Filippo Lipparini

Polarizable Force Fields and Polarizable Continuum Model: A Fluctuating Charges/PCM Approach. 1. Theory and Implementation.

We present a combined fluctuating charges-polarizable continuum model approach to describe molecules in solution. Both static and dynamic approaches are discussed: analytical first and second derivatives are shown as well as an extended lagrangian for molecular dynamics simluations. In particular, we use the polarizable continuum model to provide nonperiodic boundary conditions for molecular dynamics simulations of aqueous solutions. The extended lagrangian method is extensively discussed, with specific reference to the fluctuating charge model, from a numerical point of view by means of several examples, and a rationalization of the behavior found is presented. Several prototypical applications are shown, especially regarding solvation of ions and polar molecules in water.

A variational formulation of the polarizable continuum model

Continuum solvation models are widely used to accurately estimate solvent effects on energy, structural and spectroscopic properties of complex molecular systems. The polarizable continuum model (PCM) is one of the most versatile among the continuum models because of the variety of properties that can be computed and the diversity of methods that can be used to describe the solute from molecular mechanics (MM) to sophisticated quantum mechanical (QM) post-self-consistent field methods or even hybrid QM/MM methods. In this contribution, we present a new formulation of PCM in terms of a free energy functional whose variational parameters include the continuum polarization (represented by the apparent surface charges), the solutes atomic coordinates and-possibly-its electronic density. The problem of finding the optimized geometry of the (polarized) solute, with the corresponding self-consistent reaction field, is recast as the minimization of this free energy functional, simultaneously with respect to all its variables. The numerous potential applications of this variational formulation of PCM are discussed, including simultaneous optimization of solutes geometry and polarization charges and extended Lagrangian dynamics. In particular, we describe in details the simultaneous optimization procedure and we include several numerical examples.

Linear response theory and electronic transition energies for a fully polarizable QM/Classical Hamiltonian

A fully polarizable quantum/classical Hamiltonian including SCF (HF or DFT), fluctuating charge, and polarizable continuum regions is introduced and implemented for electronic energies of ground and excited states, using, in the latter case, a linear response formulation. After calibration and validation of the approach, preliminary results are presented for pyrimidine in aqueous solution and for retinal in a rhodopsin mimic. The results are consistent with more tested methodologies and pave the route toward fully consistent yet effective simulations of large systems of technological and/or biological interest in their natural environments.

Analytical First and Second Derivatives for a Fully Polarizable QM/Classical Hamiltonian

In this work, we present the derivation and implementation of analytical first and second derivatives for a fully polarizable QM/MM/PCM energy functional. First derivatives with respect to both QM- and MM-described nuclear coordinates and electric perturbations are derived and implemented, and some preliminary application is shown. Analytical second derivatives with respect to nuclear and electric perturbations are then derived, and some numerical test is presented both for a solvated system and for a cromophore embedded in a biological matrix.

The Optical Rotation of Methyloxirane in Aqueous Solution: A Never Ending Story?

The long-standing problem of the calculation of the optical rotation (OR) of (R)-methyloxirane in aqueous solution at different wavelengths is solved by means of a novel gauge-invariant computational protocol able to take into account at the same time for intramolecular averaging specific and bulk solvent effects, leading for the first time to a quantitative agreement (both sign and absolute value) between computed and experimental OR values at several frequencies.

Towards an accurate description of anharmonic infrared spectra in solution within the polarizable continuum model: Reaction field, cavity field and nonequilibrium effects

We present a newly developed and implemented methodology to perturbatively evaluate anharmonic vibrational frequencies and infrared (IR) intensities of solvated systems described by means of the polarizable continuum model (PCM). The essential aspects of the theoretical model and of the implementation are described and some numerical tests are shown, with special emphasis towards the evaluation of IR intensities, for which the quality of the present method is compared to other methodologies widely used in the literature. Proper account of an incomplete solvation regime in the treatment of the molecular vibration is also considered, as well as inclusion of the coupling between the solvent and the probing field (cavity field effects). In order to assess the quality of our approach, comparison with experimental findings is reported for selected cases.

Toward Ab Initio Anharmonic Vibrational Circular Dichroism Spectra in the Condensed Phase

The first implementation and calculation of anharmonic VCD rotational strengths for solvated systems is reported. Our approach, rooted in the polarizable continuum model (PCM) and in the second-order vibrational perturbation theory (VPT2), permits not only correction for anharmonicity in the signals associated with fundamental transitions but also calculation of rotational strengths of overtones and combination bands. This allows for a more physically consistent comparison between experiment and calculations together with the analysis of spectral regions dominated by anharmonic effects. The developed model is applied to a few test cases, and the computational outcomes are directly compared with experimental data.

A QM/MM Approach Using the AMOEBA Polarizable Embedding: From Ground State Energies to Electronic Excitations

A fully polarizable implementation of the hybrid quantum mechanics/molecular mechanics approach is presented, where the classical environment is described through the AMOEBA polarizable force field. A variational formalism, offering a self-consistent relaxation of both the MM induced dipoles and the QM electronic density, is used for ground state energies and extended to electronic excitations in the framework of time-dependent density functional theory combined with a state specific response of the classical part. An application to the calculation of the solvatochromism of the pyridinium N-phenolate betaine dye used to define the solvent ET(30) scale is presented. The results show that the QM/AMOEBA model not only properly describes specific and bulk effects in the ground state but it also correctly responds to the large change in the solute electronic charge distribution upon excitation.

A gauge invariant multiscale approach to magnetic spectroscopies in condensed phase: General three-layer model, computational implementation and pilot applications

Analytical equations to calculate second order electric and magnetic properties of a molecular system embedded into a polarizable environment are presented. The treatment is limited to molecules described at the self consistent field level of theory, including Hartree-Fock theory as well as Kohn-Sham density functional theory and is extended to the Gauge-Including Atomic Orbital method. The polarizable embedding is described by means of our already implemented polarizable quantum mechanical/molecular mechanical (MM) methodology, where the polarization in the MM layer is handled by means of the fluctuating charge (FQ) model. A further layer of description, i.e, the polarizable continuum model, can also be included. The FQ(/polarizable continuum model) contributions to the properties are derived, with reference to the calculation of the magnetic susceptibility, the nuclear magnetic resonance shielding tensor, electron spin resonance g-tensors, and hyperfine couplings.

Fast Domain Decomposition Algorithm for Continuum Solvation Models: Energy and First Derivatives.

In this contribution, an efficient, parallel, linear scaling implementation of the conductor-like screening model (COSMO) is presented, following the domain decomposition (dd) algorithm recently proposed by three of us. The implementation is detailed and its linear scaling properties, both in computational cost and memory requirements, are demonstrated. Such behavior is also confirmed by several numerical examples on linear and globular large-sized systems, for which the calculation of the energy and of the forces is achieved with timings compatible with the use of polarizable continuum solvation for molecular dynamics simulations.