Method to Compute the Solute-Solvent Dispersion Contribution to the Electronic Excitation Energy in Solution.

A method formulated within the polarizable continuum model of the solvent and a quantum Monte Carlo treatment of the electronic states of the solute molecule is presented for the calculation of the solute-solvent dispersion contribution to the electronic excitation energy in solution. Variational quantum Monte Carlo is exploited to measure the fluctuations of the electronic electric field of the solute molecule to compute the London's dispersion forces with the solvent. The method previously applied to the ground state of the solute is here extended to excited states. To perform the Casimir-Polder integration, we introduce a positive parameter Ω whose value is properly chosen for this purpose. We derive a general expression that for Ω = 0 reduces to that already proposed for the ground state. For an excited state, Ω must be less than the first transition electronic energy of the solvent molecule but greater than the transition energy from the ground to excited electronic state of the solute molecule. Benchmark calculations were performed on the n → π* transition for formaldehyde, acrolein, and acetone in six solvents, including water, ethanol, cyclohexane, chloroform, carbon tetrachloride, and toluene, and the π → π* transition of acrolein in cyclohexane. Solvents are characterized by their ionization potential and the refractive index at frequency Ω. In all cases, we found that the dispersion solute-solvent interaction stabilizes the excited state of the solutes leading to red (negative) solvatochromic shifts.

Introducing QMC/MMpol: Quantum Monte Carlo in Polarizable Force Fields for Excited States.

We present for the first time a quantum mechanics/molecular mechanics scheme which combines quantum Monte Carlo with the reaction field of classical polarizable dipoles (QMC/MMpol). In our approach, the optimal dipoles are self-consistently generated at the variational Monte Carlo level and then used to include environmental effects in diffusion Monte Carlo. We investigate the performance of this hybrid model in describing the vertical excitation energies of prototypical small molecules solvated in water, namely, methylenecyclopropene and s-trans acrolein. Two polarization regimes are explored where either the dipoles are optimized with respect to the ground-state solute density (polGS) or different sets of dipoles are separately brought to equilibrium with the states involved in the electronic transition (polSS). By comparing with reference supermolecular calculations where both solute and solvent are treated quantum mechanically, we find that the inclusion of the response of the environment to the excitation of the solute leads to superior results than the use of a frozen environment (point charges or polGS), in particular, when the solute-solvent coupling is dominated by electrostatic effects which are well recovered in the polSS condition. QMC/MMpol represents therefore a robust scheme to treat important environmental effects beyond static point charges, combining the accuracy of QMC with the simplicity of a classical approach.

Multiple-Resonance Local Wave Functions for Accurate Excited States in Quantum Monte Carlo.

We introduce a novel class of local multideterminant Jastrow-Slater wave functions for the efficient and accurate treatment of excited states in quantum Monte Carlo. The wave function is expanded as a linear combination of excitations built from multiple sets of localized orbitals that correspond to the bonding patterns of the different Lewis resonance structures of the molecule. We capitalize on the concept of orbital domains of local coupled-cluster methods, which is here applied to the active space to select the orbitals to correlate and construct the important transitions. The excitations are further grouped into classes, which are ordered in importance and can be systematically included in the Jastrow-Slater wave function to ensure a balanced description of all states of interest. We assess the performance of the proposed wave function in the calculation of vertical excitation energies and excited-state geometry optimization of retinal models whose π → π* state has a strong intramolecular charge-transfer character. We find that our multiresonance wave functions recover the reference values of the total energies of the ground and excited states with only a small number of excitations and that the same expansion can be flexibly used at very different geometries. Furthermore, significant computational saving can also be gained in the orbital optimization step by selectively mixing occupied and virtual orbitals based on spatial considerations without loss of accuracy on the excitation energy. Our multiresonance wave functions are therefore compact, accurate, and very promising for the calculation of multiple excited states of different character in large molecules.

Electronic Excitations in Nonpolar Solvents: Can the Polarizable Continuum Model Accurately Reproduce Solvent Effects?

In nonpolar solvents, both electrostatic and nonelectrostatic interactions play a role in tuning the electronic excitations of molecular solutes. This specificity makes the application of continuum solvation models a challenge. Here, we propose a strategy for the calculation of solvatochromic shifts on absorption spectra, using a coupling of the polarizable continuum model with a time-dependent density functional theory framework, which explicitly accounts for dispersion and repulsion, as well as for electrostatic effects. Our analysis makes a step further in the interpretation of the effects of nonpolar solvents and suggests new directions in their modeling using continuum formulations.

Study of dispersion forces with quantum Monte Carlo: toward a continuum model for solvation.

