Quantum cluster theory for the polarizable continuum model. I. The CCSD level with analytical first and second derivatives

Photoisomerization mechanism of iminoguanidinium receptors from spectroscopic methods and quantum chemical calculations

The hydrazone functional group, when coupled with a pyridyl substituent, offers a unique class of widely tunable photoswitches, whose E-to-Z photoisomerization equilibria can be controlled through intramolecular hydrogen bonding between the N-H hydrazone donor and the pyridyl acceptor. However, little is known about the photoisomerization mechanism in this class of compounds. To address this issue, we report a pyridine-appended iminoguanidinium photoswitch that is functionally related to acylhydrazones and provides insight into the photoisomerization processes between the E and Z configurations. The E-to-Z photoisomerization of the E-2-pyridyl-iminoguanidinium cation (2PyMIG) in DMSO, prepared as the bromide salt, was quantified by 1H NMR, and probed in real time with ultrafast laser spectroscopy. The photoisomerization process occurs on a picosecond timescale, resulting in low fluorescence yields. The multiconfigurational reaction path found with the growing string method features a small barrier (4.3 or 6.5 kcal mol-1) that the E isomer in the π-π* state must overcome to reach the minimum energy conical intersection (MECI) connecting the E and Z isomers of 2PyMIG. While two possible pathways exist depending on the orientation of the pyridine ring, both exhibit the same qualitative features along the path and at their MECIs, involving simultaneous changes in the CCNN and CNNC dihedral angles. Furthermore, the ground state barrier for pyridine ring rotation is readily accessible, thus a low barrier pathway to the experimentally observed Z isomer exists for both MECIs leading to a transition from the E isomer to photoproduct. Combining multiconfigurational reaction path calculations using growing string method with time-resolved fluorescence spectroscopy provided crucial insights into the photoisomerization process of 2PyMIG, resulting in both the computational and experimental results pointing to rapid photoisomerization via a surface crossing between the singlet π-π* and the ground states.

Absorption Intensities of Organic Molecules from Electronic Structure Calculations versus Experiments: the Effect of Solvation, Method, Basis Set, and Transition Moment Gauge

Recently, we derived experimental oscillator strengths (OSs) from well-defined UV-visible absorption spectral peaks of 100 molecules in solution. Here, we focus on a subset of transitions with the highest reliability to further benchmark the OSs from several wave function methods and density functionals. We consider multiple basis sets, transition moment gauges (length, velocity, and mixed), and solvent corrections. Most transitions in the comparison set come from conjugated molecules and have π → π* character. We use an automated algorithm to assign computed transitions to experimental bands. OSs computed using the Tamm-Dancoff approximation (TDA), CIS, or EOM-CCSD exhibited a strong gauge dependence, which is diminished in linear response theories (TD-DFT, TD-HF, and to a smaller degree LR-CCSD). OSs calculated from TD-DFT with PCM solvent models are systematically larger than apparent OSs derived from experimental spectra. For example, fcomp from hybrid functionals and PCM have mean absolute errors that are ∼10% of n·fexp, where n is a solvent refractive index factor that arises from the energy flux of the radiation field in a dielectric (solvent). Theoretical cavity field corrections considering spherical cavities do not improve the agreement between computed and experimental data. Corrections that account for the molecular shape and the direction of transition dipole moments, or that explicitly account for the effect of solvent molecules on the local field, should be more appropriate.

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.

Computational studies on a selection of phosphite esters as antioxidants for polymeric materials

CONTEXT

Phosphite esters, a class of organo-phosphorus compounds, are widely used as non-discolouring antioxidants in many polymeric products. Apart from normal radical scavenging, they prevent the splitting of hydroperoxides (ROOH), one of the initial products of autoxidation, from forming extremely reactive free radicals such as alkoxy (RO.) and hydroxy (.OH) radicals. The inherent molecular properties of antioxidants and the chemistry of their action are essential for researchers working in this field of science. Four organo-phosphorous compounds well-known for their antioxidant activity are selected here for theoretical analysis: Tri(m-methylphenyl) phosphite (m-TMPP), Tri(4-methyl-2,6-di-tert-butylphenyl) phosphite (TMdtBPP), Tri(allylphenyl) phosphite (TAPP) and Tri(mercaptobenzothiazoyl) thiophosphate (TMBTTP). The antioxidant activity exhibited by these compounds is theoretically verified, and the results are consistent with the available experimental data. Such theoretical predictions offer advantages in scientific research, particularly when researchers need to select certain molecules as antioxidants for experiments from a pool of molecular systems.

