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     

Excited state properties of sizable molecules in solution: from structure to reactivity

We review some recent advances in quantum mechanical methods devised specifically for the study of excited electronic state of large size molecules in solution. The adopted theoretical/computational framework is rooted in the density functional theory (DFT) and its time-dependent extension (TD-DFT) for the characterization of ground and excited states, in the polarizable continuum model (PCM) for the treatment of bulk solvent effects, and in time-dependent quantum mechanical methods for chemical dynamics. Selected applications to the simulation of absorption spectra, to the interpretation of time-resolved experiments, and to the computation of dissociative electron transfer rates are presented and discussed.     

CCSD-PCM: improving upon the reference reaction field approximation at no cost

The combination of the coupled cluster (CC) method with the polarizable continuum model (PCM) of solvation requires a much larger computational effort than gas phase CC calculations, since the PCM contribution depends nonlinearly on the CC reduced density: perturbation theory energy and density (PTED) scheme. An approximation can be introduced that neglects the "correlation" PCM contribution and only considers the "reference" PCM contribution to the free energy: PTE scheme. The PTE scheme is a computationally efficient strategy, since the cost is comparable to gas phase CC, but the difference in the free energy with respect to the PTED scheme can be significant. In this work, two intermediate approximations are presented, PTE(S) and PTES (where S stands for singles), which retain the computational efficiency of the PTE scheme while reducing the energy gap with the PTED scheme. PTE(S) only introduces an energy correction to the PTE free energy, while PTES introduces explicit PCM terms in the iterative solution of the CC equations. PTE(S) improves the PTE free energy, although such correction is small. PTES recovers 50%-80% of the PTE-PTED difference and represents a promising approach to perform calculations in solution of CC quality at a cost comparable to gas phase CC. The expressions for the CC-PTE(S) and -PTES wave functions, free energy, and free energy analytical gradients are presented, and the methods are tested with numerical examples.     

Semiempirical (ZINDO-PCM) approach to predict the radiative and nonradiative decay rates of a molecule close to metal particles

In this work, we present an extension of a model previously proposed (Andreussi et al. J. Chem. Phys. 2004, 121, 10190) to treat the effect of a metal particle on the optical properties of a molecule in solution (close to such a particle) in the framework of the polarizable continuum model (PCM). This extension concerns the combination of such a model with the semiempirical method Zerner's intermediate neglect of differential overlap (ZINDO), which allows us to treat large size molecular systems, as the ones normally used in the experiments. A refinement of the model is also introduced to take into account the effect of the metal specimen on the absorption process of the molecular system, which affects the probability that a molecule reaches the excited state. Numerical tests are presented to validate the reliability of the ZINDO results with respect to quantum-mechanical DFT methods. Comparisons with experimental results on two different large molecular systems are reported, and the effect of the metal on the absorption process is discussed.     

Structural and spectral properties of 4-bromo-1-naphthyl chalcones: a quantum chemical study

The structural and optical properties of 4-bromo-1-naphthyl chalcones (BNC) have been studied by using quantum chemical methods. The density functional theory (DFT) and the singly excited configuration interaction (CIS) methods were employed to optimize the ground and excited state geometries of unsubstituted and substituted BNC with different electron withdrawing and donating groups in both gas and solvent phases. Based on the ground and excited state geometries, the absorption and emission spectra of BNC molecules were calculated using the time-dependent density functional theory (TDDFT) method. The solvent phase calculations were performed using the polarizable continuum model (PCM). The geometrical parameters, vibrational frequencies, and relative stability of cis- and trans-isomers of unsubstituted and substituted BNC molecules have been studied. The results from the TDDFT calculations reveal that the substitution of electron withdrawing and electron donating groups affects the absorption and emission spectra of BNC.     

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.     

吲哚咔唑异构体的电子结构和光学性质

分别采用密度泛函理论(DFT)和单激发组态相互作用(CIS),在6-31G(d,p)基组水平上优化了5个吲哚咔唑分子的基态和激发态结构.在此结构的基础上,用含时密度泛函理论(TD-DFT)在相同基组水平和极化连续介质模型(PCM)下计算了模型分子的吸收和发射光谱.这几个吲哚咔唑异构体的发射光谱有明显的差别,如异构体5([3,2-b]型)有较大的振子强度,但是相对于其他异构体,其发射能量最小;异构体4([3,2-a]型)的发射能量最大;异构体2([2,3-b]型)的最大振子强度在250-450 nm范围内,与其他几个分子相比为最小.这主要是由分子的激发态几何变化和轨道能级的不同导致的.本文还考察了这类分子的一阶超极化率,结果显示5个分子极化率在同一水平,但静态第一超极化率(β0)有明显差别,异构体2的β0值最大.     

