A coupled-cluster solvent reaction field method

Dynamical Effects of Solvation on Norbornadiene/Quadricyclane Systems

Molecules that can undergo reversible chemical transformations following the absorption of light, the so-called molecular photoswitches, have attracted increasing attention in technologies, such as solar energy storage. Here, the optical and thermochemical properties of the photoswitch are central to its applicability, and these properties are influenced significantly by solvation. We investigate the effects of solvation on two norbornadiene/quadricyclane photoswitches. Emphasis is put on the energy difference between the two isomers and the optical absorption as these are central to the application of the systems in solar energy storage. Using a combined classical molecular dynamics and quantum mechanical/molecular mechanical computational scheme, we showcase that the dynamic effects of solvation are important. In particular, it is found that standard implicit solvation models generally underestimate the energy difference between the two isomers and overestimate the strength of the absorption, while the explicit solvation spectra are also less red-shifted than those obtained using implicit solvation models. We also find that the absorption spectra of the two systems are strongly correlated with specific dihedral angles. Altogether, this highlights the importance of including the dynamic effects of solvation.

Role of Singles Amplitudes in ADC(2) and CC2 for Low-Lying Electronically Excited States

The closely related second-order methods CC2 and ADC(2) usually perform very similarly for single excitations of organic molecules. However, as rationalized in this work, significant deviations between these two methods can arise if the ground state and a low-lying singly excited state arise from a strong coupling between their leading configurations. Such a configuration mixing is partially accounted for in CC2 through the ground-state singles amplitudes but is omitted in ADC(2). This can cause unusual deviations between the results obtained with these methods. In this work, we study how severe this effect can become at the example of two solvatochromic dyes: the negatively solvatochromic betaine dye N1-tBu and the positively solvatochromic bithiophene P1. These two dyes allow one to study the limits of both small and somewhat larger excitation energies and configuration mixing by tuning the S0 → S1 transition energy through the polarity of the environment. Higher-level calculations at the CC3 level provide information on the accuracy of ADC(2) and CC2 in these cases. The most extreme deviation between ADC(2) and CC2 is found for N1-tBu in vacuum, where the ADC(2) result is 0.45 eV below that of CC2. In this case, the methodical error of CC2 with respect to CC3 is only 0.05 eV. With increasing excitation energy in polar solvents, the CC2-ADC(2) deviation decreases and reaches a value of only 0.15 eV. For P1, which has larger excitation energies, these effects are reversed due to the opposite solvatochromism but also smaller in magnitude: the deviation increases from 0.08 eV in vacuum to 0.16 eV in the so-called conductor limit of the continuum solvation model. Although for these two dyes larger deviations are observed for smaller excitation energies, the extent of configuration mixing does not generally correlate with only the size of excitation energy. For example, s-triazine (0.15 eV), formamide (0.19 eV), and formaldehyde (0.23 eV) also show large deviations between CC2 and ADC(2) despite their much higher excitation energies compared to those of N1-tBu and P1.

Investigation of Solvent Effects on the Molecular Energy Storage and Optical Properties of Bicyclooctadiene/Tetracyclooctane Photoswitches

In this paper, we investigate the effects of solvation on the solar energy storage properties of bicyclooctadiene/tetracyclooctane (BOD/TCO) photoswitches. The solvent effects on the thermochemical and optical properties are studied in cyclohexane, toluene, dichloromethane, ethanol, acetonitrile, and a vacuum using density functional theory and coupled cluster theory. Our results show that the energy storage capacity of the BOD/TCO system increases as the solvent polarity increases, and the change is more significant with an unsubstituted system. The energy storage capacity of the substituted system is not dependent on the polarity of the solvent. As the solvent polarity increases, the absorption peaks shift away from each other and the absorption intensities increase. Overall, the solvents improve the performance of the optical properties and the energy storage capacities of the BOD/TCO molecular solar thermal systems.

Redfield Propagation of Photoinduced Electron Transfer Reactions in Vacuum and Solution

Dynamical simulations of ultrafast electron transfer reactions are of utmost interest. To allow for energy dissipation directly into an external surrounding environment, a solvent coupling model has been deduced, implemented, and utilized to describe the photoinduced electron transfer dynamics within a model triad system herein. The model is based on Redfield theory, and the environment is represented by harmonic oscillators filled with bosonic quanta. To imitate real solvents, the oscillators have been equipped with frequencies and polarization lifetimes characteristic of the corresponding solvent. The population was found to transfer through the energetically lowest electron transfer route regardless of the medium. The condensed population transfer dynamics were observed to be highly dependent on the solvent parameters. In particular, an increase in the solvent coupling entailed a detainment in the population transfer from the initially prepared diabatic state and a promotion in the population transfer through the other electron transfer route. Two explanations based on the diagonal and off-diagonal matrix elements of the Kohn-Sham Fock matrix, respectively, have been provided. The lifetime of the populated partially charge-separated state was prolonged with increasing solvent polarity, and it was explained in terms of attractive interactions between the solvent's dipole moments and the fragments' charges. The high-frequency vibrational fine-structure in the correlation function was demonstrated to be important for the transfer dynamics, and the importance of dephasing effects in polar solvents was verified and precised to concern the optical polarization of the solvents.

