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.

We present an implementation of single residues for response functions to arbitrary order using a recursive approach. Explicit expressions in terms of density-matrix-based response theory for the single residues of the linear, quadratic, cubic, and quartic response functions are also presented. These residues correspond to one-, two-, three- and four-photon transition matrix elements. The newly developed code is used to calculate the one-, two-, three- and four-photon absorption cross sections of para-nitroaniline and para-nitroaminostilbene, making this the first treatment of four-photon absorption in the framework of response theory. We find that the calculated multiphoton absorption cross sections are not very sensitive to the size of the basis set as long as a reasonably large basis set with diffuse functions is used. The choice of exchange–correlation functional, however, significantly affects the calculated cross sections of both charge-transfer transitions and other transitions, in particular, for the larger para-nitroaminostilbene molecule. We therefore recommend the use of a range-separated exchange–correlation functional in combination with the augmented correlation-consistent double-ζ basis set aug-cc-pVDZ for the calculation of multiphoton absorption properties.

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.

An open‐source program named VeloxChem has been developed for the calculation of electronic real and complex linear response functions at the levels of Hartree–Fock and Kohn–Sham density functional theories. With an object‐oriented program structure written in a Python/C++ layered fashion, VeloxChem enables time‐efficient prototyping of novel scientific approaches without sacrificing computational efficiency, so that molecular systems involving up to and beyond 500 second‐row atoms (or some 10,000 contracted and in part diffuse Gaussian basis functions) can be routinely addressed. In addition, VeloxChem is equipped with a polarizable embedding scheme for the treatment of the classical electrostatic interactions with an environment that in turn is modeled by atomic site charges and polarizabilities. The underlying hybrid message passing interface (MPI)/open multiprocessing (OpenMP) parallelization scheme makes VeloxChem suitable for execution in high‐performance computing cluster environments, showing even slightly beyond linear scaling for the Fock matrix construction with use of up to 16,384 central processing unit (CPU) cores. An efficient—with respect to convergence rate and overall computational cost—multifrequency/gradient complex linear response equation solver enables calculations not only of conventional spectra, such as visible/ultraviolet/X‐ray electronic absorption and circular dichroism spectra, but also time‐resolved linear response signals as due to ultra‐short weak laser pulses. VeloxChem distributed under the GNU Lesser General Public License version 2.1 (LGPLv2.1) license and made available for download from the homepage https://veloxchem.org. This article is categorized under: Software > Quantum Chemistry Electronic Structure Theory > Density Functional Theory Theoretical and Physical Chemistry > Spectroscopy

Geometric energy derivatives which rely on core-corrected focal-point energies extrapolated to the complete basis set (CBS) limit of coupled cluster theory with iterative and noniterative quadruple excitations, CCSDTQ and CCSDT(Q), are used as elements of molecular gradients and, in the case of CCSDT(Q), expansion coefficients of an anharmonic force field. These gradients are used to determine the CCSDTQ/CBS and CCSDT(Q)/CBS equilibrium structure of the S ground state of HCO where excellent agreement is observed with previous work and experimentally derived results. A fourth-order expansion about this CCSDT(Q)/CBS reference geometry using the same level of theory produces an exceptional level of agreement to spectroscopically observed vibrational band origins with a MAE of 0.57 cm. Second-order vibrational perturbation theory (VPT2) and variational discrete variable representation (DVR) results are contrasted and discussed. Vibration-rotation, anharmonicity, and centrifugal distortion constants from the VPT2 analysis are reported and compared to previous work. Additionally, an initial application of a sum-over-states fourth-order vibrational perturbation theory (VPT4) formalism is employed herein, utilizing quintic and sextic derivatives obtained with a recursive algorithmic approach for response theory.