicitly. This leads to quadratic convergence of the microiterations but requires many additional evaluations of reduced (transition) density matrices. In difficult optimization problems with a strong coupling of the orbitals and CI coefficients, it leads to much improved convergence of both the macroiterations and the microiterations. Third, the orbital-CI coupling is treated approximately using a quasi-Newton approach with Broyden–Fletcher–Goldfarb–Shanno updates of the orbital Hessian. It is demonstrated that this converges almost as well as the explicitly coupled method but avoids the additional effort for computing many transition density matrices. The performance of the three methods is compared for a set of 21 aromatic molecules, an Fe(ii)-porphine transition metal complex, as well as for the [ C u 2 O 2 ( N H 3 ) 6 ]2+, FeCl3, Co2(CO)6C2H2, and Al4O2 complexes. In all cases, faster and more stable convergence than with the original implementation is achieved. [ABSTRACT FROM AUTHOR]

The method of direct variational quantum nuclear dynamics in a basis of Gaussian wavepackets, combined with the potential energy surfaces fitted on-the-fly using Gaussian process regression, is described together with its implementation. Enabling exact and efficient analytic evaluation of Hamiltonian matrix elements, this approach allows for black-box quantum dynamics of multidimensional anharmonic molecular systems. Example calculations of intra-molecular proton transfer on the electronic ground state of salicylaldimine are provided, and future algorithmic improvements as well as the potential for multiple-state non-adiabatic dynamics are discussed. [ABSTRACT FROM AUTHOR]

Quasi-variational coupled-cluster methods are applied to a selection of diatomic molecules. The potential energy curves, spectroscopic constants, and size consistency errors are calculated and compared to those obtained from both single- and multi-reference methods. The effects of connected triple excitations are introduced with either the standard perturbative (T) formulation, or in the renormalised form, and its symmetrised approximation. It is found that the renormalised ansatz is significantly superior to the standard formulation when describing bond breaking and that in most circumstances, the computationally simpler symmetrisation gives nearly identical results. [ABSTRACT FROM AUTHOR]

A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the △MPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except △MPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 but converges at the full-configurationinteraction (FCI) limit at n = ∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or △MPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of △MPn and MBGF in the diagonal and frequency-independent approximations at 1 ≤ n ≤ 3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams. [ABSTRACT FROM AUTHOR]

Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in imaginary time independently from the first and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the Hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments, and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation. [ABSTRACT FROM AUTHOR]

We present a pilot application of the recently proposed quasi-variational coupled cluster method to the energies, polarizabilities, and second hyperpolarizabilities of model hydrogen chains. Relative to other single-reference methods of equivalent computational complexity, we demonstrate this method to be highly robust and especially useful when traditional coupled cluster theory fails to perform adequately. In particular, our results indicate it to be a suitable method for the black-box treatment of multiradicals, making it of widespread general interest and applicability. [ABSTRACT FROM AUTHOR]

We extend our previous work on the construction of new approximations of the variational coupled cluster method. By combining several linked pair functional transformations in such a way as to give appropriately balanced infinite-order contributions, in order to approximate L well at all orders, we formulate a new quantum chemical method, which we name quasi-variational coupled cluster. We demonstrate this method to be particularly robust in the regime of strong static electron correlation, improving significantly on our earlier approximate variational coupled cluster approach. [ABSTRACT FROM AUTHOR]

We show that it is possible to construct an accurate approximation to the variational coupled cluster method, limited to double substitutions, from the minimization of a functional that is rigorously extensive, exact for isolated two-electron subsystems and invariant to transformations of the underlying orbital basis. This approximate variational coupled cluster theory is a modification and enhancement of our earlier linked pair functional theory. It is first motivated by the constraint that the inverse square root of the matrix that transforms the cluster amplitudes must exist. Low-order corrections are then included to enhance the accuracy of the approximation of variational coupled cluster, while ensuring that the computational complexity of the method never exceeds that of the standard traditional coupled cluster method. The effects of single excitations are included by energy minimization with respect to the orbitals defining the reference wavefunction. The resulting quantum chemical method is demonstrated to be a robust approach to the calculation of molecular electronic structure and performs well when static correlation effects are strong. [ABSTRACT FROM AUTHOR]