Cluster perturbation theory. VI. Ground-state energy series using the Lagrangian

In this paper, we derive alternative cluster perturbation series to the energy cluster perturbation (ECP) series of Paper I. The ECP series were derived using the standard coupled cluster energy framework. Here, we use the coupled cluster Lagrangian framework to derive the Lagrangian cluster perturbation (LCP) series and show that a slightly modified order concept means that the ECP and the LCP series become identical. Using the Lagrangian, we also derive a perturbation series where total cluster amplitudes and multipliers are determined through the same orders as dictated by the 2n+1/2n+2 rule, the VCP series. The VCP energies have errors that are bilinear in the errors of the total cluster amplitudes and multipliers. Test calculations have been performed for S(D) and SD(T) orbital excitation spaces. The convergence of the test calculations can be divided into two groups. The first group contains molecules that exhibit a slow monotonic geometric convergence pattern in both orbital spaces. The second group, containing the rest of the molecules, exhibits a fast low order convergence. For the S(D) calculations, the deviations in fourth order from the coupled cluster singles and doubles energy are below 1.3 per cent for the LCP series and 0.3 per cent for the VCP series, respectively. For the SD(T) calculations, the second group hardly shows any difference between the low order convergence of the three series ECP, LCP, and LCP and at fourth order the deviations from the triples correlation energy are less than 1 per cent.

Implicit solvation in domain based pair natural orbital coupled cluster (DLPNO-CCSD) theory

A nearly linear scaling implementation of coupled-cluster with singles and doubles excitations (CCSD) can be achieved by means of the domain-based local pair natural orbital (DLPNO) method. The combination of DLPNO-CCSD with implicit solvation methods allows the calculation of accurate energies and chemical properties of solvated systems at an affordable computational cost. We have efficiently implemented different schemes within the conductor-like polarizable continuum model (C-PCM) for DLPNO-CCSD in the ORCA quantum chemistry suite. In our implementation, the overhead due to the additional solvent terms amounts to less than 5% of the time the equivalent gas phase job takes. Our results for organic neutrals and open-shell ions in water show that for most systems, adding solvation terms to the coupled-cluster amplitudes equations and to the energy leads to small changes in the total energy compared to only considering solvated orbitals and corrections to the reference energy. However, when the solute contains certain functional groups, such as carbonyl or nitrile groups, the changes in the energy are larger and estimated to be around 0.04 and 0.02 kcal/mol for each carbonyl and nitrile group in the solute, respectively. For solutes containing metals, the use of accurate CC/C-PCM schemes is crucial to account for correlation solvation effects. Simultaneously, we have calculated the electrostatic component of the solvation energy for neutrals and ions in water for the different DLPNO-CCSD/C-PCM schemes. We observe negligible changes in the deviation between DLPNO-CCSD and canonical-CCSD data. Here, DLPNO-CCSD results outperform those for Hartree-Fock and density functional theory calculations.

Coupled Cluster Theory with Induced Dipole Polarizable Embedding for Ground and Excited States

In this work, we present the theory and implementation of the coupled cluster single and double excitations (CCSD) method combined with a classical polarizable molecular mechanics force field (MMPol) based on the induced dipole model. The method is developed to compute electronic excitation energies within the state specific (SS) and linear response (LR) formalisms for the interaction of the quantum mechanical and classical regions. Furthermore, we consider an approximate expression of the correlation energy, originally developed for CCSD with implicit solvation models, where the interaction term is linear in the coupled cluster density. This approximation allows us to include the explicit contribution of the environment to the CC equations without increasing the computational effort. The test calculations on microsolvated systems, where the CCSD/MMPol method is compared to full CCSD calculations, demonstrates the reliability of this computational protocol for all interaction schemes (errors < 2%). We also show that it is important to include induced dipoles on all atom centers of the classical region and that too diffuse functions in the basis set may be problematic due to too strong interaction with the environment.