METHODS

The chemical computations presented in this report are done in Gaussian 16 program package. The procedure of density functional theory (DFT) with the model chemistry B3LYP/6-31G(d,p) is used to generate computational data. Global reactivity indices, thermochemical data, Fukui functions, molecular electrostatic potential and NMR spectra are computed for the chosen molecular systems from their optimized geometries.

Consistent Analytical Second Derivatives of the Kohn-Sham DFT Energy in the Framework of the Conductor-Like Screening Model through Gaussian Charge Distributions

The use of implicit solvation models such as the conductor-like screening model (COSMO) in quantum chemical calculations is very common, as both a rough estimate of solvation effects as well as a general tool for stabilizing ionic molecular structures. In order to generate a smooth potential energy surface as well as consistent gradients, it is necessary to apply the Gaussian charge model (GCM) for the COSMO charges. This work introduces an efficient implementation for consistent analytical second derivatives of the electronic energy with COSMO-GCM in the framework of the Kohn-Sham density functional theory. This is used to investigate the infrared spectroscopy of amino acids in aqueous solution, where the impact of pH on the molecular structure and vibrational spectra is examined. Furthermore, the structure and stability of selected all-metal aromatic cluster ions are assessed.

Isolated and solvated chiroptical behavior in conformationally flexible butanamines

The nonresonant optical activity of two highly flexible aliphatic amines, (2R)-3-methyl-2-butanamine (R-MBA) and (2R)-(3,3)-dimethyl-2-butanamine (R-DMBA), has been probed under isolated and solvated conditions to examine the roles of conformational isomerism and to explore the influence of extrinsic perturbations. The optical rotatory dispersion (ORD) measured in six solvents presented uniformly negative rotatory powers over the 320-590 nm region, with the long-wavelength magnitude of chiroptical response growing nearly monotonically as the dielectric constant of the surroundings diminished. The intrinsic specific optical rotation,α λ T (in deg dm-1 [g/mL]-1 ), extracted for ambient vapor-phase samples of R-MBA [-11.031(98) and -2.29 (11)] and R-DMBA [-9.434 (72) and -1.350 (48)] at 355 and 633 nm were best reproduced by counterintuitive solvents of high polarity (yet low polarizability) like acetonitrile and methanol. Attempts to interpret observed spectral signatures quantitatively relied on the linear-response frameworks of density-functional theory (B3LYP, cam-B3LYP, and dispersion-corrected analogs) and coupled-cluster theory (CCSD), with variants of the polarizable continuum model (PCM) deployed to account for the effects of implicit solvation. Building on the identification of several low-lying equilibrium geometries (nine for R-MBA and three for R-DMBA), ensemble-averaged ORD profiles were calculated at T = 300 K by means of the independent-conformer ansatz, which enabled response properties predicted for the optimized structure of each isomer to be combined through Boltzmann-weighted population fractions derived from corresponding relative internal-energy or free-energy values, the latter of which stemmed from composite CBS-APNO and G4 analyses. Although reasonable accord between theory and experiment was realized for the isolated (vapor-phase) species, the solution-phase results were less satisfactory and tended to degrade progressively as the solvent polarity increased. These trends were attributed to solvent-mediated changes in structural parameters and energy metrics for the transition states that separate and putatively isolate the equilibrium conformations supported by the ground electronic potential-energy surface, with the resulting displacement of barrier locations and/or decrease of barrier heights compromising the underlying premise of the independent-conformer ansatz.

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.

