Coupled‐cluster theory for the polarizable continuum model. III. A response theory for molecules in solution

A coupled‐cluster (CC) response functions theory for molecular solutes described with the framework of the polarizable continuum model (PCM) is presented. The theory is an extension to the dynamical molecular properties of the PCM‐CC analytic derivatives recently proposed for the calculation of static molecular properties (Cammi, Jr Chem Phys 2009, 131, 164104). The theory is presented for linear and quadratic response functions, and the operative expressions of these response functions can accurately account for the nonequilibrium solvation effects. The excitation energies and transition moments of the solvated chromophores have been determined from the linear response functions. Accurate expressions for gradients of excitation energies for the evaluation of the excited state properties have been also discussed. © 2012 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Brueckner doubles coupled cluster method with the polarizable continuum model of solvation

We present the theory and implementation for computing the (free) energy and its analytical gradients with the Brueckner doubles (BD) coupled cluster method in solution, in combination with the polarizable continuum model of solvation (PCM). The complete model, called PTED, and an efficient approximation, called PTE, are introduced and tested with numerical examples. Implementation details are also discussed. A comparison with the coupled-cluster singles and doubles CCSD-PCM-PTED and CCSD-PCM-PTE schemes, which use Hartree-Fock (HF) orbitals, is presented. The results show that the two PTED approaches are mostly equivalent, while BD-PCM-PTE is shown to be superior to the corresponding CCSD scheme when the HF reference wave function is unstable. The BD-PCM-PTE scheme, whose computational cost is equivalent to gas phase BD, is therefore a promising approach to study molecular systems with complicated electronic structure in solution.     

Wavelet formulation of the polarizable continuum model

The first implementation of a wavelet discretization of the Integral Equation Formalism (IEF) for the Polarizable Continuum Model (PCM) is presented here. The method is based on the application of a general purpose wavelet solver on the cavity boundary to solve the integral equations of the IEF‐PCM problem. Wavelet methods provide attractive properties for the solution of the electrostatic problem at the cavity boundary: the system matrix is highly sparse and iterative solution schemes can be applied efficiently; the accuracy of the solver can be increased systematically and arbitrarily; for a given system, discretization error accuracy is achieved at a computational expense that scales linearly with the number of unknowns. The scaling of the computational time with the number of atoms N is formally quadratic but a N^1.5 scaling has been observed in practice. The current bottleneck is the evaluation of the potential integrals at the cavity boundary which scales linearly with the system size. To reduce this overhead, interpolation of the potential integrals on the cavity surface has been successfully used. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Coupled cluster response theory in parameter subspaces

We introduce a response function formalism that enables smaller number of parameters than that defined in standard coupled cluster response theory. This is essential in the development of reduced scaling methods. The formalism is general and it applies to all parameterizations at all levels of the coupled cluster hierarchy. We show that to achieve physically reasonable results the parameterization must fulfill certain criteria. The linear response functions are derived and discussed in the context of optimized virtual orbitals and Cholesky decomposition of the cluster amplitudes. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Polarizable continuum model with the fragment molecular orbital-based time-dependent density functional theory

The polarizable continuum model (PCM) for describing the solvent effect was combined with the fragment molecular orbital-based time-dependent density functional theory (TDDFT). Several levels of the many-body expansion were implemented, and the importance of the many-body contributions to the singlet-excited states was discussed. To calibrate the accuracy, we performed a number of the model calculations using our method and the regular TDDFT in solution, applying them to phenol and polypeptides at the long-range corrected BLYP/6-31G* level. It was found that for systems up to 192 atoms the largest error in the excitation energy was 0.006 eV (vs. the regular TDDFT/PCM of the full system). The solvent shifts and the conformer effects were discussed, and the scaling was found to be nearly linear. Finally, we applied our method to the lowest singlet excitation of the photoactive yellow protein (PYP) in aqueous solution and determined the excitation energy to be in reasonable agreement with experiment. The excitation energy analysis provided the contributions of individual residues, and the main factors as well as their solvent shifts were determined.     

On the description of the environment polarization response to electronic transitions

This paper addresses the issue of accurately describing the structures and properties of electronically excited systems embedded in an environment, through multiscale approaches combining quantum-mechanical (QM) and polarizable classical representations of the system and environment, respectively. Such approaches represent an efficient strategy and allow to effectively study the excited states of molecular systems in the condensed phase, still maintaining the computational efficiency and the physical reliability of the ground-state calculations. The most important theoretical and computational aspects of the coupling between the QM system and the polarizable environment are presented and discussed. Even if these approaches already reached an evident degree of maturity, they can still be subject to further development, in order to achieve their full potential. This perspective presents an overview of the state of the art of these strategies, showing the fields of applicability and indicating the current limitations, which need to be overcome in future developments.     