Solvent effects on electron-driven proton-transfer processes: adenine-thymine base pairs

Time-Dependent Density Functional Theory (TD-DFT) computations, with M05-2X and PBE0 functionals, have been employed for a detailed study of the Electron-Driven Proton-Transfer (PT) processes in an Adenine-Thymine Watson-Crick Base Pair in the gas phase and in solution, with the bulk solvent described by the polarizable continuum model. In the gas phase, TD-DFT computations predict that the Adenine → Thymine Charge Transfer (CT) excited state undergoes a barrierless PT reaction, in agreement with CC2 computations (S. Perun, A. Sobolewski, W. Domcke, J. Phys. Chem. A, 2006, 110, 9031.). The good agreement between the TD-DFT approach and CC2 results validates the former for the studies of excited state properties, excited state proton transfer reaction, and deactivation mechanisms in the DNA base pairs. Next, it is shown that inclusion of solvent effects significantly influences the possibility of both barrier-less excited state proton transfer and radiation-less deactivation through conical intersection with the ground state, affecting the energy of the CT excited state in the Franck-Condon region, the energy barrier associated to the PT process and the energy gap with the ground electronic state. These findings clearly indicate that environmental effects, with a special attention to proper treatment of dynamical solvation effects, have to be included for reliable computational analysis of photophysical and photochemical processes occurring in condensed phases.     

Extending the power of quantum chemistry to large systems with the fragment molecular orbital method

Following the brief review of the modern fragment-based methods and other approaches to perform quantum-mechanical calculations of large systems, the theoretical development of the fragment molecular orbital method (FMO) is covered in detail, with the emphasis on the physical properties, which can be computed with FMO. The FMO-based polarizable continuum model (PCM) for treating the solvent effects in large systems and the pair interaction energy decomposition analysis (PIEDA) are described in some detail, and a range of applications of FMO to biological studies is introduced. The factors determining the relative stability of polypeptide conformers (alpha-helix, beta-turn, and extended form) are elucidated using FMO/PCM and PIEDA, and the interactions in the Trp-cage miniprotein construct (PDB: 1L2Y) are analyzed using PIEDA.     

Theory and algorithms for the excited states of large molecules and molecular aggregates

This project aims to attack the frontiers of electronic structure calculations on the excited states of large molecules and molecular aggregates by developing novel theoretical and computational methods. The methodology development is especially based on the time-dependent density functional theory (TDDFT) and valence bond (VB) theory, and is expected to be computationally effective and accurate as well. Research works on the following related subjects will be performed: (1) The analytical energy-derivative approaches for electronically excited state within TDDFT will be developed to reduce bypass the computational costs in the calculation of molecular excited-state properties. (2) The ab initio methods for electronically excited state based on VB theory and hybrid TDDFT-VB method will be developed to overcome the limitations of current TDDFT in simulating photophysics and photochemistry. (3) For larger aggregates, neither ab initio methods nor TDDFT is applicable. We intend to build the effective model Hamiltonian by developing novel theoretical and computational methods to calculate the involved microscopic physical parameters from the first-principles methods. The constructed effective Hamiltonian is then used to describe the excitonic states and excitonic dynamics of the natural or artificial photosynthesized systems, organic or inorganic photovoltaic cell. (4) The condensed phase environment is taken into account by combining the developed theories and algorithms based on TDDFT and VB with the polarizable continuum solvent models (PCM), molecular mechanism (MM), classical electrodynamics (ED) or molecular dynamics (MD) theory. (5) Highly efficient software packages will be designed and developed.     

Computational and experimental studies of the effect of substituents on the singlet-triplet energy gap in phenyl(carbomethoxy)carbene

The effect of aromatic substitution on the singlet-triplet energy gap in substituted phenyl(carbomethoxy)carbene (X-Ph-C-CO(2)CH(3), PCC) has been explored by time-resolved infrared (TRIR) spectroscopy and gas-phase computational methods. The ground state of para-substituted PCC is calculated to change from the triplet state in p-NO(2)-PCC (Delta G(ST) = 6.1 kcal/mol) to the singlet state in p-NH(2)-PCC (Delta G(ST) = -2.8 kcal/mol). The absence of solvent perturbation in the TRIR spectra of p-N(CH(3))(2)-PCC (which should have electronic properties similar to p-NH(2)-PCC) and parent PCC is consistent with their ground states lying > +/-2 kcal/mol from the next available electronic state, in line with the computational results. The observation of solvent perturbation in the TRIR spectra of p-OCH(3)-PCC and p-CH(3)-PCC implies that their ground states lie < +/-1 kcal/mol from their next available electronic state. This is in agreement with our computational results, which predict a gas-phase Delta G(ST) of -0.8 and 1.6 kcal/mol for p-OCH(3)-PCC and p-CH(3)-PCC as compared to Delta G(ST) values of -3.9 and -1.3 kcal/mol from polarizable continuum model (PCM) calculations with acetonitrile as a solvent. Gas-phase computational results for the meta- and ortho-substituted PCC species are also presented, along with selected linear free energy (LFE) relationships for the para and meta species.     

