Multiwavelets are emerging as an attractive alternative to traditional basis sets such as Gaussian-type orbitals and plane waves. One of their distinctive properties is the ability to reach the basis set limit (often a chimera for traditional approaches) reliably and consistently by fixing the desired precision ε. We present our multiwavelet implementation of the linear response formalism, applied to static magnetic properties, at the self-consistent field level of theory (both for Hartree-Fock and density functional theories). We demonstrate that the multiwavelets consistently improve the accuracy of the results when increasing the desired precision, yielding results that have four to five digits precision, thus providing a very useful benchmark which could otherwise only be estimated by extrapolation methods. Our results show that magnetizabilities obtained with the augmented quadruple-ζ basis (aug-cc-pCVQZ) are practically at the basis set limit, whereas absolute nuclear magnetic resonance shielding tensors are more challenging: even by making use of a standard extrapolation method, the accuracy is not substantially improved. In contrast, our results provide a benchmark that: (1) confirms the validity of the extrapolation ansatz; (2) can be used as a reference to achieve a property-specific extrapolation scheme, thus providing a means to obtain much better extrapolated results; (3) allows us to separate functional-specific errors from basis-set ones and thus to assess the level of cancellation between basis set and functional errors often exploited in density functional theory.

New derivations of origin-independent expressions for the electric permittivity are presented, starting either from the response function of the current density that defines the absorption coefficient, or from the off-resonance single-photon scattering amplitude that leads to the Kramers–Heisenberg dispersion formula. The resulting expression for the permittivity is compared with earlier work on the origin dependence of the material constants. Different origin-independent expressions for the permittivity, the inverse permeability and the magnetisability are calculated and discussed. By considering electromagnetic plane waves in the absence of external sources, the macroscopic Maxwell equations are used to describe the response of matter to external fields. In combination with the constitutive relations, a wave equation expressed in terms of the material constants is derived. It is shown that the different definitions of the material constants lead to the same wave equation. The non-uniqueness of the definitions of the material constants is discussed in this context. Finally, based on the discussions, we propose a possible unique, origin-independent definition of the material constants.

We present a new implementation of a recent open‐ended response theory formulation for time‐ and perturbation‐dependent basis sets (Thorvaldsen et al., J. Chem. Phys. 2008, 129, 214108) at the Hartree–Fock and density functional levels of theory. A novel feature of the new implementation is the use of recursive programming techniques, making it possible to write highly compact code for the analytic calculation of any response property at any valid choice of rule for the order of perturbation at which to include perturbed density matrices. The formalism is expressed in terms of the density matrix in the atomic orbital basis, allowing the recursive scheme presented here to be used in linear‐scaling formulations of response theory as well as with two‐ and four‐component relativistic wave functions. To demonstrate the new code, we present calculations of the third geometrical derivatives of the frequency‐dependent second hyperpolarizability for HSOH at the Hartree–Fock level of theory, a seventh‐order energy derivative involving basis sets that are both time and perturbation dependent. © 2014 Wiley Periodicals, Inc.

We present the first analytic implementation of cubic and quartic force constants at the level of Kohn-Sham density-functional theory. The implementation is based on an open-ended formalism for the evaluation of energy derivatives in an atomic-orbital basis. The implementation relies on the availability of open-ended codes for evaluation of one- and two-electron integrals differentiated with respect to nuclear displacements as well as automatic differentiation of the exchange-correlation kernels. We use generalized second-order vibrational perturbation theory to calculate the fundamental frequencies of methane, ethane, benzene, and aniline, comparing B3LYP, BLYP, and Hartree-Fock results. The Hartree-Fock anharmonic corrections agree well with the B3LYP corrections when calculated at the B3LYP geometry and from B3LYP normal coordinates, suggesting that the inclusion of electron correlation is not essential for the reliable calculation of cubic and quartic force constants.

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

We present the first gauge-origin independent formulation of Jones birefringence at the Hartree-Fock level of theory. Gauge-origin independence is achieved through the use of London atomic orbitals. The implementation is based on a recently proposed atomic orbital-based response theory formulation that allows for the use of both time- and perturbation-dependent basis sets [Thorvaldsen, Ruud, Kristensen, Jo̸rgensen, and Coriani, J. Chem. Phys. 129, 214108 (2008)]. We present the detailed expressions for the response functions entering the Jones birefringence when London atomic orbitals are used. The implementation is tested on a set of polar and dipolar molecules at the Hartree-Fock level of theory. It is demonstrated that London orbitals lead to much improved basis-set convergence, and that the use of small, conventional basis sets may lead to the wrong sign for the calculated birefringence. For large basis sets, London orbitals and conventional basis sets converge to the same results.