Comparative benchmark calculations are presented for coupled cluster theory in its standard formulation, as well as variational, extended, and unitary coupled cluster methods. The systems studied include HF, N2, and CN, and with cluster operators that for the first time include up to quadruple excitations. In cases where static correlation effects are weak, the differences between the predictions of molecular properties from each theory are negligible. When, however, static correlation is strong, it is demonstrated that variational coupled cluster theory can be significantly more robust than the traditional ansatz and offers a starting point on which to base single-determinant reference methods that can be used beyond the normal domain of applicability. These conclusions hold at all levels of truncation of the cluster operator, with the variational approach showing significantly smaller errors. [ABSTRACT FROM AUTHOR]

A modification of the variational configuration interaction functional in the first-order interacting space for molecular electronic structure is presented. The modified functional is a fully linked expression that by construction is extensive and invariant to transformations of the underlying orbital basis and is exact for an ensemble of separated two-electron subsystems. In addition, an approximation to variational coupled cluster is generated through truncation of the exponential cluster operator. When combined, these methods demonstrate accuracy that exceeds that of the standard coupled-cluster method, in particular in situations where the reference Slater determinant is not a good approximation. [ABSTRACT FROM AUTHOR]

We apply density fitting approximations to generate the 2-electron integrals in local MP2 (LMP2) to produce a method denoted DF-LMP2. The method can equally be seen as a local version of the well-known RI-MP2 method, which in this work is referred to as DF-MP2. Local approximations reduce the asymptotic scaling of computational resources to O(N), and the most expensive step of DF-MP2 [the O(N[sup 5]] assembly) is rendered negligible in DF-LMP2. It is demonstrated that for large molecules DF-LMP2 is much faster (1–2 orders of magnitude) than either LMP2 or DF-MP2. The availablility of LMP2, DF-MP2 and DF-LMP2 has for the first time made it possible to assess the accuracy of local and density fitting approximations for extended molecules using cc-pVDZ and cc-pVTZ basis sets. The density fitting errors are found to be consistently small, but the errors arising from local approximations are somewhat larger than expected from calculations on smaller systems. It is proposed to apply local density fitting approximations also for the Fock matrix construction in Hartree-Fock calculations. Preliminary results demonstrate that this can lead to significant savings in the Hartree-Fock calculation. © 2003 American Institute of Physics. [ABSTRACT FROM AUTHOR]

A new radial coordinate transformation and associated integration grid scheme is presented for the problem of integrating functions of atomic electron density. Remarkable accuracy and stability is attained. Together with standard atomic partitioning and angular quadrature schemes, the new radial grid is applied to molecular density-functional theory, and it is shown that acceptable accuracy is attained with significantly fewer grid points than in previously presented schemes. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The coupled cluster method restricted to single and double excitations (CCSD) is considered for the case of a spin restricted Hartree–Fock open shell reference determinant. A spin–orbital based formulation, in which the cluster operator spans exactly the minimal first order interacting space, is presented, and computationally optimal working equations are given. In the limit of a large number of closed shell orbitals, the cost is identical to that of an optimum treatment of an equivalent closed shell problem, which is obtained as a special case of the formulation presented. The theory is applied to the calculation of a number of diatomic potential energy functions and compared with spin-unrestricted theory. [ABSTRACT FROM AUTHOR]