Theoretical Study of Kinetics and Mechanism of Reactions of Hydroxylamine and Amineoxide Anion with Methyl Iodide in Gas and Aqueous Phases

The kinetics and mechanism of the reactions of hydroxylamine and aminoxide anion with methyl iodide were studied with ab initio calculations, Monte-Carlo and QM/MM simulations in gas and aqueous phases. Geometrical parameters and charge calculations show that these reactions proceed through the SN2 (bimolecular nucleophilic displacement) mechanism only. The solvent effects on these reactions were studied by inserting water molecules in reaction media, Onsager model, Monte-Carlo and QM/MM simulations. Activation parameters indicate the expected variation in activation energy and rate coefficient in aqueous phase in comparison to the gas phase. The shift of potential energy barrier through the reactants or products for the studied reactions in the gas phase is in the opposite direction in comparison to the aqueous phase.

Heterogeneous nucleation of polymorphs on polymer surfaces: polymer-molecule interactions using a heterogeneous dielectric solvation model

We have investigated the mechanism of the nucleation of acetaminophen on poly(methyl-methacrylate) and poly(vinyl-acetate) utilizing a combination of quantum mechanical computations and electrostatic models. We have used a heterogeneous dielectric solvation model to determine the stability of different orientations of acetaminophen on polymer surfaces. We find that for the nucleation of acetaminophen on the polymer surfaces in vacuum, the most stable orientation is a flat orientation. For the nucleation process in solution where acetaminophen and the polymer surface are surrounded by a solvent, we find that the heterogeneous dielectric solvation model predicts that a sideways orientation is the most stable orientation.

An EOM-CCSD-PCM Benchmark for Electronic Excitation Energies of Solvated Molecules

In this work, we benchmark the equation of motion coupled cluster with single and double excitations (EOM-CCSD) method combined with the polarizable continuum model (PCM) for the calculation of electronic excitation energies of solvated molecules. EOM-CCSD is one of the most accurate methods for computing one-electron excitation energies, and accounting for the solvent effect on this property is a key challenge. PCM is one of the most widely employed solvation models due to its adaptability to virtually any solute and its efficient implementation with density functional theory methods (DFT). Our goal in this work is to evaluate the reliability of EOM-CCSD-PCM, especially compared to time-dependent DFT-PCM (TDDFT-PCM). Comparisons between calculated and experimental excitation energies show that EOM-CCSD-PCM consistently overestimates experimental results by 0.4-0.5 eV, which is larger than the expected EOM-CCSD error in vacuo. We attribute this decrease in accuracy to the approximated solvation model. Thus, we investigate a particularly important source of error: the lack of H-bonding interactions in PCM. We show that this issue can be addressed by computing an energy shift, Δ_HB, from bare-PCM to microsolvation + PCM at DFT level. Our results show that such a shift is independent of the functional used, contrary to the absolute value of the excitation energy. Hence, we suggest an efficient protocol where the EOM-CCSD-PCM transition energy is corrected by Δ_HB(DFT), which consistently improves the agreement with the experimental measurements.

Communication: A simplified coupled-cluster Lagrangian for polarizable embedding

A simplified coupled-cluster Lagrangian, which is linear in the Lagrangian multipliers, is proposed for the coupled-cluster treatment of a quantum mechanical system in a polarizable environment. In the simplified approach, the amplitude equations are decoupled from the Lagrangian multipliers and the energy obtained from the projected coupled-cluster equation corresponds to a stationary point of the Lagrangian.

Evaluation of the SCF Combination of KS-DFT and 3D-RISM-KH; Solvation Effect on Conformational Equilibria, Tautomerization Energies, and Activation Barriers

The effect of solvation on conformational equilibria, tautomerization energies, and activation barriers in simple SN2 reactions is reproduced by using the self-consistent field coupling of the Kohn-Sham density functional theory (KS-DFT) for electronic structure and the three-dimensional reference interaction site model with the closure approximation of Kovalenko and Hirata (3D-RISM-KH) for molecular solvation structure. These examples are used in order to validate the implementation of the 3D-RISM-KH method in the Amsterdam Density Functional package. The computations of the free energy difference in the trans/gauche conformational equilibrium for 1,2-dichloroethane in different solvents; the relative tautomerization free energy for cytosine, isocytosine, and guanine; and the free energy activation barrier for a CH3X-type (X = F, Cl, Br) SN2 reaction exhibit agreement with the experimental data. The method is also applied to the electronic and hydration structure of carbon single-wall nanotubes of different diameters, including the effect of water located in the inner space of the nanotubes. A comparison with continuum models of solvation (including COSMO) as well as with other more precise and computationally more expensive calculations is made to demonstrate the accuracy and predictive capability of the new KS-DFT/3D-RISM-KH method.