We report an upgrade of the Dalton code to include post Born-Oppenheimer nuclear mass corrections in the calculations of (ro-)vibrational averages of molecular properties. These corrections are necessary to achieve an accuracy of 10(-4) debye in the calculations of isotopic dipole moments. Calculations on the self-consistent field level present this accuracy, while numerical instabilities compromise correlated calculations. Applications to HD, ethane, and ethylene isotopologues are implemented, all of them approaching the experimental values.

Density-functional and electron correlated study of five linear birefringences-Kerr, Cotton-Mouton, Buckingham, Jones and magnetoelectric-in gaseous benzene (vol 121, pg 8814, 2004)

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The Gaussian-type orbital and Gaussian-type geminal (GGn) model is applied to the water molecule, at the level of second-order Møller-Plesset (MP2) theory. In GGn theory, correlation factors are attached to all doubly-occupied orbital pairs (GG0), to all doubly-occupied and singly-excited pairs (GG1), or to all orbital pairs (GG2). Optimizing the GG2 model using a weak-orthogonality functional, we obtain the current best estimate of the all-electron MP2 correlation energy of water, -361.95 mE(h). In agreement with previous observations, the GG1 model performs almost as well as the GG2 model (-361.26 mE(h)), whereas the GG0 model is poorer (-351.36 mE(h)). For the barrier to linearity of water, we obtain an MP2 correlation contribution of -463 +/- 5 cm(-1).

We have implemented the use of mixed basis sets of Gaussian one- and two-electron (geminal) functions for the calculation of second-order Møller-Plesset (MP2) correlation energies. In this paper, we describe some aspects of this implementation, including different forms chosen for the pair functions. Computational results are presented for some closed-shell atoms and diatomics. Our calculations indicate that the method presented is capable of yielding highly accurate second-order correlation energies with rather modest Gaussian orbital basis sets, providing an alternative route to highly accurate wave functions. For the neon atom, the hydrogen molecule, and the hydrogen fluoride molecule, our calculations yield the most accurate MP2 energies published so far. A critical comparison is made with established MP2-R12 methods, revealing an erratic behaviour of some of these methods, even in large basis sets.

In MP2‐GGn theory, the second‐order Mo/ller–Plesset (MP2) energy is recovered by a combined Gaussian‐orbital—Gaussian‐geminal (GG) expansion of the first‐order wave function. While the restriction of geminals to doubly occupied orbital pairs (MP2‐GG0) provides a modest improvement on standard MP2 theory, their inclusion also in all singly‐excited (MP2‐GG1) and doubly‐excited (MP2‐GG2) pairs recovers essentially all of the correlation energy in small (double‐ and triple‐zeta) basis sets. For several small systems, our MP2‐GGn energies represent the best MP2 energies reported in the literature.

We review Kohn-Sham density-functional theory for time-dependent response functions up to and including cubic response. The working expressions are derived from an explicit exponential parametrization of the density operator and tire Ehrenfest principle, alternatively the quasi-energy ansatz. While the theory retains the adiabatic approximation, implying that the time-dependency of the functional is obtained Only implicitly-through the time-dependency of the density itself rather than through the form of the exchange-correlation functionals-our implementation generalizes previous time-dependent approaches in that arbitrary functionals can be chosen for the perturbed densities (energy derivatives or response functions). Thus, the response of the density can always be obtained using the stated density functional, or optionally different functionals can be applied for the unperturbed and perturbed densities, even different functionals for different response order. In particular, general density functionals beyond the local density approximation can be applied, such as hybrid functionals with exchange-correlation at the generalized gradient-approximation level and fractional exact Hartree-Fock exchange. We also review some recent progress in time-dependent density functional theory for open-shell systems, in particular spin-restricted and spin restricted-unrestricted formalisms for property calculations. We highlight a sample of applications of the theory

An ab initio coupled cluster investigation of the electric field gradient induced birefringence of three dipolar linear molecules—CO, N2O, and OCS—is presented. Special emphasis is given to the effect of triple excitations in the cluster operator on the so-called effective quadrupole center as well as to the accurate determination of the molecular electric quadrupole moment relative to this origin. Triple excitations are found to be essential in the case of CO, with reference in particular to the existing disagreement between two semiclassical theories for the interpretation of the experimentally observed birefringence. The present results favor the older theory due to Buckingham and Longuet-Higgins.