Achieving linear-scaling computational cost for the polarizable continuum model of solvation

This work describes a new and low-scaling implementation of the polarizable continuum model (PCM) for computing the self-consistent solvent reaction field. The PCM approach is both general and accurate. It is applicable in the framework of both quantum and classical calculations, and also to hybrid quantum/classical methods. In order to further extend the range of applicability of PCM we addressed the problem of its computational cost. The generation of the finite-elements molecular cavity has been reviewed and reimplemented, achieving linear scaling for systems containing up to 500 atoms. Linear scaling behavior has been achieved also for the iterative solution of the PCM equations, by exploiting the fast multipole method (FMM) for computing electrostatic interactions. Numerical results for large (both linear and globular) chemical systems are discussed.     

Torsional effects on excitation energies of thiophene derivatives induced by beta-substituents: comparison between time-dependent density functional theory and approximated coupled cluster approaches

The influence of methyl or phenyl substitution in beta-position of dioxygenated terthiophene and diphenylthiophene on the optical properties is investigated by first-principles calculations. We compare the approximated singles and doubles coupled cluster (CC2) approach with time-dependent density functional theory methods. CC2 reproduces experimental excitation energies with an accuracy of 0.1 eV. We find that the different substituents modify the inter-ring torsional angle which in turn strongly influences the excitation energies. The steric contribution to the excitation energies have been separated from the total substituent effects.     

Exploiting graphical processing units to enable quantum chemistry calculation of large solvated molecules with conductor-like polarizable continuum models

The conductor-like polarizable continuum model (C-PCM) with switching/Gaussian smooth discretization is a widely used implicit solvation model in quantum chemistry. We have previously implemented C-PCM solvation for Hartree-Fock (HF) and density functional theory (DFT) on graphical processing units (GPUs), enabling the quantum mechanical treatment of large solvated biomolecules. Here, we first propose a GPU-based algorithm for the PCM conjugate gradient linear solver that greatly improves the performance for very large molecules. The overhead for PCM-related evaluations now consumes less than 15% of the total runtime for DFT calculations on large molecules. Second, we demonstrate that our algorithms tailored for ground state C-PCM are transferable to excited state properties. Using a single GPU, our method evaluates the analytic gradient of the linear response PCM time-dependent density functional theory energy up to 80× faster than a conventional central processing unit (CPU)-based implementation. In addition, our C-PCM algorithms are transferable to other methods that require electrostatic potential (ESP) evaluations. For example, we achieve speed-ups of up to 130× for restricted ESP-based atomic charge evaluations, when compared to CPU-based codes. We also summarize and compare the different PCM cavity discretization schemes used in some popular quantum chemistry packages as a reference for both users and developers.     

Solvation effects on reaction profiles by the polarizable continuum model coupled with the Gaussian density functional method

An efficient version of the polarizable continuum model for solvation has been implemented in the Gaussian density-functional-based code called deMon. Solvation free energies of representative compounds have been calculated as a preliminary test. The hydration effects on the reaction profile of the Cl⁻+CH₃Cl→ClCH₃+Cl⁻ reaction and the thermodynamics of the Menschutkin reaction have also been investigated. Finally, the conformational behavior of the 1,2-diazene cis–trans isomerization process in water was examined. Comparisons between the results obtained and the available experimental data and previous theoretical computations have been made. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 290–299, 1998     

Combining the polarizable Drude force field with a continuum electrostatic Poisson–Boltzmann implicit solvation model

In this work, we have combined the polarizable force field based on the classical Drude oscillator with a continuum Poisson–Boltzmann/solvent‐accessible surface area (PB/SASA) model. In practice, the positions of the Drude particles experiencing the solvent reaction field arising from the fixed charges and induced polarization of the solute must be optimized in a self‐consistent manner. Here, we parameterized the model to reproduce experimental solvation free energies of a set of small molecules. The model reproduces well‐experimental solvation free energies of 70 molecules, yielding a root mean square difference of 0.8 kcal/mol versus 2.5 kcal/mol for the CHARMM36 additive force field. The polarization work associated with the solute transfer from the gas‐phase to the polar solvent, a term neglected in the framework of additive force fields, was found to make a large contribution to the total solvation free energy, comparable to the polar solute–solvent solvation contribution. The Drude PB/SASA also reproduces well the electronic polarization from the explicit solvent simulations of a small protein, BPTI. Model validation was based on comparisons with the experimental relative binding free energies of 371 single alanine mutations. With the Drude PB/SASA model the root mean square deviation between the predicted and experimental relative binding free energies is 3.35 kcal/mol, lower than 5.11 kcal/mol computed with the CHARMM36 additive force field. Overall, the results indicate that the main limitation of the Drude PB/SASA model is the inability of the SASA term to accurately capture non‐polar solvation effects. © 2018 Wiley Periodicals, Inc.     

