Implementation of the analytic energy gradient for the combined time-dependent density functional theory/effective fragment potential method: application to excited-state molecular dynamics simulations

Excited-state quantum mechanics/molecular mechanics molecular dynamics simulations are performed, to examine the solvent effects on the fluorescence spectra of aqueous formaldehyde. For that purpose, the analytical energy gradient has been derived and implemented for the linear-response time-dependent density functional theory (TDDFT) combined with the effective fragment potential (EFP) method. The EFP method is an efficient ab initio based polarizable model that describes the explicit solvent effects on electronic excitations, in the present work within a hybrid TDDFT/EFP scheme. The new method is applied to the excited-state MD of aqueous formaldehyde in the n-π* state. The calculated π*→n transition energy and solvatochromic shift are in good agreement with other theoretical results.     

On the performance of quantum chemical methods to predict solvatochromic effects: the case of acrolein in aqueous solution

The performance of the Hartree-Fock method and the three density functionals B3LYP, PBE0, and CAM-B3LYP is compared to results based on the coupled cluster singles and doubles model in predictions of the solvatochromic effects on the vertical n-->pi* and pi-->pi* electronic excitation energies of acrolein. All electronic structure methods employed the same solvent model, which is based on the combined quantum mechanics/molecular mechanics approach together with a dynamical averaging scheme. In addition to the predicted solvatochromic effects, we have also performed spectroscopic UV measurements of acrolein in vapor phase and aqueous solution. The gas-to-aqueous solution shift of the n-->pi* excitation energy is well reproduced by using all density functional methods considered. However, the B3LYP and PBE0 functionals completely fail to describe the pi-->pi* electronic transition in solution, whereas the recent CAM-B3LYP functional performs well also in this case. The pi-->pi* excitation energy of acrolein in water solution is found to be very dependent on intermolecular induction and nonelectrostatic interactions. The computed excitation energies of acrolein in vacuum and solution compare well to experimental data.     

Non-adiabatic molecular dynamics with quantum solvent effects

Three novel approaches extending quantum-classical non-adiabatic (NA) molecular dynamics (MD) to include quantum effects of solvent environments are described. In a standard NA-MD the solute subsystem is treated quantum mechanically, while the larger solvent part of a system is treated classically. The three novel approaches presented here are based on the Bohmian formulation of quantum mechanics, the stochastic Schrödinger equation for the evolution of open quantum systems and the quantized Hamilton dynamics generalization of classical mechanics. The approaches extend the standard NA-MD to incorporate the following quantum effects of the solvent. (1) Branching, i.e. the ability of solvent quantum wave packets to split and follow asymptotically diverging trajectories correlated with different quantum states of the solute. (2) Decoherence, i.e. loss of quantum interference within the solute subsystem induced by the diverging solvent trajectories. (3) Zero point energy that contributes to NA coupling and must be preserved during the energy exchange between solvent and solute degrees of freedom. The Bohmian quantum-classical mechanics, stochastic mean-field and quantized mean-field approximations incorporate the quantum solvent effects into the standard quantum-classical NA-MD in a straightforward and efficient way that can be easily applied to quantum dynamics of condensed phase chemical systems.     

A new method to locate saddle points for reactions in solution by using the free-energy gradient method and the mean field approximation

A new method for calculating saddle points of reactions in solution is presented. The main characteristics of the method are: (1) the solute-solvent system is described by the averaged solvent electrostatic potential/molecular dynamics method (ASEP/MD). This is a quantum mechanics/molecular mechanics method (QM/MM) that makes use of the mean field approximation (MFA) and that permits one to simultaneously optimize the electronic structure and geometry of the solute molecule and the solvent structure around it. (2) The transition state is located by the joint use of the free-energy gradient method and the mean field approximation. An application to the study of the Menshutkin reaction between NH(3) and CH(3)Cl in aqueous solution is discussed. The accuracy and usefulness of the proposed method is checked through comparison with other methods.     

