Coupled cluster response theory for solvated molecules in equilibrium and nonequilibrium solvation

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.

Pushing the limits: Efficient wavefunction methods for excited states in complex systems using frozen-density embedding

Frozen density embedding (FDE) is an embedding method for complex environments that is simple for users to set up. It reduces the computation time by dividing the total system into small subsystems and approximating the interaction by a functional of their densities. Its combination with wavefunction methods is, however, limited to small- or medium-sized molecules because of the steep scaling in computation time of these methods. To mitigate this limitation, we present a combination of the FDE approach with pair natural orbitals (PNOs) in the TURBOMOLE software package. It combines the uncoupled FDE (FDEu) approach for excitation energy calculations with efficient implementations of second-order correlation methods in the ricc2 and pnoccsd programs. The performance of this combination is tested for tetraazaperopyrene (TAPP) molecular crystals. It is shown that the PNO truncation error on environment-induced shifts is significantly smaller than the shifts themselves and, thus, that the local approximations of PNO-based wavefunction methods can without the loss of relevant digits be combined with the FDE method. Computational wall times are presented for two TAPP systems. The scaling of the wall times is compared to conventional supermolecular calculations and demonstrates large computational savings for the combination of FDE- and PNO-based methods. Additionally, the behavior of excitation energies with the system size is investigated. It is found that the excitation energies converge quickly with the size of the embedding environment for the TAPPs investigated in the current study.

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.

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.

COSMO-RI-ADC(2) excitation energies and excited state gradients

Evaluating vertical excitation energies and excited state analytic gradients in solution at COSMO-ADC(2).

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.

Polarization Effects in Aqueous and Nonaqueous Solutions

Polarization effects in aqueous and nonaqueous solutions were analyzed for nine neutral and three charged organic solutes by the SM8 universal implicit solvation model and class IV partial atomic charges based on Charge Model 4M (CM4M) with the M06-2X density functional. The CM4M partial atomic charges in neutral and ionic solutes and in the corresponding clustered solutes (supersolutes), which included one solute molecule and one or two solvent molecules, were modeled in three solvents (benzene, methylene chloride, and water) and compared to those in the gas phase. The use of the supersolute approach (microsolvation) allows one to account for charge transfer from the solute to the solvent, and we find charge transfers as large as 0.06 atomic units for neutral solutes (pyridine in water) and 0.32 atomic units for ions (methoxide anion in water). Relaxation of the electronic structure of the solute in the presence of solvent increases the polarization free energy of the neutral solutes studied here, on average, by 16% in benzene, 30% in methylene chloride, and 43% in water. The increase for the ions in water averaged 43%.

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.

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.

Statistical mechanically averaged molecular properties of liquid water calculated using the combined coupled cluster/molecular dynamics method

Liquid water is investigated theoretically using combined molecular dynamics (MD) simulations and accurate electronic structure methods. The statistical mechanically averaged molecular properties of liquid water are calculated using the combined coupled cluster/molecular mechanics (CC/MM) method for a large number of configurations generated from MD simulations. The method includes electron correlation effects at the coupled cluster singles and doubles level and the use of a large correlation consistent basis set. A polarizable force field has been used for the molecular dynamics part in both the CC/MM method and in the MD simulation. We describe how the methodology can be optimized with respect to computational costs while maintaining the quality of the results. Using the optimized method we study the energetic properties including the heat of vaporization and electronic excitation energies as well as electric dipole and quadrupole moments, the frequency dependent electric (dipole) polarizability, and electric-field-induced second harmonic generation first and second hyperpolarizabilities. Comparisons with experiments are performed where reliable data are available. Furthermore, we discuss the important issue on how to compare the calculated microscopic nonlocal properties to the experimental macroscopic measurements.

Degenerate four-wave mixing in solution by cubic response theory and the polarizable continuum model

We have derived and implemented the solvent contribution to the cubic response function for the polarizable continuum model in its integral equation formulation. The present formulation is valid both at the Hartree-Fock and at the Kohn-Sham density functional levels of theory, because both bear the same formal description of the solvent contribution through an additional additive term in the Hamiltonian operator. This new implementation is used to compute the solvent effect for the degenerate four-wave mixing process on three different classes of heteroaromatic chromophores: (I) triazine, benzoxazole, benzimidazole, and benzothiazole; (II) three benzothiazole derivatives; and (III) three tri-s-triazine derivatives. The results are first discussed in terms of the solvent effects on the calculated property and then compared to experimental data for the substrates of class (I) and (II).