Implementation of the CCSD-PCM linear response function for frequency dependent properties in solution: Application to polarizability and specific rotation

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.

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.

Combining multilevel Hartree–Fock and multilevel coupled cluster approaches with molecular mechanics: a study of electronic excitations in solutions

We present the coupling of different quantum-embedding approaches with a third molecular-mechanics layer, which can be either polarizable or non-polarizable.

Calculation of Linear and Non-linear Electric Response Properties of Systems in Aqueous Solution: A Polarizable Quantum/Classical Approach with Quantum Repulsion Effects

We present a computational study of polarizabilities and hyperpolarizabilities of organic molecules in aqueous solutions, focusing on solute-water interactions and the way they affect a molecule's linear and non-linear electric response properties. We employ a polarizable quantum mechanics/molecular mechanics (QM/MM) computational model that treats the solute at the QM level while the solvent is treated classically using a force field that includes polarizable charges and dipoles, which dynamically respond to the solute's quantum-mechanical electron density. Quantum confinement effects are also treated by means of a recently implemented method that endows solvent molecules with a parametric electron density, which exerts Pauli repulsion forces upon the solute. By applying the method to a set of aromatic molecules in solution we show that, for both polarizabilities and first hyperpolarizabilities, observed solution values are the result of a delicate balance between electrostatics, hydrogen-bonding, and non-electrostatic solute solvent interactions.

Multi-ionization of the Cl2 molecule in the near-infrared femtosecond laser field

The multi-electron ionization and subsequent dissociation of the Cl₂ molecule in a near-infrared femtosecond laser field was investigated via the dc-sliced ion imaging technique. The single charged molecular ions, Cl₂⁺, dissociate from two excited states, ²Π_u and ²Σ_g⁺, with the electrons ionized from the HOMO−1 and HOMO−2 orbital, respectively. For the multi-charged molecular ions, Cl₂ⁿ⁺ (n = 2–8), our results showed that the stretch of the inter-nuclear distance benefitted the ionization of the electrons to produce highly-charged molecular ions. In addition, compared with the traditional charge resonance enhanced ionization (CREI) model, the critical distance (R_c) for the Cl₂ molecule in our experiment was a short range that depended on the charge state rather than a single point.

The multi-electron ionization and subsequent dissociation of the Cl₂ molecule in a near-infrared femtosecond laser field was investigated via the dc-sliced ion imaging technique.

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.

Comparison of measured and predicted specific optical rotation in gas and solution phases: A test for the polarizable continuum model of solvation

A comparative theoretical and experimental study of dispersive optical activity is presented for a set of small, rigid organic molecules in gas and solution phases. Target species were chosen to facilitate wavelength-resolved measurements of specific rotation in rarefied vapors and in organic solvents having different polarities, while avoiding complications due to conformational flexibility. Calculations were performed with two density functionals (B3LYP and CAM-B3LYP) and with the coupled-cluster singles and doubles (CCSD) ansatz, and solvent effects were included through use of the polarizable continuum model (PCM). Across the various theoretical methods surveyed, CCSD with the modified velocity gauge provided the best overall performance for both isolated and solvated conditions. Zero-point vibrational corrections to equilibrium calculations of chiroptical response tended to improve agreement with gas-phase experiments, but the quality of performance realized for solutions varied markedly. Direct comparison of measured and predicted specific-rotation suggests that PCM, in general, is not able to reproduce attendant solvent shifts (neither between gas and solution phases nor among solvents) and fares better in estimating actual medium-dependent values of this property (although the error is rather system dependent). Thus, more elaborate solvation models seem necessary for a proper theoretical description of solvation in dispersive optical activity.

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.

Effective Fully Polarizable QM/MM Approach To Model Vibrational Circular Dichroism Spectra of Systems in Aqueous Solution

We propose a methodology, based on the combination of classical Molecular Dynamics (MD) simulations with a fully polarizable Quantum Mechanical (QM)/Molecular Mechanics (MM)/Polarizable Continuum Model (PCM) Hamiltonian, to calculate Vibrational Circular Dichroism (VCD) spectra of chiral systems in aqueous solution. Polarization effects are included in the MM force field by exploiting an approach based on Fluctuating Charges (FQ). By performing the MD, the description of the solvating environment is enriched by taking into account the dynamical aspects of the solute-solvent interactions. On the other hand, the QM/FQ/PCM calculation of the VCD spectrum ensures an accurate description of the electronic density of the solute and a proper account for the specific interactions in solution. The application of our approach to (R)-methyloxirane and (l)-alanine in aqueous solution gives calculated spectra in remarkable agreement with their experimental counterparts and a substantial improvement with respect to the same spectra calculated with the PCM.

Benchmarking the Bethe-Salpeter Formalism on a Standard Organic Molecular Set

We perform benchmark calculations of the Bethe-Salpeter vertical excitation energies for the set of 28 molecules constituting the well-known Thiel’s set, complemented by a series of small molecules representative of the dye chemistry field. We show that Bethe-Salpeter calculations based on a molecular orbital energy spectrum obtained with non-self-consistent G0W0 calculations starting from semilocal DFT functionals dramatically underestimate the transition energies. Starting from the popular PBE0 hybrid functional significantly improves the results even though this leads to an average -0.59 eV redshift compared to reference calculations for Thiel’s set. It is shown, however, that a simple self-consistent scheme at the GW level, with an update of the quasiparticle energies, not only leads to a much better agreement with reference values, but also significantly reduces the impact of the starting DFT functional. On average, the Bethe-Salpeter scheme based on self-consistent GW calculations comes close to the best time-dependent DFT calculations with the PBE0 functional with a 0.98 correlation coefficient and a 0.18 (0.25) eV mean absolute deviation compared to TD-PBE0 (theoretical best estimates) with a tendency to be red-shifted. We also observe that TD-DFT and the standard adiabatic Bethe-Salpeter implementation may differ significantly for states implying a large multiple excitation character.

Assessment of density functional methods for exciton binding energies and related optoelectronic properties

Mean absolute error (MAE) in exciton binding energy (E_b) from 9 DFT methods against benchmark CCSD and EOM-CCSD.

Unveiling solvents effect on excited-state polarizabilities with the corrected linear-response model

Aiming to assess the environmental effects on the dipole moments and polarizabilities of electronically excited-states, we have applied a combined Polarizable Continuum Model/Time-Dependent Density Functional Theory (PCM/TD-DFT) approach on six representative chromophores. For the first time, we compare polarizabilities obtained with gas phase, linear-response and corrected linear response continuum models and we also investigate the relative importance of direct (electronic) and indirect (geometric) environmental contributions for these properties. It is shown that the solvent effects on excited-state polarizabilities tend to be large and can often, but not always, be captured with the computationally efficient linear-response formalism.