The potential energy function of the N2 molecule is calculated using the internally contracted multireference CI method (CMRCI) and complete active space SCF (CASSCF) reference wave functions. A full CI calculation in a DZP basis set is used to estimate the errors associated with the CMRCI wave function. The dependence of the computed spectroscopic constants and the dissociation energy on the basis set is also investigated. Uncontracted and segmented basis sets are compared with ANO (atomic natural orbital) and other generally contracted basis sets. It is found that the energy optimized ‘‘correlation consistent’’ basis sets of Dunning yield substantially better results than ANO basis sets of the same size. In the largest calculations, which included up to h type basis functions and also accounted for core–core and core–valence correlation effects, the remaining errors are 0. 0003 Å, 8 cm-1, and 0.7 kcal/mol for re, ωe, and De, respectively. The inclusion of an i type basis function reduces the error in the dissociation energy to 0.3 kcal/mol (0.013 eV). [ABSTRACT FROM AUTHOR]

Potential energy, dipole moment, and electronic transition moment functions have been calculated for the X 2Σ+, A2Π, and B 2Σ+ states of the CN radical using internally contracted CASSCF-CI electronic wave functions (configuration interaction with complete active space self-consistent-field reference functions) and large basis sets. All molecular orbitals which can be formed from the atomic 2s and 2p orbitals were included in the active space. The effect of adding δ orbitals to the active space was found to be small. The largest calculations included up to 987 reference configurations and were equivalent to uncontracted MR-CI calculations with 11.8 million configurations. These calculations are the most accurate that have been carried out to date in terms of the size of the basis set and the treatment of electron correlation effects. Using the theoretical transition moment functions and RKR potential energy functions, radiative lifetimes of the A 2Π and B 2Σ+ states have been derived. The lifetimes of the A state vary between 11.2 μs for v’=0 and 5.3 μs for v’=10. The lifetime of the B, v’=0 state is calculated to be 60.7 ns. These values are estimated to be accurate within 5% and are compared to previous experimental and theoretical data. The most recent experimentally measured lifetimes differ by 20% to 35% from the calculated values, while our results are in close agreement with other theoretical studies. Einstein coefficients of spontaneous emission and oscillator strengths for A–X, B–X, and B–A transitions are tabulated. Dipole moment functions have also been determined, and radiative transition probabilities between vibrational levels of the ground state are presented. [ABSTRACT FROM AUTHOR]

A new internally contracted direct multiconfiguration–reference configuration interaction (MRCI) method is described which allows the use of much larger reference spaces than any previous MRCI method. The configurations with two electrons in the external orbital space are generated by applying pair excitation operators to the reference wave function as a whole, while the singly external and internal configurations are standard uncontracted spin eigenfunctions. A new efficient and simple method for the calculation of the coupling coefficients is used, which is well suited for vector machines, and allows the recalculation of all coupling coefficients each time they are needed. The vector H·c is computed partly in a nonorthogonal configuration basis. In order to test the accuracy of the internally contracted wave functions, benchmark calculations have been performed for F-, H2O, NH2, CH2, CH3, OH, NO, N2, and O2 at various geometries. The deviations of the energies obtained with internally contracted and uncontracted MRCI wave functions are mostly smaller than 1 mH and typically 3–5 times smaller than the deviations between the uncontracted MRCI and the full CI. Dipole moments, electric dipole polarizabilities, and electronic dipole transition moments calculated with uncontracted and contracted MRCI wave functions also are found to be in close agreement. The efficiency of the method is demonstrated in large scale calculations for the CN, NH3, CO2, and Cr2 molecules. In these calculations up to 3088 reference configurations and up to 154 orbitals were employed. The biggest calculation is equivalent to an uncontracted MRCI with more than 78 million configurations. [ABSTRACT FROM AUTHOR]

A practical scheme for obtaining unrestricted Mo\ller–Plesset energies at second order (UMP2), with spin contamination removed from the wave function, is described and demonstrated. The algebra increases with the number of spin projections, and it appears to be practical to include only two spin projections. Full formulas are given, for which the cost is proportional to M3, where M is the number of basis functions. The results of these calculations give remarkably enhanced accuracy at fractionally extra cost. Four examples are included to demonstrate this: (i) the potential curve for the symmetric dissociation of H2O; (ii) the potential curve for the abstraction of H from CH4; (iii) the barrier for the addition of H to C2H4; and (iv) the electron affinity of CN. It is recommended that this procedure should be added at the end of all UMP2 calculations. [ABSTRACT FROM AUTHOR]

Demonstrates the extraction of the true Kohn-Sham exchange-correlation potential from near-exact electronic densities in the two-electron systems of helium and hydrogen. Techniques in obtaining the reference density from a standard configuration interaction calculation; Orbital basis sets required to obtain convergence.