Solvent effects on the nπ* transition of pyrimidine in aqueous solution

A hybrid quantum mechanical and molecular mechanical potential is used in Monte Carlo simulations to examine the solvent effects on the electronic excitation energy for the n→π* transition of pyrimidine in aqueous solution. In the present study, the pyrimidine molecule is described by the semi-empirical AM1 model, while the solvent molecules are treated classically. Two sets of calculations are performed: the first involves the use of the pairwise three-point charge TIP3P model for water, and the second computation employs a polarizable many-body potential for the solvent. The latter calculation takes into account the effect of solvent polarization following the solute electronic excitation, and makes a correction to the energies determined using pairwise potentials, which neglects such fast polarization effects and overestimates the solute-solvent interactions on the Franck-Condon excited states. Our simulation studies of pyrimidine in water indicate that the solvent charge redistribution following the solute electronic excitation makes modest corrections (about −130␣cm⁻¹) to the energy predicted by using pairwise potentials. Specific hydrogen bonding interactions between pyrimidine and water are important for the prediction of solvatochromic shifts for pyrimidine. The computed n→π* blue shift is 2275±110 cm⁻¹, which may be compared with the experimental value (2700 cm⁻¹) from isooctane to water. Received: 14 January 1997 / Accepted: 21 February 1997     

Solvent effects on the asymmetric Diels–Alder reaction between cyclopentadiene and (−)-menthyl acrylate revisited with the three-layer hybrid local self-consistent field/molecular mechanics/self-consistent reaction field method

The construction of the three-layer hybrid local self-consistent field/molecular mechanics/self-consistent reaction field method is detailed. This method is specifically devoted to the study of the reactivity of large chemical systems in solution. The solvent, modeled by a polarizable continuum, surrounds the whole solute molecule. Solute–solvent interactions are taken into account by means of the self-consistent reaction field approach. The solute system is treated by both quantum and molecular mechanics, the former being principally applied to the reactive part, i.e., the part undertaking bond forming or breaking, the latter being reserved for the ancillary encumbering groups. The connection between the molecular mechanics and the quantum mechanics part is accomplished by a strictly localized bond orbital that remains frozen within the local self-consistent field framework. As a test system, the asymmetric Diels–Alder reaction between cyclopentadiene and (–)-menthyl acrylate is studied for the first time with steric interactions and electrostatic solvent effects taken into account simultaneously. The results indicate that the coupling of both interactions leads to conclusions that could not have been guessed from separate calculations.Proceedings of the 11th International Congress of Quantum chemistry satellite meeting in honour of Jean-Louis Rivail     

丙酮分子n→π%*跃迁光谱的平均溶剂静电势/分子动力学方法研究

采用量子力学/分子动力学方法研究了具体溶剂分子结构对溶质光谱行为的静电影响. 通过拟合溶质所处外电场和引入溶剂分子极化率, 考虑了溶质溶剂分子之间的相互极化效应, 得到合理的溶质和溶剂分子的电荷分布. 经过严格推导发现, 在传统的显溶剂模型中, 平衡和非平衡溶剂化能表达式均未考虑溶剂分子永久偶极弹簧能的贡献. 因此, 在正确计算永久偶极弹簧能的基础上, 重新建立了溶剂化能的表达式和新的吸收/发射光谱移动公式. 采用修改后的ASEP/MD程序, 计算得到了与实验值比较吻合的丙酮在水溶液中n→π*跃迁的光谱移动值, 验证了新公式的合理性.     

Long-range electrostatic interactions in hybrid quantum and molecular mechanical dynamics using a lattice summation approach

A method based on a lattice summation technique for treating long-range electrostatic interactions in hybrid quantum mechanics/molecular mechanics simulations is presented in this article. The quantum subsystem is studied at the semiempirical level, whereas the solvent is described by a two-body potential of molecular mechanics. Molecular dynamics simulations of a (quantum) chloride ion in (classical) water have been performed to test this technique. It is observed that the application of the lattice summations to solvent-solvent interactions as well as on solute-solvent ones has a significant effect on solvation energy and diffusion coefficient. Moreover, two schemes for the computation of the long-range contribution to the electrostatic interaction energy are investigated. The first one replaces the exact charge distribution of the quantum solute by a Mulliken charge distribution. The long-range electrostatic interactions are then calculated for this charge distribution that interacts with the solvent molecule charges. The second one is more accurate and involves a modified Fock operator containing long-range electron-charge interactions. It is shown here that both schemes lead to similar results, the method using Mulliken charges for the evaluation of long-range interactions being, however, much more computationally efficient.     