Investigation of oxygen influence to the optical properties of tirapazamine

New data on 3-amino-1,2,4-benzotriazine 1,4-dioxide (tirapazamine) fluorescence has been obtained using the Perkin-Elmer Lambda 950 UV-Vis-NIR spectrophotometer experimental technique in combination with the extensive DFT-theory approach. Based on the results obtained, we revealed that the optical properties of the molecule under study remain significantly unchanged when the number of oxygen substitutions decreases from 2 to 0. Here we also present the results of the study of the influence of acetonitrile and ethyl acetate on the fluorescence of tirapazamine with the different number of oxygen atoms. Results of our investigation indicate the formation of anion in the case of 3-amino-1,2,4-benzotriazine 1,4-dioxide with two oxygen atoms and their transformation to tirapazamine with one oxygen atom.

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.

Optical Activity in Saturated Cyclic Amines: Untangling the Roles of Nitrogen-Inversion and Ring-Puckering Dynamics

The dispersive optical activity of two saturated cyclic amines, (R)-2-methylpyrrolidine (R-2MPY) and (S)-2-methylpiperidine (S-2MPI), has been interrogated under isolated and solvated conditions to elucidate the roles of large-amplitude motion associated with nitrogen-center inversion and ring-puckering dynamics. Experimental optical rotatory dispersion profiles were almost mirror images of one another and displayed parallel solvent dependencies. Quantum-chemical analyses built on density-functional and coupled-cluster methods revealed four low-lying conformers for each molecule, which are distinguished by axial/equatorial orientations of their amino hydrogens and methyl substituents. Chiroptical signatures predicted for these species were combined through an independent-conformer ansatz to simulate the ensemble-averaged response, with a polarizable continuum model (PCM) being used to treat implicit solute-solvent interactions. The intrinsic behavior observed for isolated (gaseous) R-2MPY and S-2MPI was reproduced best by merging coupled-cluster (CCSD) estimates of rotatory powers with thermal population fractions deduced from complete basis set (CBS-APNO) free-energy calculations. Although prior claims of sizable chiroptical contributions arising from helically twisted (chiral) heterocyclic frameworks could be discounted, less satisfactory agreement between experiment and theory was realized for solution phases. Response properties sustained modest isomer-dependent changes in the presence of PCM solvation, but the corresponding energy metrics showed systematic trends, whereby structures having larger electric-dipole moments were stabilized preferentially in media of high polarity. Despite the fact that R-2MPY conformations were predicted to undergo a progressive reordering of their relative energies across the six solvents of interest, S-2MPI was found to exhibit more pronounced solvent-induced perturbations at long wavelengths (viz., in regions far removed from electronic resonances). Experimental results are discussed in terms of the distinct ring-puckering mechanisms for R-2MPY and S-2MPI, which are expected to be dominated by hindered pseudorotation among envelope/twist motifs and semi-inversion between chairlike antipodes, respectively.

Multiscale Models for Light-Driven Processes

Multiscale models combining quantum mechanical and classical descriptions are a very popular strategy to simulate properties and processes of complex systems. Many alternative formulations have been developed, and they are now available in all of the most widely used quantum chemistry packages. Their application to the study of light-driven processes, however, is more recent, and some methodological and numerical problems have yet to be solved. This is especially the case for the polarizable formulation of these models, the recent advances in which we review here. Specifically, we identify and describe the most important specificities that the polarizable formulation introduces into both the simulation of excited-state dynamics and the modeling of excitation energy and electron transfer processes.

eT 1.0: An open source electronic structure program with emphasis on coupled cluster and multilevel methods

The e^T program is an open source electronic structure package with emphasis on coupled cluster and multilevel methods. It includes efficient spin adapted implementations of ground and excited singlet states, as well as equation of motion oscillator strengths, for CCS, CC2, CCSD, and CC3. Furthermore, e^T provides unique capabilities such as multilevel Hartree-Fock and multilevel CC2, real-time propagation for CCS and CCSD, and efficient CC3 oscillator strengths. With a coupled cluster code based on an efficient Cholesky decomposition algorithm for the electronic repulsion integrals, e^T has similar advantages as codes using density fitting, but with strict error control. Here, we present the main features of the program and demonstrate its performance through example calculations. Because of its availability, performance, and unique capabilities, we expect e^T to become a valuable resource to the electronic structure community.