An MCSCF procedure is described which is based on the direct minimization of an approximate energy expression which is periodic and correct to second order in the changes in the orthonormal orbitals. Within this approximation, the CI coefficients are fully optimized, thereby accounting for the coupling between orbital rotations and CI coefficients to higher order than in previous treatments. Additional transformations among the internal orbitals and their associated one- and two-electron integrals are performed which amounts to treating the rotations among internal orbitals to higher than second order. These extra steps are cheap compared to the four index transformation performed in each iteration, but lead to a remarkable enhancement of convergence and overall efficiency. In all calculations attempted to date, convergence has been achieved in at most three iterations. The energy has been observed to converge better than quadratically from the first iteration even when the initial Hessian matrix has many negative eigenvalues. [ABSTRACT FROM AUTHOR]

We have observed and assigned seven microwave and millimeter wave lines arising from rovibronic components of the A 2Σ+g←X 2Σ+u electronic spectrum of the He+2 ion; this is the first observation of any spectrum of the homonuclear 4He4He+ species. The vibration-rotation levels involved in our observations all lie within 8 cm-1 of the lowest degenerate He(1S)+He+(2S) dissociation limits for both electronic states. We use an ion beam technique in which weakly bound levels dissociate in an applied electric field to produce He+ fragments. These fragments are separated from all other ions with an electrostatic kinetic energy analyzer, and microwave transitions are detected as changes in the He+ fragment current arising from resonant population transfer. Four of the transitions are detected using a single microwave frequency; the remaining three are measured by means of a microwave–microwave double resonance method. The assignment of the spectrum is achieved by means of ab initio electronic structure calculations, made within the Born–Oppenheimer approximation. The agreement between experiment and theory is excellent and leads to an accurate characterization of the He...He+ 2Σ+g charge/induced-dipole state. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Based on extensive ab initio multiconfiguration reference configuration interaction (MRCI) electronic structure calculations, three-dimensional potential energy functions for the A 2A1(Πu)–X 2B1 linear/bent Renner–Teller systems of H2O+, HDO+, and D2O+ have been generated and used in beyond Born–Oppenheimer calculations of the spin–rovibronic energy levels by a variational approach. The effects of anharmonicity, rotation–vibration, electronic angular momenta, and spin coupling effects have been accounted for. For H2O+, HDO+, and D2O+ vibronic band origins for the bending levels to Ka=5 and for selected stretching and combination levels are given. Almost all experimentally known data have been reproduced with an accuracy better than 10 cm-1 after minor modifications of the ab initio potential energy functions. Our calculated values will facilitate further experimental assignments. A consistent interpretation of the photoelectron spectra for the different isotopes of water is given. Previous assignments of the bending modes in the A 2A1 state have been revised by two quantum numbers. [ABSTRACT FROM AUTHOR]

The potential energy surfaces of the two lowest-lying singlet electronic states of methylene (CH2) are determined by internally contracted multireference configuration interaction calculations, using a full-valence reference space, with an extended Gaussian basis set. The rotation–vibration levels on these surfaces are calculated by diagonalizing the rovibrational Hamiltonian matrix in a contracted basis. The rovibronic mixing due to the strong Renner–Teller interaction in this system is treated through the Coriolis term in the kinetic energy operator, using geometry-dependent electronic angular momentum matrix elements calculated from ab initio wave functions. The agreement between experiment and this high-quality ab initio calculation is sufficiently good that the calculation can be used to assign the observed vibronic bands in this very complex spectrum, where 90% of the observed lines remain unassigned. Many of the previous vibronic band labels are found to be incorrect. Most of the K>0 bands previously labeled b 1B1 are actually predominantly a 1A1 in character, and the vibrational numbering of their b 1B1 components are also incorrect. This work demonstrates the importance of supplementing experimental data with good quality ab initio calculations. [ABSTRACT FROM AUTHOR]