Solvent effect on the absorption spectra of coumarin 120 in water: A combined quantum mechanical and molecular mechanical study

The solvent effect on the absorption spectra of coumarin 120 (C120) in water was studied utilizing the combined quantum mechanical∕molecular mechanical (QM∕MM) method. In molecular dynamics (MD) simulation, a new sampling scheme was introduced to provide enough samples for both solute and solvent molecules to obtain the average physical properties of the molecules in solution. We sampled the structure of the solute and solvent molecules separately. First, we executed a QM∕MM MD simulation, where we sampled the solute molecule in solution. Next, we chose random solute structures from this simulation and performed classical MD simulation for each chosen solute structure with its geometry fixed. This new scheme allowed us to sample the solute molecule quantum mechanically and sample many solvent structures classically. Excitation energy calculations using the selected samples were carried out by the generalized multiconfigurational perturbation theory. We succeeded in constructing the absorption spectra and realizing the red shift of the absorption spectra found in polar solvents. To understand the motion of C120 in water, we carried out principal component analysis and found that the motion of the methyl group made the largest contribution and the motion of the amino group the second largest. The solvent effect on the absorption spectrum was studied by decomposing it in two components: the effect from the distortion of the solute molecule and the field effect from the solvent molecules. The solvent effect from the solvent molecules shows large contribution to the solvent shift of the peak of the absorption spectrum, while the solvent effect from the solute molecule shows no contribution. The solvent effect from the solute molecule mainly contributes to the broadening of the absorption spectrum. In the solvent effect, the variation in C-C bond length has the largest contribution on the absorption spectrum from the solute molecule. For the solvent effect on the absorption spectrum from the solvent molecules, the solvent structure around the amino group of C120 plays the key role.     

Asequential Monte Carlo quantum mechanics study of the hydrogen-bond interaction and the solvatochromic shift of the n-pi* transition of acrolein in water

The sequential Monte Carlo (MC) quantum mechanics (QM) methodology, using time-dependent density-functional theory (TD-DFT), is used to study the solvatochromic shift of the n-pi* transition of trans-acrolein in water. Using structures obtained from the isothermal-isobaric Metropolis MC simulation TD-DFT calculations, within the B3LYP functional, are performed for the absorption spectrum of acrolein in water. In the average acrolein makes one hydrogen bond with water and the hydrogen-bond shell is responsible for 30% of the total solvatochromic shift, considerably less than the shift obtained for the minimum-energy configurations. MC configurations are sampled after analysis of the statistical correlation and 100 configurations are extracted for subsequent QM calculations. All-electron TD-DFT B3LYP calculations of the absorption transition including acrolein and all explicit solvent molecules within the first hydration shell, 26 water molecules, give a solvatochromic shift of 0.18 +/- 0.11 eV. Using simple point charges to represent the solvent the shifts are calculated for the first, second, and third solvation shells. The results converge for the calculated shift of 0.20 +/- 0.10 eV in very good agreement with the experimentally inferred result of 0.20 +/- 0.05 eV. All average results presented are statistically converged.     

Quantum Mechanical Molecular Interactions for Calculating the Excitation Energy in Molecular Environments: A First‐Order Interacting Space Approach

Intermolecular interactions regulate the molecular properties in proteins and solutions such as solvatochromic systems. Some of the interactions have to be described at an electronic‐structure level. In this study, a commutator for calculating the excitation energy is used for deriving a first‐order interacting space (FOIS) to describe the environmental response to solute excitation. The FOIS wave function for a solute‐in‐solvent cluster is solved by second‐order perturbation theory. The contributions to the excitation energy are decomposed into each interaction and for each solvent.     

Theoretical study of the role of solvent Stark effect in electron transitions

The possible influence of the solvent Stark effect (SSE) on the solvatochromic shift in electron transitions has been analyzed by using the ASEP/MD (averaged solvent electrostatic potential from molecular dynamics) method. With this purpose, four molecules, two polar (acrolein and formaldehyde) and two non-polar (p-difluorobenzene and trans-difluoroethene) have been studied in solvents of diverse polarity. Independently of the nature of the system we found that the contribution of SSE on the average value of the solvent shift or on the multipole moment values is negligible. In the case of centro-symmetric molecules, our results permit to discard the SSE as cause of the solvent shift found, which must be assigned to the electrostatic interaction of the solute quadrupole and higher multipoles with the solvent. As the SSE values provide also a measure of the errors introduced by the mean field approximation (MFA), these results indicate that MFA permits a very accurate determination of the solvent shift at the same time that it reduces drastically the computational cost. Finally, a new procedure suited to the ASEP/MD method has been presented that permits to estimate the inhomogeneous broadening of spectral bands, complementing the information provided by mean field theories. This procedure does not need additional quantum calculations and its computational cost is minimal.     