We present a general method to compute dispersion interaction energy that, starting from London's interpretation, is based on the measure of the electronic electric field fluctuations, evaluated on electronic sampled configurations generated by quantum Monte Carlo. A damped electric field was considered in order to avoid divergence in the variance. Dispersion atom-atom C6 van der Waals coefficients were computed by coupling electric field fluctuations with static dipole polarizabilities. The dipole polarizability was evaluated at the diffusion Monte Carlo level by studying the response of the system to a constant external electric field. We extended the method to the calculation of the dispersion contribution to the free energy of solvation in the framework of the polarizable continuum model. We performed test calculations on pairs of some atomic systems. We considered He in ground and low lying excited states and Ne in the ground state and obtained a good agreement with literature data. We also made calculations on He, Ne, and F(-) in water as the solvent. Resulting dispersion contribution to the free energy of solvation shows the reliability of the method illustrated here.

Electronic excitations in a dielectric continuum solvent with quantum Monte Carlo: acrolein in water.

We investigate here the vertical n → π(*) and π → π(*) transitions of s-trans-acrolein in aqueous solution by means of a polarizable continuum model (PCM) we have developed for the treatment of the solute at the quantum Monte Carlo (QMC) level of the theory. We employ the QMC approach which allows us to work with highly correlated electronic wave functions for both the solute ground and excited states and, to study the vertical transitions in the solvent, adopt the commonly used scheme of considering fast and slow dielectric polarization. To perform calculations in a non-equilibrium solvation regime for the solute excited state, we add a correction to the global dielectric polarization charge density, obtained self consistently with the solute ground-state wave function by assuming a linear-response scheme. For the solvent polarization in the field of the solute in the ground state, we use the static dielectric constant while, for the electronic dielectric polarization, we employ the solvent refractive index evaluated at the same frequency of the photon absorbed by the solute for the transition. This choice is shown to be better than adopting the most commonly used value of refractive index measured in the region of visible radiation. Our QMC calculations show that, for standard cavities, the solvatochromic shifts obtained with the PCM are underestimated, even though of the correct sign, for both transitions of acrolein in water. Only by reducing the size of the cavity to values where more than one electron is escaped to the solvent region, we regain the experimental shift for the n → π(*) case and also improve considerably the shift for the π → π(*) transition.

Solvent Effects on Excited-State Structures: A Quantum Monte Carlo and Density Functional Study.

We present the first application of quantum Monte Carlo (QMC) in its variational flavor combined with the polarizable continuum model (PCM) to perform excited-state geometry optimization in solution. Our implementation of the PCM model is based on a reaction field that includes both volume and surface polarization charges and is determined self-consistently with the molecular wave function during the QMC optimization of the solute geometry. For acrolein, acetone, methylenecyclopropene, and the propenoic acid anion, we compute the optimal exited-state geometries in water and compare our results with the structures obtained with second-order perturbation theory (CASPT2) and other correlated methods, and with time-dependent density functional theory (TDDFT). We find that QMC predicts a structural response to solvation in good agreement with CASPT2 with the only exception of the π → π* state of acrolein where the robustness of the QMC geometry must be contrasted to the sensitivity of the perturbation result to the details of the calculation. As regards TDDFT, we show that all investigated functionals systematically overestimate the geometrical changes from the gas phase to solution, sometimes giving bond variations opposite in trend to QMC.

Multi-level quantum Monte Carlo wave functions for complex reactions: the decomposition of α-hydroxy-dimethylnitrosamine.

We present here several novel features of our recently proposed Jastrow linear generalized valence bond (J-LGVB) wave functions, which allow a consistently accurate description of complex potential energy surfaces (PES) of medium-large systems within quantum Monte Carlo (QMC). In particular, we develop a multilevel scheme to treat different regions of the molecule at different levels of the theory. As prototypical study case, we investigate the decomposition of α-hydroxy-dimethylnitrosamine, a carcinogenic metabolite of dimethylnitrosamine (NDMA), through a two-step mechanism of isomerization followed by a retro-ene reaction. We compute a reliable reaction path with the quadratic configuration interaction method and employ QMC for the calculation of the electronic energies. We show that the use of multideterminantal wave functions is very important to correctly describe the critical points of this PES within QMC, and that our multilevel J-LGVB approach is an effective tool to significantly reduce the cost of QMC calculations without loss of accuracy. As regards the complex PES of α-hydroxy-dimethylnitrosamine, the accurate energies computed with our approach allows us to confirm the validity of the two-step reaction mechanism of decomposition originally proposed within density functional theory, but with some important differences in the barrier heights of the individual steps.

Barrier Heights in Quantum Monte Carlo with Linear-Scaling Generalized-Valence-Bond Wave Functions.