The Dalton quantum chemistry program system

Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree-Fock, Kohn-Sham, multiconfigurational self-consistent-field, Møller-Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

Vertical Electronic Excitations in Solution with the EOM-CCSD Method Combined with a Polarizable Explicit/Implicit Solvent Model

The accurate calculation of electronic transition energies and properties of isolated chromophores is not sufficient to provide a realistic simulation of their excited states in solution. In fact, the solvent influences the solute geometry, electronic structure, and response to external fields. Therefore, a proper description of the solvent effect is fundamental. This can be achieved by combining polarizable explicit and implicit representations of the solvent. The former provides a realistic description of solvent molecules around the solute, while the latter introduces the electrostatic effect of the bulk solution and reduces the need of too large a number of explicit solvent molecules. This strategy is particularly appealing when an accurate method such as equation of motion coupled cluster singles and doubles (EOM-CCSD) is employed for the treatment of the chromophore. In this contribution, we present the coupling of EOM-CCSD with a fluctuating charges (FQ) model and polarizable continuum model (PCM) of solvation for vertical excitations in a state-specific framework. The theory, implementation, and prototypical applications of the method are presented. Numerical tests on small solute-water clusters show very good agreement between full EOM-CCSD and EOM-CCSD-FQ calculations, with and without PCM, with differences ≤ 0.1 eV. Additionally, approximated schemes that further reduce the computational cost of the method are introduced and showed to perform well compared to the full method (errors ≤ 0.1 eV).

Absorption and Emission Spectra of Solvated Molecules with the EOM-CCSD-PCM Method

The accurate calculation of transition energies and properties of isolated molecules is not enough for realistic simulations of their absorption and emission spectra in solution. In fact, the solvent influences the solute geometry, electronic structure, and response to external fields, and a proper description of the solvent effect is fundamental. However, the computational cost of including explicit solvent molecules around the solute becomes rather onerous when an accurate method such as the equation of motion coupled cluster singles and doubles (EOM-CCSD) is employed. The polarizable continuum model of solvation (PCM) may provide an efficient alternative to explicit models, since the sampling of solvent configurations is implicit and the solute-solvent mutual polarization is naturally accounted for. In this contribution, the absorption and emission spectra of molecules in solution are modeled through the EOM-CCSD-PCM method. The equilibrium solvation regime is employed for the geometry optimization of the solute molecule in the ground and excited states, while the nonequilibrium solvation regime is employed for vertical transitions. The theory, implementation, and prototypical applications of the method are presented. The numerical tests involve solvents that are particularly challenging for PCM: low-polar and protic polar solvents. Nonetheless, the experimental trends are well reproduced, and the overall agreement with the measured data is remarkable.

Study of the optical and magnetic properties of pyrimidine in water combining PCM and QM/MM methodologies

The solvent effects on the low-lying absorption spectrum and on the (15)N chemical shielding of pyrimidine in water are calculated using the combined and sequential Monte Carlo simulation and quantum mechanical calculations. Special attention is devoted to the solute polarization. This is included by an iterative procedure previously developed where the solute is electrostatically equilibrated with the solvent. In addition, we verify the simple yet unexplored alternative of combining the polarizable continuum model (PCM) and the hybrid QM/MM method. We use PCM to obtain the average solute polarization and include this in the MM part of the sequential QM/MM methodology, PCM-MM/QM. These procedures are compared and further used in the discrete and the explicit solvent models. The use of the PCM polarization implemented in the MM part seems to generate a very good description of the average solute polarization leading to very good results for the n-π* excitation energy and the (15)N nuclear chemical shield of pyrimidine in aqueous environment. The best results obtained here using the solute pyrimidine surrounded by 28 explicit water molecules embedded in the electrostatic field of the remaining 472 molecules give the statistically converged values for the low lying n-π* absorption transition in water of 36 900 ± 100 (PCM polarization) and 36 950 ± 100 cm(-1) (iterative polarization), in excellent agreement among one another and with the experimental value observed with a band maximum at 36 900 cm(-1). For the nuclear shielding (15)N the corresponding gas-water chemical shift obtained using the solute pyrimidine surrounded by 9 explicit water molecules embedded in the electrostatic field of the remaining 491 molecules give the statistically converged values of 24.4 ± 0.8 and 28.5 ± 0.8 ppm, compared with the inferred experimental value of 19 ± 2 ppm. Considering the simplicity of the PCM over the iterative polarization this is an important aspect and the computational savings point to the possibility of dealing with larger solute molecules. This PCM-MM/QM approach reconciles the simplicity of the PCM model with the reliability of the combined QM/MM approaches.