Simulations of X-ray absorption spectra: the effect of the solvent

We perform quantum mechanics/molecular mechanics molecular dynamics simulations on the [Pt(2)(P(2)O(5)H(2))(4)](4-) (abbreviated PtPOP) complex; in water, dimethylformamide and ethanol. These are used to calculate the ground state X-ray absorption spectrum of the complex. The structural parameters from X-ray spectra are usually extracted using a fit of the experimental data. In such simulations the solvent is neglected meaning that any effect of the local environment will be compensated for by structural changes of the solute, leading to possible discrepancies in the extracted structural parameters. Our simulations show a significant solvent effect on the spectra, which has important implications for the structural analysis of molecules in solution.     

Solvatochromism and Nonradiative Decay of Intramolecular Charge‐Transfer Excited States: Bands‐of‐Energy Model,Thermodynamics, and Self‐Organization

The fluctuations of orientation and induction interactions in solution and their impact on the broadening of absorption and fluorescence spectra are considered in terms of a bands‐of‐energy model. Also covered is the application of principles of thermodynamics and self‐organization of systems for calculation of solvatochromic shift, among them a component owing to the work on electronic polarization of solvent at the instant of electronic transition in the solute. The findings on solvatochromic shift and spectral broadening open the way to the calculation of solvent effects on the rate constant of nonradiative transitions. As demonstrated herein for 15 fluorophores, the novel theory of nonradiative decay of the intramolecular charge‐transfer excited states is carried out for dyes and organic compounds of different nature, both for polar and nonpolar media.     

Theoretical study of the relative stability of rotational conformers of alpha and beta-D-glucopyranose in gas phase and aqueous solution

The alpha-beta anomer energy difference and the stability of 10 rotamers of counterclockwise D-glucopyranose were studied in vacuo and in aqueous solution at the B3LYP/6-31+G(d,p) level. To obtain the solute charge distribution and the solvent structure around it, we used the averaged solvent electrostatic potential from molecular dynamics method, ASEP/MD, which alternates molecular dynamics and quantum mechanics calculations in an iterative procedure. The main characteristics of the anomeric equilibrium, both in vacuo and in solution, are well reproduced. The relative stability of the different anomers is related to the availability of the free pairs of electrons in the anomeric oxygen to interact with the water molecules. The influence of solvation in the conformer equilibrium is also analyzed.     

Probing supercritical water with the n-pi* transition of acetone: a Monte Carlo/quantum mechanics study

The n-pi(*) electronic transition of acetone is a convenient and important probe to study supercritical water. The solvatochromic shift of this transition in supercritical water (adopting the experimental condition of P=340.2 atm and T=673 K) has been studied theoretically using Metropolis NPT Monte Carlo (MC) simulation and quantum mechanics (QM) calculations based on INDO/CIS and TDDFT-B3LYP6-31+G(d) methods. MC simulations are used to analyze hydration shells, solute-solvent interaction, and for generating statistically relevant configurations for subsequent QM calculations of the n-pi(*) transition of acetone. The results show that the average number of hydrogen bonds between acetone and water is essentially 13 of that in normal water condition of temperature and pressure. But these hydrogen bonds have an important contribution in the solute stabilization and in the solute-solvent interaction. In addition, they respond for nearly half of the solvatochromic shift. The INDO/CIS calculations explicitly considering all valence electrons of the water molecules, using different solvation shells, up to the third shell (170 water molecules), give a solvatochromic shift of 670+/-36 cm(-1) in very good agreement with the experimentally inferred result of 500-700 cm(-1). It is found that the solvatochromic effect on n-pi(*) transition of acetone in the supercritical condition is essentially given by the first solvation shell. The time-dependent density-functional theory (TDDFT) calculations are also performed including all solvent molecules up to the third shell, now represented by point charges. This TDDFT-B3LYP6-31+G(d) also gives a good but slightly overestimated result of 825+/-65 cm(-1). For comparison the same study is also made for acetone in water at normal condition. Finally, all average results reported here are statistically converged.     

