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A Mo/ller–Plesset energy functional (Lagrangian) which is variational in all variables (the Lagrange multipliers, the orbital rotation parameters, and the orbital energies) is constructed. The variational property ensures that the responses of the orbitals and orbital energies to order n in geometrical perturbations determine the energy derivatives to order 2n+1. The Lagrange multipliers satisfy the somewhat stronger 2n+2 rule. The multipliers, orbital rotations, and orbital energy responses are determined from coupled perturbed Hartree–Fock-type equations using an exponential parametrization of the orbitals. This ensures that the orbital rotations and energy responses are treated in the same way and calculated from a single set of linear equations. Explicit expressions for energy derivatives up to third order are derived for the second-order Mo/ller–Plesset energy.

A suite of tools for the analysis of magnetically induced currents is introduced.These are applicable to both the weak-field regime, well described by linear response perturbation theory, and to the high-field regime, which is inaccessible to such methods.A disc-based quadrature scheme is proposed for the analysis of magnetically induced current susceptibilities, providing quadratures that are consistently defined between different molecular systems and applicable to both planar 2D and general 3D molecular systems in a black-box manner. The applicability of the approach is demonstrated for a range of planar ring systems, the ground and excited states of the benzene molecule and the ring, bowl and cage isomers of the C 20 molecule in the presence of a weak magnetic field. In the presence of a strong magnetic field, the para-to dia-magnetic transition of the BH molecule is studied, demonstrating that magnetically induced currents present a visual interpretation of this phenomenon, providing insight beyond that accessible using linear-response methods.

The Dalton Project provides a uniform platform access to the underlying full-fledged quantum chemistry codes Dalton and LSDalton as well as the PyFraME package for automatized fragmentation and parameterization of complex molecular environments. The platform is written in Python and defines a means for library communication and interaction. Intermediate data such as integrals are exposed to the platform and made accessible to the user in the form of NumPy arrays, and the resulting data are extracted, analyzed, and visualized. Complex computational protocols that may, for instance, arise due to a need for environment fragmentation and configuration-space sampling of biochemical systems are readily assisted by the platform. The platform is designed to host additional software libraries and will serve as a hub for future modular software development efforts in the distributed Dalton community.

In this paper, the history, present status, and future of density-functional theory (DFT) is informally reviewed and discussed by 70 workers in the field, including molecular scientists, materials scientists, method...

We outline a method for the calculation of nonlinear properties such as dynamic hyperpolarizabilities for self-consistent-field (SCF) wave functions. In this method, twoelectron integrals are only addressed in the evaluation of Fock matrices and Fock matrices with one-index transformed integrals. These matrices are determined directly in terms of integrals evaluated in the atomic orbital basis, avoiding expensive integral transformations between atomic and molecular orbital bases as well as storing and retrieving the twoelectron integrals. The method is double direct-direct in the sense of constructing Fock matrices from atomic integrals, and direct in the sense of solving the response equations iteratively using direct linear transformations of a generating matrix times trial vectors. Applications can be performed on species of the same size as in direct SCF. The cost of evaluating a single nonlinear molecular property is comparable to that of optimizing the wave function. Additional properties can be obtained at little extra cost by solving all response equations simultaneously. As a demonstration, we calculate the static and dynamic hyperpolarizabilities of para-nitroaniline.

We compare the performance of three approximate methods for speeding up evaluation of the exchange contribution in Hartree-Fock and hybrid Kohn-Sham calculations: the chain-of-spheres algorithm (COSX; Neese , F. Chem. Phys. 2008 , 356 , 98 - 109 ), the pair-atomic resolution-of-identity method (PARI-K; Merlot , P. J. Comput. Chem. 2013 , 34 , 1486 - 1496 ), and the auxiliary density matrix method (ADMM; Guidon , M. J. Chem. Theory Comput. 2010 , 6 , 2348 - 2364 ). Both the efficiency relative to that of a conventional linear-scaling algorithm and the accuracy of total, atomization, and orbital energies are compared for a subset containing 25 of the 200 molecules in the Rx200 set using double-, triple-, and quadruple-ζ basis sets. The accuracy of relative energies is further compared for small alkane conformers (ACONF test set) and Diels-Alder reactions (DARC test set). Overall, we find that the COSX method provides good accuracy for orbital energies as well as total and relative energies, and the method delivers a satisfactory speedup. The PARI-K and in particular ADMM algorithms require further development and optimization to fully exploit their indisputable potential.