Abstract
The study of high-order absorption properties of molecules is a field of growing importance. Quantum-chemical studies can help design chromophores with desirable characteristics. Given that most experiments are performed in solution, it is important to devise a cost-effective strategy to include solvation effects in quantum-chemical studies of these properties. We here present an open-ended formulation of self-consistent field (SCF) response theory for a molecular solute coupled to a polarizable continuum model (PCM) description of the solvent. Our formulation relies on the open-ended, density matrix-based quasienergy formulation of SCF response theory of Thorvaldsen, et al., [J. Chem. Phys., 2008, 129, 214108] and the variational formulation of the PCM, as presented by Lipparini et al., [J. Chem. Phys., 2010, 133, 014106]. Within the PCM approach to solvation, the mutual solute-solvent polarization is represented by means of an apparent surface charge (ASC) spread over the molecular cavity defining the solute-solvent boundary. In the variational formulation, the ASC is an independent, variational degree of freedom. This allows us to formulate response theory for molecular solutes in the fixed-cavity approximation up to arbitrary order and with arbitrary perturbation operators. For electric dipole perturbations, pole and residue analyses of the response functions naturally lead to the identification of excitation energies and transition moments. We document the implementation of this approach in the Dalton program package using a recently developed open-ended response code and the PCMSolver libraries and present results for one-, two-, three-, four- and five-photon absorption processes of three small molecules in solution.
Highlights
An important challenge in molecular sciences is the study at the quantum molecular mechanical level of systems of growing complexity
It is possible to make other formulations of response theory for which truncation rules for perturbed arguments between and including the n + 1 and 2n + 1 rules are possible.[9,10,47]. This entails the introduction of Lagrange multipliers k~a and f~a to take into consideration the idempotency of the density matrix and the time-dependent selfconsistent field (SCF) (TD-SCF) equations, respectively, so that the idempotency condition is expressed with the matrix Yand the TD-SCF condition with the matrix Z, where where the subscript integers k and n in the various forms shown in this expression denote a given choice of truncation rule
We have presented the theory and implementation for calculating molecular response properties to arbitrary order in solution within the framework of the polarizable continuum model
Summary
An important challenge in molecular sciences is the study at the quantum molecular mechanical level of systems of growing complexity. Methods that used to be proof-of-principle concepts are today routinely employed to study increasingly complex systems An example of such a class of experiments is multiphoton absorption (MPA): the simultaneous absorption of several photons. The open-ended response formalism is able to address the challenge of the ever-growing variety of spectroscopic methods available, significantly reducing the development effort and the time required to model new spectroscopic processes for relevant applications. Crucial aspects of our work are the variational formulation of the PCM equations[37] and the modular approach employed in the implementation Both PCMSolver and the open-ended response code[10] are two independent modules which can be interfaced to any quantum chemistry software.
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