An explicit quantum chemical method for modeling large solvation shells applied to aminocoumarin C151

The absorption spectra of aminocoumarin C151 in water and n-hexane solution are investigated by an explicit quantum chemical solvent model. We improved the efficiency of the frozen-density embedding scheme, as used in a former study on solvatochromism (J. Chem. Phys. 2005, 122, 094115) to describe very large solvent shells. The computer time used in this new implementation scales approximately linearly (with a low prefactor) with the number of solvent molecules. We test the ability of the frozen-density embedding to describe specific solvent effects due to hydrogen bonding for a small example system, as well as the convergence of the excitation energy with the number of solvent molecules considered in the solvation shell. Calculations with up to 500 water molecules (1500 atoms) in the solvent system are carried out. The absorption spectra are studied for C151 in aqueous or n-hexane solution for direct comparison with experimental data. To obtain snapshots of the dye molecule in solution, for which subsequent excitation energies are calculated, we use a classical molecular dynamics (MD) simulation with a force field adapted to first-principles calculations. In the calculation of solvatochromic shifts between solvents of different polarity, the vertical excitation energy obtained at the equilibrium structure of the isolated chromophore is sometimes taken as a guess for the excitation energy in a nonpolar solvent. Our results show that this is, in general, not an appropriate assumption. This is mainly due to the fact that the solute dynamics is neglected. The experimental shift between n-hexane and water as solvents is qualitatively reproduced, even by the simplest embedding approximation, and the results can be improved by a partial polarization of the frozen density. It is shown that the shift is mainly due to the electronic effect of the water molecules, and the structural effects are similar in n-hexane and water. By including water molecules, which might be directly involved in the excitation, in the embedded region, an agreement with experimental values within 0.05 eV is achieved.     

A Monte Carlo-quantum mechanics study of the lowest n-pi* and pi-pi* states of uracil in water

The solvatochromic shifts of the n-pi(*) and pi-pi(*) states of uracil in water are analyzed using a combined and sequential Monte Carlo/quantum mechanics (MC/QM) approach. The role of the solute polarization and electronic delocalization into the solvent region are investigated. Electronic polarization of the solute is obtained using the HF/6-31G(d), the polarizable continuum model (PCM) and an iterative procedure using MP2/aug-cc-pVDZ in the MC/QM. The in-water dipole moment of uracil is obtained, respectively, as 5.12 D, 6.12 D and 7.01 +/- 0.05 D. This latter result, corresponding to an increase of 60% with respect to the gas phase value, is used in the classical potential of the MC simulation to obtain statistically uncorrelated configurations for subsequent QM calculations of the ultraviolet-visible absorption spectrum of uracil in water. QM calculations are performed at the time-dependent density-functional theory (TD-DFT) combined with the B3LYP and B3PW91 functionals, multiconfigurational (CASSCF) and the semi-empirical all-valence electron INDO/CIS methods. Using 60 solute-solvent configurations with the explicit inclusion of 200 water molecules the solvatochromic shift is obtained as a blue shift of 0.50 eV for the n-pi(*) state and a red shift of 0.19 eV for the pi-pi(*) state, in good agreement with experimentally-inferred values. These results are compared with TD-DFT results in conjunction with PCM approaches and the importance of solute polarization and wave function delocalization over the solvent region is discussed. Our results suggest that the elusive n-pi(*) state of uracil in water lies around 255 nm hidden by the intense and broad pi-pi(*) transition with a maximum at 260 nm, inverting the relative locations of these states compared to the gas phase. This is further supported by considering the in-water dipole moment changes upon excitation, as obtained from CASSCF calculations.     

A smooth, nonsingular, and faithful discretization scheme for polarizable continuum models: the switching/Gaussian approach

Polarizable continuum models (PCMs) are a widely used family of implicit solvent models based on reaction-field theory and boundary-element discretization of the solute/continuum interface. An often overlooked aspect of these theories is that discretization of the interface typically does not afford a continuous potential energy surface for the solute. In addition, we show that discretization can lead to numerical singularities and violations of exact variational conditions. To fix these problems, we introduce the switching/Gaussian (SWIG) method, a discretization scheme that overcomes several longstanding problems with PCMs. Our approach generalizes a procedure introduced by York and Karplus [J. Phys. Chem. A 103, 11060 (1999)], extending it beyond the conductor-like screening model. Comparison to other purportedly smooth PCM implementations reveals certain artifacts in these alternative approaches, which are avoided using the SWIG methodology. The versatility of our approach is demonstrated via geometry optimizations, vibrational frequency calculations, and molecular dynamics simulations, for solutes described using quantum mechanics and molecular mechanics.