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

Delving into the catalytic mechanism of molybdenum cofactors: a novel coupled cluster study

In this work, we use modern electronic structure methods to model the catalytic mechanism of different variants of the molybdenum cofactor (Moco). We investigate the dependence of various Moco model systems on structural relaxation and the importance of environmental effects for five critical points along the reaction coordinate with the DMSO and NO3- substrates. Furthermore, we scrutinize the performance of various coupled-cluster approaches for modeling the relative energies along the investigated reaction paths, focusing on several pair coupled cluster doubles (pCCD) flavors and conventional coupled cluster approximations. Moreover, we elucidate the Mo-O bond formation using orbital-based quantum information measures, which highlight the flow of σM-O bond formation and σN/S-O bond breaking. Our study shows that pCCD-based models are a viable alternative to conventional methods and offer us unique insights into the bonding situation along a reaction coordinate. Finally, this work highlights the importance of environmental effects or changes in the core and, consequently, in the model itself to elucidate the change in activity of different Moco variants.

Recent developments and applications of reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED): A hybrid model of quantum chemistry and integral equation theory of molecular liquids

The significance of solvent effects in electronic structure calculations has long been noted, and various methods have been developed to consider this effect. The reference interaction site model self-consistent field with constrained spatial electron density (RISM-SCF-cSED) is a hybrid model that combines the integral equation theory of molecular liquids with quantum chemistry. This method can consider the statistically convergent solvent distribution at a significantly lower cost than molecular dynamics simulations. Because the RISM theory explicitly considers the solvent structure, it performs well for systems where hydrogen bonds are formed between the solute and solvent molecules, which is a challenge for continuum solvent models. Taking advantage of being founded on the variational principle, theoretical developments have been made in calculating various properties and incorporating electron correlation effects. In this review, we organize the theoretical aspects of RISM-SCF-cSED and its distinctions from other hybrid methods involving integral equation theories. Furthermore, we carefully present its progress in terms of theoretical developments and recent applications.

Quantum Simulation of Molecules in Solution

Quantum chemical calculations on quantum computers have been focused mostly on simulating molecules in the gas phase. Molecules in liquid solution are, however, most relevant for chemistry. Continuum solvation models represent a good compromise between computational affordability and accuracy in describing solvation effects within a quantum chemical description of solute molecules. In this work, we extend the variational quantum eigensolver to simulate solvated systems using the polarizable continuum model. To account for the state dependent solute-solvent interaction we generalize the variational quantum eigensolver algorithm to treat non-linear molecular Hamiltonians. We show that including solvation effects does not impact the algorithmic efficiency. Numerical results of noiseless simulations for molecular systems with up to 12 spin-orbitals (qubits) are presented. Furthermore, calculations performed on a simulated noisy quantum hardware (IBM Q, Mumbai) yield computed solvation free energies in fair agreement with the classical calculations.

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.

Ionization Energies and Redox Potentials of Hydrated Transition Metal Ions: Evaluation of Domain-Based Local Pair Natural Orbital Coupled Cluster Approaches

Hydrated transition metal ions are prototypical systems that can be used to model properties of transition metals in complex chemical environments. These seemingly simple systems present challenges for computational chemistry and are thus crucial in evaluations of quantum chemical methods for spin-state and redox energetics. In this work, we explore the applicability of the domain-based pair natural orbital implementation of coupled cluster (DLPNO-CC) theory to the calculation of ionization energies and redox potentials for hydrated ions of all first transition row (3d) metals in the 2+/3+ oxidation states, in connection with various solvation approaches. In terms of model definition, we investigate the construction of a minimally explicitly hydrated quantum cluster with a first and second hydration layer. We report on the convergence with respect to the coupled cluster expansion and the PNO space, as well as on the role of perturbative triple excitations. A recent implementation of the conductor-like polarizable continuum model (CPCM) for the DLPNO-CC approach is employed to determine self-consistent redox potentials at the coupled cluster level. Our results establish conditions for the convergence of DLPNO-CCSD(T) energetics and stress the absolute necessity to explicitly consider the second solvation sphere even when CPCM is used. The achievable accuracy for redox potentials of a practical DLPNO-based approach is, on average, 0.13 V. Furthermore, multilayer approaches that combine a higher-level DLPNO-CCSD(T) description of the first solvation sphere with a lower-level description of the second solvation layer are investigated. The present work establishes optimal and transferable methodological choices for employing DLPNO-based coupled cluster theory, the associated CPCM implementation, and cost-efficient multilayer derivatives of the approach for open-shell transition metal systems in complex environments.

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.

Unveiling the complex pattern of intermolecular interactions responsible for the stability of the DNA duplex

Herein, we provide new insights into the intermolecular interactions responsible for the intrinsic stability of the duplex structure of a large portion of human B-DNA by using advanced quantum mechanical methods. Our results indicate that (i) the effect of non-neighboring bases on the inter-strand interaction is negligibly small, (ii) London dispersion effects are essential for the stability of the duplex structure, (iii) the largest contribution to the stability of the duplex structure is the Watson-Crick base pairing - consistent with previous computational investigations, (iv) the effect of stacking between adjacent bases is relatively small but still essential for the duplex structure stability and (v) there are no cooperativity effects between intra-strand stacking and inter-strand base pairing interactions. These results are consistent with atomic force microscope measurements and provide the first theoretical validation of nearest neighbor approaches for predicting thermodynamic data of arbitrary DNA sequences.