Examining the degradation of environmentally-daunting per- and poly-fluoroalkyl substances from a fundamental chemical perspective

In this work, ground and excited-state properties were used as descriptors for probing mechanisms as well as to assess potential alternatives for tackling the elimination of per- and poly-fluoroalkyl substances (PFAS).

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.

Stabilization of cationic aluminum hydroxide clusters in high pH environments with a CaCl2/l-arginine matrix

We present a way of stabilizing cationic partially hydrolyzed aluminum clusters in a non-acidic environment, through Ca2+ and l-Arginine doping. The Keggin Al13-mer (ε-AlO4Al12(OH)24(H2O)127+) aluminum cluster can be stabilized with CaCl2 and l-arginine in a way to preserve the metal clusters. We use size-exclusion chromatography (SEC) and 27Al nuclear magnetic resonance (NMR) spectroscopy to demonstrate that positively-charged Keggin structures are preserved and that the conversion to Al(OH)3 materials is halted even at alkaline pH. The system serves to stabilize acidic Al clusters in alkaline or neutral conditions, while preserving their inherent cationic behavior.

Analytical calculation of pressure for confined atomic and molecular systems using the eXtreme-Pressure Polarizable Continuum Model

We show that the pressure acting on atoms and molecular systems within the compression cavity of the eXtreme-Pressure Polarizable Continuum method can be expressed in terms of the electron density of the systems and of the Pauli-repulsion confining potential. The analytical expression holds for spherical cavities as well as for cavities constructed from van der Waals spheres of the constituting atoms of the molecular systems. © 2018 Wiley Periodicals, Inc.

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.

Quantum, classical, and hybrid QM/MM calculations in solution: general implementation of the ddCOSMO linear scaling strategy

We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.

An efficient computational scheme for electronic excitation spectra of molecules in solution using the symmetry-adapted cluster-configuration interaction method: the accuracy of excitation energies and intuitive charge-transfer indices

Solvent effects on electronic excitation spectra are considerable in many situations; therefore, we propose an efficient and reliable computational scheme that is based on the symmetry-adapted cluster-configuration interaction (SAC-CI) method and the polarizable continuum model (PCM) for describing electronic excitations in solution. The new scheme combines the recently proposed first-order PCM SAC-CI method with the PTE (perturbation theory at the energy level) PCM SAC scheme. This is essentially equivalent to the usual SAC and SAC-CI computations with using the PCM Hartree-Fock orbital and integrals, except for the additional correction terms that represent solute-solvent interactions. The test calculations demonstrate that the present method is a very good approximation of the more costly iterative PCM SAC-CI method for excitation energies of closed-shell molecules in their equilibrium geometry. This method provides very accurate values of electric dipole moments but is insufficient for describing the charge-transfer (CT) indices in polar solvent. The present method accurately reproduces the absorption spectra and their solvatochromism of push-pull type 2,2'-bithiophene molecules. Significant solvent and substituent effects on these molecules are intuitively visualized using the CT indices. The present method is the simplest and theoretically consistent extension of SAC-CI method for including PCM environment, and therefore, it is useful for theoretical and computational spectroscopy.

The virial theorem for the Polarizable Continuum Model

The electronic virial theorem is extended to molecular systems within the framework of the Polarizable Continuum Model (PCM) to describe solvation effects. The theorem is given in the form of a relation involving the components of the energy (kinetic and potential) of a molecular solute and its electrostatic properties (potential and field) at the boundary of the cavity in the continuum medium. The virial theorem is also derived in the presence of the Pauli repulsion component of the solute-solvent interaction. Furthermore, it is shown that these forms of the PCM virial theorem may be related to the virial theorem of more simple systems as a molecule in the presence of fixed point charges, and as an atom in a spherical box with confining potential.

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).