We describe an investigation of the energetics of the dissociation of ground state hydrazoic acid HN3. The study is limited to the lowest energy spin-allowed and spin-forbidden decomposition pathways, namely HN3(X 1A’)→N2(X 1Σg+) +NH(a 1Δ,X 3Σ-) and HN3(X 1A’) →N3(X 2Πg)+H(2S). Complete active space SCF and multireference configuration interaction calculations with large basis sets are used (a) to determine the NNN–H and NN–NH bond dissociation energies of HN3, (b) to locate the geometry of the transition state for the spin-forbidden decomposition and the corresponding activation energy, and (c) to investigate the magnitude and origin of the exit channel barrier in the spin-allowed decomposition channel. [ABSTRACT FROM AUTHOR]

The potential energy, dipole moment, and electronic transition moment curves of the X 2 Σ+ and A 2 Π states of the doubly charged CF++ ion have been calculated from internally contracted multireference CI wave functions with full valence complete active space self-consistent field reference wave functions and large Gaussian basis sets. Both states are predicted to be metastable with equilibrium geometries Re(X 2 Σ+ )=2.139 Bohr and Re(A 2 Π)=3.073 Bohr. These minima lie above and are separated from their asymptotes by broad barriers with a height of 4.99 eV (X 2 Σ+ ) and 1.04 eV (A 2 Π), respectively. Similar to the isoelectronic NO++, the Π state intersects the barrier of the X 2 Σ+ state. Radiative and nonradiative (tunneling) lifetimes of all vibrational levels have been calculated by standard quantum mechanical scattering techniques. [ABSTRACT FROM AUTHOR]

Full configuration-interaction (FCI) calculations are performed at selected geometries for the 1∑+ state of HF and the 2B1 and 2A1 states of NH2 using both DZ and DZP Gaussian basis sets. Higher excitations become more important when the bonds are stretched and the SCF reference becomes a poorer zeroth-order description of the wave function. The CASSCF-MRCI procedure gives excellent agreement with the FCI potentials, especially when corrected with a multireference analog of the Davidson correction. [ABSTRACT FROM AUTHOR]

In very large full configuration interaction (full CI), nearly all of the CI coefficients are very small. Calculations, using a newly developed algorithm which exploits this fact, on NH3 with a DZP basis are reported, involving 2×108 Slater determinants. Such calculations are impossible with other existing full CI codes. The new algorithm opens up the opportunity of full CI calculations which are unlimited in size. [ABSTRACT FROM AUTHOR]

Ab initio calculations for the lowest quartet state of He+4 are reported. The resulting delocalized D2d structure, binding energy, and electronic spectrum provide a rationalization for the experimental observation of an especially stable He+4 cluster. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

We show that, by making use of the linked tensor objects inherent to the approach, Orbital-optimised Quasi-Variational Coupled Cluster Theory (OQVCCD) leads naturally to a computationally-trivial, rigorously extensive, and orbital-invariant renormalization of the standard (T) correction for the perturbative inclusion of the effects of connected triple excitations. The resulting prototype method, renormalized perturbative triple OQVCCD (R-OQVCCD(T)), is demonstrated to predict potential energy curves for single bond-breaking processes of significantly higher accuracy than OQVCCD with the standard perturbative triple-excitation correction (OQVCCD(T)) itself, and to be in good numerical correspondence with the existing renormalized (R-CCSD(T)) and completely renormalized (CR-CCSD(T)) coupled-cluster singles doubles triples methods, while continuing to provide descriptions of multiple bond-breaking processes of OQVCCD(T) quality. [ABSTRACT FROM AUTHOR]