Fock space multireference coupled cluster theory: noniterative inclusion of triples for excitation energies

In this paper we propose and numerically implement a specific scheme for calculating the excitation energies (EEs) within the Fock space multireference coupled cluster framework, which includes the contributions from noniterative triples cluster amplitudes. These contribute to the EEs at the third order. We present results for CH⁺ and N2, and study the effects of these noniterative triples on EEs. Received: 28 July 1997 / Accepted: 8 December 1997     

Two-photon absorption in solution by means of time-dependent density-functional theory and the polarizable continuum model

We present the first study of two-photon absorption (TPA) of solvated molecules based on direct evaluation of TPA cross sections from the quadratic response of time-dependent perturbations. A set of prototypical two-photon (TP) chromophores has been selected and analyzed: a pure pi system (t-stilbene) and its substituted homologs obtained employing a donor (D) and an acceptor (A) group to probe the solvent effects along the series pi, D-pi-D, A-pi-D, and A-pi-A. For the selected systems we have calculated the TPA cross sections in different environments by means of the polarizable continuum model. The data have been analyzed to evaluate how the structural and environmental parameters contribute to the final two-photon absorption cross section. These include molecular structure, geometry relaxation in solution, polarity, and refractive index of the solvent. The performances of the three common functionals SVWN, BLYP, and B3LYP have been compared. The results show a significant solvent dependence of the TPA cross section and an unusual trend when passing from cyclohexane to water. The data have also been rationalized in terms of the main orbital excitations leading to the transitions. Finally, trends along the series have been described and comparison with experiments and previous calculations has been drawn.     

Coupled cluster and DFT calculations of 14N nuclear quadrupole coupling constants

The dependence of ¹⁴N quadrupole coupling constants calculated using coupled cluster theory on the level of approximation is examined for a series of small molecules. For HCN, HNC, CH₃CN, and CH₃NC, we use the coupled cluster singles‐and‐doubles with a noniterative perturbative triples correction—CCSD(T)—approach, and we analyze the basis set dependence of the results. For aziridine, diazirine, and cyclopropyl cyanide, we use the CCSD(T) approach, but smaller basis sets, and for the largest studied molecules—quinuclidine and hexamine—we present CCSD results. The differences between computed and experimental values for the best basis sets used are ≈ 5% at the CCSD level and decrease noticeably at the CCSD(T) level. The ‐ N≡C bonds are an exception—in this case the quadrupole coupling constants are very small, hence the differences between theory and experiment become larger (up to 9%). We also consider the performance of density functional theory, comparing the results for different density functionals with the coupled cluster values of the same constants. Most of the functionals provide results systematically improved with respect to the Hartree–Fock values, with ¹⁴N coupling constants in ‐ N≡C bonds being again an exception. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Correlation and solvation effects. IV. A systematic analysis of the influence of cavity size and shape on solvation properties in the polarizable continuum model with electron correlation

From the standpoint of models that use a polarizable continuum to represent the solvent in studying the phenomenon of solvation, a systematic and detailed analysis is made of the influence of the cavity size and shape on calculated energies. The solute is represented by its ab initio wavefunction, and the electronic part of the solvation energy is calculated including terms that take into account electron correlation up to third order. The analysis shows the convenience of modeling the cavity according to considerations of homogeneity, which are based fundamentally on how the solute wavefunction is constructed, i.e., the basis set used.     

Coupled‐cluster reaction barriers of : An application of the coupled‐cluster//Kohn–Sham density functional theory model chemistry

In this work, we report a theoretical investigation concerning the use of the popular coupled‐cluster//Kohn‐Sham density functional theory (CC//KS‐DFT) model chemistry, here applied to study the entrance channel of the reaction, namely by comparing CC//KS‐DFT calculations with KS‐DFT, MRPT2//CASSCF, and CC//CASSCF results from our previous investigations. This was done by performing single point energy calculations employing several coupled cluster methods and using KS‐DFT geometries optimized with six different functionals, while conducting a detailed analysis of the barrier heights and topological features of the curves and surfaces here obtained. The quality of this model chemistry is critically discussed in the context of the title reaction and also in a wider context. © 2013 Wiley Periodicals, Inc.     

Dispersion and repulsion contributions to the solvation free energy: comparison of quantum mechanical and classical approaches in the polarizable continuum model

We report a systematic comparison of the dispersion and repulsion contributions to the free energy of solvation determined using quantum mechanical self-consistent reaction field (QM-SCRF) and classical methods. In particular, QM-SCRF computations have been performed using the dispersion and repulsion expressions developed in the framework of the integral equation formalism of the polarizable continuum model, whereas classical methods involve both empirical pairwise potential and surface-dependent approaches. Calculations have been performed for a series of aliphatic and aromatic compounds containing prototypical functional groups in four solvents: water, octanol, chloroform, and carbon tetrachloride. The analysis is focused on the dependence of the dispersion and repulsion components on the level of theory used in QM-SCRF computations, the contribution of those terms in different solvents, and the magnitude of the coupling between electrostatic and dispersion-repulsion components. Finally, comparison is made between the dispersion-repulsion contributions obtained from QM-SCRF calculations and the results determined from classical approaches.