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This work reports an efficient density‐fitting implementation of the density‐based basis‐set correction (DBBSC) method in the MOLPRO software. This method consists in correcting the energy calculated by a wave‐function method with a given basis set by an adapted basis‐set correction density functional incorporating the short‐range electron correlation effects missing in the basis set, resulting in an accelerated convergence to the complete‐basis‐set limit. Different basis‐set correction density‐functional approximations are explored and the complementary‐auxiliary‐basis‐set single‐excitation correction is added. The method is tested on a benchmark set of reaction energies at the second‐order Møller–Plesset (MP2) level and a comparison with the explicitly correlated MP2‐F12 method is provided. The results show that the DBBSC method greatly accelerates the basis convergence of MP2 reaction energies, without reaching the accuracy of the MP2‐F12 method but with a lower computational cost. [ABSTRACT FROM AUTHOR]

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 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]

The spectrum of water vapor is of fundamental importance for a variety of processes, including the absorption and retention of sunlight in Earth's atmosphere. Therefore, there has long been an urgent need for a robust and accurate predictive model for this spectrum. In our work on the high-resolution spectrum of water, we report first-principles calculations that approach experimental accuracy. To achieve this, we performed exceptionally large electronic structure calculations and considered a variety of effects, including quantum electrodynamics, which have routinely been neglected in studies of small many-electron molecules. The high accuracy of the resulting ab initio procedure is demonstrated for the main isotopomers of water., The absorption and emission of light by water vapor is responsible for ~70% of the known absorption of sunlight and the majority of the greenhouse effect (1). Hot steam is [...]

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]