Ab initio semiglobal potential energy and dipole moment hypersurfaces for the isomerising HCN–HNC system are computed, using a grid of 242 points, principally at the all-electron cc-pCVQZ CCSD(T) level. Several potential energy hypersurfaces (PES) are presented including one which simultaneously fits 1527 points from earlier ab initio, smaller basis CCSD(T) calculations of Bowman et al. [J. Chem. Phys. 99, 308 (1993)]. The resulting potential is then morphed with 17 aug-cc-pCVQZ CCSD(T) points calculated at HNC geometries to improve the representation of the HNC part of the surface. The PES is further adjusted to coincide with three ab initio points calculated, at the cc-pCV5Z CCSD(T) level, at the critical points of the system. The final PES includes relativistic and adiabatic corrections. Vibrational band origins for HCN and HNC with energy up to 12 400 cm-1 above the HCN zero-point energy are calculated variationally with the new surfaces. Band transition dipoles for the fundamentals of HCN and HNC, and a few overtone and hot band transitions for HCN have been calculated with the new dipole surface, giving generally very good agreement with experiment. The rotational levels of ground and vibrationally excited states are reproduced to high accuracy. © 2001 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Systematic sequences of basis sets are used to calculate the spin-orbit splittings of the halogen atoms F, Cl, and Br in the framework of first-order perturbation theory with the Breit-Pauli operator and internally contracted configuration interaction wave functions. The effects of both higher angular momentum functions and the presence of tight functions are studied. By systematically converging the one-particle basis set, an unambiguous evaluation of the effects of correlating different numbers of electrons in the Cl treatment is carried out. Correlation of the 2p-electrons in chlorine increases the spin-orbit splitting by ∼80 cm-1, while in bromine we observe incremental increases of 130, 145, and 93 cm-1, when adding the 3d, 3p, and 2p electrons to the set of explicitly correlated electrons, respectively. For fluorine and chlorine the final basis set limit, all-electrons correlated results match the experimentally observed spin-orbit splittings to within ∼5 cm-1, while for bromine the Breit-Pauli operator underestimates the splitting by about 100 cm-1. More extensive treatment of electron correlation results in only a slight lowering of the spin-orbit matrix elements. Thus, the discrepancy for bromine is proposed to arise from the nonrelativistic character of the underlying wave function. © 2000 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Presents corrections to the article 'Coupled cluster theory for high spin, open shell reference wave functions,' published in the year 1993 issue of the 'Journal of Chemical Physics' periodical.

A thorough analytical and numerical characterization of the whole perturbation series of one-particle many-body Green's function (MBGF) theory is presented in a pedagogical manner. Three distinct but equivalent algebraic (first-quantized) recursive definitions of the perturbation series of the Green's function are derived, which can be combined with the well-known recursion for the self-energy. Six general-order algorithms of MBGF are developed, each implementing one of the three recursions, the ΔMPn method (where n is the perturbation order) [S. Hirata et al., J. Chem. Theory Comput. 11, 1595 (2015)], the automatic generation and interpretation of diagrams, or the numerical differentiation of the exact Green's function with a perturbation-scaled Hamiltonian. They all display the identical, nondivergent perturbation series except ΔMPn, which agrees with MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 but converges at the full-configuration-interaction (FCI) limit at n=∞ (unless it diverges). Numerical data of the perturbation series are presented for Koopmans and non-Koopmans states to quantify the rate of convergence towards the FCI limit and the impact of the diagonal, frequency-independent, or ΔMPn approximation. The diagrammatic linkedness and thus size-consistency of the one-particle Green's function and self-energy are demonstrated at any perturbation order on the basis of the algebraic recursions in an entirely time-independent (frequency-domain) framework. The trimming of external lines in a one-particle Green's function to expose a self-energy diagram and the removal of reducible diagrams are also justified mathematically using the factorization theorem of Frantz and Mills. Equivalence of ΔMPn and MBGF in the diagonal and frequency-independent approximations at 1≤n≤3 is algebraically proven, also ascribing the differences at n = 4 to the so-called semi-reducible and linked-disconnected diagrams.