We investigate here the performance of our recently developed linear-scaling Jastrow-generalized-valence-bond (J-LGVB) wave functions based on localized orbitals, for the quantum Monte Carlo (QMC) calculation of the barrier heights and reaction energies of five prototypical chemical reactions. Using the geometrical parameters from the Minnesota database collection, we consider three hydrogen-exchanges, one heavy-atom exchange, and one association reaction and compare our results with the best available experimental and theoretical data. For the three hydrogen-exchange reactions, we find that the J-LGVB wave functions yield excellent QMC results, with average deviations from the reference values below 0.5 kcal/mol. For the heavy-atom exchange and association reactions, additional resonance structures are important, and we therefore extend our original formulation to include multiple coupling schemes characterized by different sets of localized orbitals. We denote these wave functions as J-MC-LGVB, where MC indicates the multiconfiguration generalization, and show that such a form leads to very accurate barrier heights and reaction energies also for the last two reactions. We can therefore conclude that the J-LGVB theory for constructing QMC wave functions, with its multiconfiguration generalization, is valid for the study of large portions of ground-state potential energy surfaces including, in particular, the region of transition states.

A density functional and quantum Monte Carlo study of glutamic acid in vacuo and in a dielectric continuum medium.

We present density functional theory (DFT) and quantum Monte Carlo (QMC) calculations of the glutamic acid and glutamate ion in vacuo and in various dielectric continuum media within the polarizable continuum model (PCM). In DFT, we employ the integral equation formalism variant of PCM while, in QMC, we use a PCM scheme we have developed to include both surface and volume polarization. We investigate the gas-phase protonation thermochemistry of the glutamic acid using a large set of structural conformations, and find that QMC is in excellent agreement with the best available theoretical and experimental results. For the solvated glutamic acid and glutamate ion, we perform DFT calculations for dielectric constants, ε, between 4 and 78. We find that the glutamate ion in the zwitterionic form is more stable than the non-zwitterionic form over the whole range of dielectric constants, while the glutamic acid is more stable in its non-zwitterionic form at ε = 4. The dielectric constant at which the two glutamic acid species have the same energy depends on the cavity size and lies between 5 and 12.5. We validate these results with QMC for the two limiting values of the dielectric constant, and find qualitative agreement with DFT even though the solvent polarization is less pronounced at the QMC level.

Size-Extensive Wave Functions for Quantum Monte Carlo: A Linear Scaling Generalized Valence Bond Approach.

We propose a new class of multideterminantal Jastrow-Slater wave functions constructed with localized orbitals and designed to describe complex potential energy surfaces of molecular systems for use in quantum Monte Carlo (QMC). Inspired by the generalized valence bond formalism, we elaborate a coupling scheme between electron pairs which progressively includes new classes of excitations in the determinantal component of the wave function. In this scheme, we exploit the local nature of the orbitals to construct wave functions which have increasing complexity but scale linearly. The resulting wave functions are compact, can correlate all valence electrons, and are size extensive. We assess the performance of our wave functions in QMC calculations of the homolytic fragmentation of N-N, N-O, C-O, and C-N bonds, very common in molecules of biological interest. We find excellent agreement with experiments, and, even with the simplest forms of our wave functions, we satisfy chemical accuracy and obtain dissociation energies of equivalent quality to the CCSD(T) results computed with the large cc-pV5Z basis set.

Quantum Monte Carlo formulation of volume polarization in dielectric continuum theory.

We present a novel formulation based on quantum Monte Carlo techniques for the treatment of volume polarization due to quantum mechanical penetration of the solute charge density in the solvent domain. The method allows to accurately solve Poisson's equation of the solvation model coupled with the Schrodinger equation for the solute. We demonstrate the performance of the approach on a representative set of solutes in water solvent and give a detailed analysis of the dependence of the volume polarization on the solute cavity and the treatment of electron correlation.

Coupling quantum Monte Carlo to a nonlinear polarizable continuum model for spherical solutes.

Starting from the nonlinear dielectric response model of Sandberg and Edholm, we derive an analytical expression of the polarization contribution to the solvation free energy in terms of the electronic density of the solute and the dielectric properties of the solvent. The solvent inhomogeneity is taken into account with the use of a smooth switching function whose spacial variation is established on the basis of how the solvent is arranged around the solute. An explicit form of a local potential representing the solvent effect on the solute is thus obtained by functional analysis. This effective potential can be combined with density functional or quantum chemical methods for the quantum mechanical treatment of the solute. Here, we use quantum Monte Carlo techniques for the solute and apply the method to the hydration of atomic ions finding very good agreement with experimental data.