On the calculations of interaction energies and induced electric properties within the polarizable continuum model

In this work we investigate the influence of a polarizable environment on the interaction energies and the interaction-induced (excess) static electric dipole properties for the selected model hydrogen-bonded complexes. The excess properties were estimated for water and hydrogen fluoride dimers using the supermolecular approach and assuming the polarizable continuum model (PCM) as a representation of the polarizable environment. We analyze in this context the performance of the counterpoise correction and the consequences of various possible monomer cavity choices. The polarizable environment reduces the absolute magnitudes of interaction energies and interaction-induced dipole moments, whereas an increase is observed for the absolute magnitudes of induced polarizabilities and first hyperpolarizabilities. Our results indicate that the use of either monomeric (MC) or dimeric (DC) cavities in calculations of monomer properties does not change qualitatively the resultant excess properties. We conclude that the DC scheme is more consistent with the definition of the interaction energy and consequently also the interaction-induced property, whereas the MC scheme corresponds to the definition of stabilization energy. Our results indicate also a good performance of the counterpoise correction scheme for the self-consistent methods in the case of all studied properties.     

How to model solvent effects on molecular properties using quantum chemistry? Insights from polarizable discrete or continuum solvation models

We present a comparative study of solvent effects on the 15N NMR shielding constants and the lowest electronic excitation energy (n --> pi*) in the three diazines (pyrazine, pyrimidine, and pyridazine) in aqueous solution. This solvent is modeled using either a polarizable continuum model (PCM) or a discrete polarizable model (DPM). We analyze the results obtained with the two models in terms of differences/similarities in the reaction field produced at the solute. The PCM reaction field is found to be quite sensitive to the dimension of the cavity and so are the molecular properties. However, constructing the cavity so that the DPM and PCM reaction fields become similar in magnitude leads to quite similar results for the studied molecular properties modeling the solvent using either the PCM or the DPM. Compared to experimental data, the most accurate predicted results are obtained by describing the closest water molecules at the same level of sophistication as that of the solute, whereas the bulk solvent may be described using either PCM or MM. Finally, a comparison with geometry-optimized clusters seems to show that it is important to check potential deficiencies in the force field in order for this to treat hydrogen bonding in a consistent manner.     

Peculiarities of the environmental influence on the optical properties of push-pull nonlinear optical molecules: a theoretical study

Gas-phase geometry optimization of NLO-active molecules is one of the standard approaches in the first principle computational methodology, whereas the important role of the environment is usually not considered during the evaluation of structural parameters. With a wide variety of environmentally influenced models in most cases only the high quality single point calculations are prepared. Among different approaches, the most used polarizable continuum model (PCM) seems to be promising. In this study, we have compared the electronic properties of gas-phase optimized geometries of imidazole-derived push-pull compounds with those optimized using PCM solvation approach including CH(2)Cl(2) and PMMA as media. We have focused particularly on the linear optical properties of investigated molecules, namely on the UV-vis absorption spectra. The analysis of presented results shows the applicability of the different quantum chemical (QC) methods for the UV-vis spectra calculations of linear NLO molecules. Herein we also present the need of molecule geometry optimization affected by the environment. Following the performed calculations, the electronic properties of gas-phase optimized molecules give conformable results with respect to those obtained by more time-consuming continuum optimizations. All computational data are supported by experimental investigations.     

A state-specific polarizable continuum model time dependent density functional theory method for excited state calculations in solution

An effective state specific (SS) model for the inclusion of solvent effects in time dependent density functional theory (TD-DFT) computations of excited electronic states has been developed and coded in the framework of the so-called polarizable continuum model (PCM). Different relaxation time regimes can be treated thus giving access to a number of different spectroscopic properties together with solvent relaxation energies of paramount relevance in electron transfer processes. SS and conventional linear response (LR) models have been compared for two benchmark systems (coumarin 153 and formaldehyde in different solvents) and in the limiting simple case of a dipolar solute embedded in a spherical cavity. The results point out the complementarity of LR and SS approaches and the advantages of the latter model especially for polar solvents. The favorable scaling properties of PCM-TD-DFT models in both SS and LR variants and their availability in effective quantum mechanical codes pave the route for the computation of reliable spectroscopic properties of large molecules of technological and/or biological interest in their natural environments.