Analytical Nuclear Gradients for the Multiconfigurational Self-Consistent Field Method Coupled with the Polarizable Fluctuating Charges Model

TL;DR

This work addresses the challenge of accurately describing multireference solute systems in condensed phases while obtaining analytic energy derivatives. It introduces state-specific analytical nuclear gradients for a multiconfiguration self-consistent field (MCSCF) wavefunction coupled to the Fluctuating Charges (FQ) polarizable solvent model, implemented in OpenMolcas with Alaska integration. Using MD sampling and a vibronic protocol, benzene and phenol in water are simulated, comparing vertical and adiabatic vibronic models across two FQ parameterizations; the approach yields $dE/dξ$ grad"ients and spectra that closely match experimental profiles. The results demonstrate that the MCSCF/FQ framework can capture both the multireference character of the solute and explicit solvent effects, offering a robust route to accurate solvation-dependent spectroscopy and paving the way for including dynamical correlation and non-electrostatic solute–solvent interactions in future work.

Abstract

The multiscale model combining the multiconfigurational self-consistent field (MCSCF) method with the fully atomistic polarizable Fluctuating Charges (FQ) force field (J. Chem. Theory Comput. 2024, 20, 9954-9967) is here extended to the calculation of analytical nuclear gradients. The gradients are derived from first principles, implemented in the OpenMolcas package, and validated against numerical references. The resulting MCSCF/FQ nuclear gradients are employed to simulate vibronic absorption spectra of aromatic molecules in aqueous solution, namely benzene and phenol. By integrating this approach with molecular dynamics simulations, both solute conformational flexibility and the dynamical aspects of solvation are properly captured. The computed spectra reproduce experimental profiles and relative band intensities with remarkable accuracy, demonstrating the capability of the MCSCF/FQ model to simultaneously describe the multireference character of the solute and its interaction with the solvent environment.

Figures (7)

• Figure 1: Test systems employed for validating and debugging the CASSCF/FQ analytical gradient implementation: a) formaldehyde (QM) and two water molecules (MM) (system A), b) formaldehyde (QM) surrounded by 505 water molecules (MM) (system B), c) two water molecules, one described at the QM level and the other at the MM level (system C).
• Figure 2: Representative snapshots of benzene (left) and phenol (right) in aqueous solution, extracted from MD simulations. The radius of the solvation spheres is 18 Å for both solutes and includes $\sim$ 850 water molecules.
• Figure 3: System C. One water molecule is treated at the CASSCF level, while the other at the FQ level.
• Figure 4: Active orbitals selected for CASSCF(6,6)/FQ calculations. They are obtained with the GuessOrb program in OpenMolcas. li2023openmolcas
• Figure 5: CASSCF(6,6)/FQ$^{(b,c)}$ vibronic spectra of benzene in aqueous solution, obtained with vertical (VG and VH) and adiabatic (AS and AH) approximations. In blue (left), spectra obtained with FQ$^b$ parametrization. In red (right), spectra obtained with FQ$^c$ parameterization. The experimental spectrum (black, dotted) adapted from Ref. ilan1976photochemistry is superimposed.