Multireference Perturbation Theory Combined with PCM and RISM Solvation Models: A Benchmark Study for Chemical Energetics

The polarizable continuum model (PCM) has been one of the most widely used approaches to take into account the solvation effect in quantum chemical calculations. In this paper, we performed a series of benchmark calculations to assess the accuracy of the PCM scheme combined with the second-order complete-active-space perturbation theory (CASPT2) for molecular systems in polar solvents. For solute molecules with extensive conjugated π orbitals, exemplified by elongated conjugated arylcarbenes, we have incorporated the ab initio density matrix renormalization group algorithm into the PCM-CASPT2 method. In the previous work, we presented a combination of the DMRG-CASPT2 method with the reference interaction site model (RISM) theory for describing the solvation effect using the radial distribution function and compared its performance to the widely used density-functional approaches (PCM-TD-DFT). The work here allows us to further show a more thorough assessment of the RISM model compared to the PCM with an equal level of the wave function treatment, the (DMRG-)CASPT2 theory, toward a high-accuracy electronic structure calculations for solvated chemical systems. With the exception that the PCM models are not capable of properly describing the hydrogen bondings, accuracy of the PCM-CASPT2 model is in most cases quite comparable to the RISM counterpart.

Modeling solvation effects on absorption and fluorescence spectra of indole in aqueous solution

Modeling the optical spectra of molecules in solution presents a challenge, so it is important to understand which of the solvation effects (i.e., electrostatics, mutual polarization, and hydrogen bonding interactions between solute and solvent molecules) are crucial in reproducing the various features of the absorption and fluorescence spectra and to identify a sufficient theoretical model that accurately captures these effects with minimal computational cost. In this study, we use various implicit and explicit solvation models, such as molecular dynamics coupled with non-polarizable and polarizable force fields, as well as Car-Parrinello molecular dynamics, to model the absorption and fluorescence spectra of indole in aqueous solution. The excited states are computed using the equation of motion coupled cluster with single and double excitations combined with the effective fragment potential to represent water molecules, which we found to be a computationally efficient approach for modeling large solute-solvent clusters at a high level of quantum theory. We find that modeling mutual polarization, compared to other solvation effects, is a dominating factor for accurately reproducing the position of the peaks and spectral line shape of the absorption spectrum of indole in solution. We present an in-depth analysis of the influence that different solvation models have on the electronic excited states responsible for the features of the absorption spectra. Modeling fluorescence is more challenging since it is hard to reproduce even the correct emitting state, and force field parameters need to be re-evaluated.

Polarizable embedding QM/MM: the future gold standard for complex (bio)systems?

We provide a perspective of the induced dipole formulation of polarizable QM/MM, showing how efficient implementations will enable their application to the modeling of dynamics, spectroscopy, and reactivity in complex biosystems.

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.

Coupled Cluster Theory Combined with Reference Interaction Site Model Self-Consistent Field Explicitly Including Spatial Electron Density Distribution

Calculating the geometry and energy of a molecule in a solution is one of the most important tasks in chemistry. However, performing an accurate calculation in a solution is still a difficult task because the electronic structure and solute-solvent interactions are required to be accurately evaluated with an efficient computational cost. To overcome this difficulty, we proposed the coupled cluster with single and double excitations and perturbative triple excitations combined with the reference interaction site model (RISM) by employing our fitting approach. Our method correctly reproduced the relative stabilities of 1,2,3-triazole, isonicotinic acid, cytosine, and 6-chloro-2-pyridone in the aqueous phase, whereas the dielectric continuum model provided incorrect results for isonicotinic acid and 6-chloro-2-pyridone. Our method provided accurate results because the RISM captured the local solvation structure, such as hydrogen bonds.

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.

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.

General Time Dependent Approach to Vibronic Spectroscopy Including Franck-Condon, Herzberg-Teller, and Duschinsky Effects

An effective time-dependent (TD) approach to compute vibrationally resolved optical spectra from first principles is presented for the computation of one-photon electronic spectra induced by either electric or magnetic transition dipoles or by their mutual interaction, namely absorption, emission, and circular dichroism. Particular care has been devoted to generality, modularity, and numerical stability including all the contributions that play a role at the harmonic level of approximation, namely Franck-Condon, Herzberg-Teller, and Dushinsky (i.e., mode mixing) effects. The implementation shares the same general framework of our previous time-independent (TI) model, thus allowing an effective integration between both approaches with the consequent enhancement of their respective strengths (e.g., spectrum completeness and straightforward account of temperature effects for the TD route versus band resolution and assignment for the TI route) using a single set of starting data. Implementation of both models in the same general computer program allows comprehensive studies using several levels of electronic structure description together with effective account of environmental effects by atomistic and/or continuum models of different sophistication. A few medium-size molecules (furan, phenyl radical, anthracene, dimethyloxirane, coumarin 339) have been studied in order to fully validate the approach.

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.