Electronic excitation energies in solution at equation of motion CCSD level within a state specific polarizable continuum model approach

We present a study of excitation energies in solution at the equation of motion coupled cluster singles and doubles (EOM-CCSD) level of theory. The solvent effect is introduced with a state specific polarizable continuum model (PCM), where the solute-solvent interaction is specific for the state of interest. Three definitions of the excited state one-particle density matrix (1PDM) are tested in order to gain information for the development of an integrated EOM-CCSD/PCM method. The calculations show the accuracy of this approach for the computation of such property in solution. Solvent shifts between nonpolar and polar solvents are in good agreement with experiment for the test cases. The completely unrelaxed 1PDM is shown to be a balanced choice between computational effort and accuracy for vertical excitation energies, whereas the response of the ground state CCSD amplitudes and of the molecular orbitals is important for other properties, as for instance the dipole moment.

Prediction of spin-spin coupling constants in solution based on combined density functional theory/molecular mechanics

We present theory and implementation of calculation of spin-spin coupling constants within combined quantum mechanics/molecular mechanics methods. Special attention is given to the role of explicit solvent polarization as well as the molecular consequences due to hydrogen bonding. The model is generally applicable but is here implemented for the case of density functional theory. First applications to liquid water and acetylene in aqueous solution are presented. Good agreement between theory and experiment is obtained in both cases, thereby showing the strength of our approach. Finally, spin-spin coupling constants across hydrogen bonds are discussed considering for the first time the role of an explicit solvent on this class of spin-spin couplings.

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.

Conformational Equilibrium of 1,2-Dichloroethane in Water: Comparison of PCM and RISM-SCF Methods

The RISM-SCF and polarizable continuum model (PCM) approaches have been applied to study the conformational equilibrium of 1,2-dichloroethane (DCE) in water. Both the electron correlation effect and basis sets play an important role in the relative energies of the gauche and trans conformers in gas and solution phases. Both PCM and RISM-MP2 methods resulted in a consistent trend with the previous experimental and theoretical studies that the population of the gauche conformer increases in going from the gas phase to the aqueous solution. However, the PCM treatment could not describe the solvent effect completely in that the sign of the relative free energy of the gauche and trans forms is opposite to the most recent experimental and theoretical data, while the RISM-MP2 gives the right sign in the free energy difference. We found that the larger excess chemical potential gain (by ca. -4.1 kcal/mol) for the gauche conformer is large enough to result in the gauche preference of DCE in water, though it has to compensate for more solute reorganization energy (approximately 1.6 kcal/mol) and overcome the energy difference (approximately 1.6 kcal/mol) in the gas phase. The radial distribution functions between DCE and the nearest water shows that the electrostatic repulsion between chlorine and oxygen atoms is higher in the trans conformer than in the gauche one, while the attractive interaction between chlorine and hydrogen of water is higher in the gauche conformer.

Second harmonic generation second hyperpolarizability of water calculated using the combined coupled cluster dielectric continuum or different molecular mechanics methods

In this article we report the first calculations of second harmonic generation second hyperpolarizability of liquid water using coupled cluster/molecular mechanics (CC/MM) methods or coupled cluster/dielectric continuum (CC/DC) methods. The latter approach treats the solvent as an isotropic homogeneous fluid while the former accounts for the discrete nature of the solvent molecules. The CC/MM approach may include or exclude polarization effects explicitly. Alternatively, polarization effects may be included using perturbation theory. The CC descriptions implemented are the coupled cluster second-order approximate singles and doubles (CC2) and coupled cluster singles and doubles models. The second harmonic generation second hyperpolarizabilities are, depending on the model, obtained using either an analytical implementation of the cubic response function or using an analytical implementation of the quadratic response function combined with the finite field technique. The CC/MM results for the second harmonic generation second hyperpolarizability compare excellently with experimental data while a significant overestimation is found when using the CC/DC model. Particular, the cavity radius in the CC/DC calculations have an enormous effects on this fourth-order property.

CORRELATED ELECTRONIC STRUCTURE NONLINEAR RESPONSE METHODS FOR STRUCTURED ENVIRONMENTS

▪ Abstract  This contribution concerns a brief outline of structural environment models where correlated electronic structure response methods are utilized for the determination of nonlinear optical properties of molecules. The presentation provides theory and applications of a heterogeneous dielectric media model and a quantum mechanical–classical mechanical model at the level of correlated electronic structure response methods. The correlated electronic structure response methods include the multiconfigurational self-consistent field method.