Unraveling Water Solvation Effects with Quantum Mechanics/Molecular Mechanics Semiclassical Vibrational Spectroscopy: The Case of Thymidine.

We introduce a quantum mechanics/molecular mechanics semiclassical method for studying the solvation process of molecules in water at the nuclear quantum mechanical level with atomistic detail. We employ it in vibrational spectroscopy calculations because this is a tool that is very sensitive to the molecular environment. Specifically, we look at the vibrational spectroscopy of thymidine in liquid water. We find that the C═O frequency red shift and the C═C frequency blue shift, experienced by thymidyne upon solvation, are mainly due to reciprocal polarization effects, that the molecule and the water solvent exert on each other, and nuclear zero-point energy effects. In general, this work provides an accurate and practical tool to study quantum vibrational spectroscopy in solution and condensed phase, incorporating high-level and computationally affordable descriptions of both electronic and nuclear problems.

Breaking the Rules: On the Relative Stability of Some Methylencyclopropane and Methylcyclopropene Derivatives.

The structure of the spirocyclic product obtained by reacting catechol with 1,1-dichloro-2-(chloromethyl)cyclopropane is shown by NMR and X-ray analysis to be that of a 2-methylcyclopropene (MeCP), instead of the previously reported 2-methylenecyclopropane (MCP) one. The study of the equilibration between the two isomeric forms by experimental and computational means (including both Density Functional Theory - DFT - and Coupled Cluster with single, double, and perturbative triple excitations - CCSD(T) - calculations) revealed that, at variance with most of the alkylidenecyclopropane/alkylcyclopropene systems described to date, for the compounds of the present study the MeCP derivative is more stable by≈ 2.5-3.0 Kcal mol-1 than the MCP one. The extension of the DFT and CCSD(T) study to other spiro-MCP/MeCP pairs suggests that the origin of the unexpected shift of the equilibrium position can be tracked back to a combination of electronic and ring-strain effects. These findings lead to re-think a long-standing, and substantially undisputed belief in the area of unsaturated cyclopropane derivatives.

Changing aromatic properties through stacking: the face-to-face dimer of Ni(II) bis(pentafluorophenyl)norcorrole.

Nuclear magnetic resonance (NMR) shielding constants have been calculated for Ni(II) bis(pentafluorophenyl)norcorrole and its face-to-face stacked dimer at the Hartree-Fock (HF), second-order Møller-Plesset perturbation theory (MP2), complete-active-space self-consistent-field (CASSCF) levels as well as at density functional theory (DFT) levels using several functionals. The calculated 1H NMR shielding constants agree rather well with the experimental ones. The shielding constants of N and Ni calculated at DFT, HF, and MP2 levels differ from those obtained in the CASSCF calculations due to near-degeneracy effects at the Ni atom. The calculated magnetically induced current densities show that the monomer is antiaromatic, sustaining a strong global paratropic ring current, and the dimer is aromatic, sustaining a strong diatropic ring current. Qualitatively the same current density is obtained at the employed levels of theory. The most accurate ring-current strengths are probably obtained at the MP2 level. The aromatic dimer has a short intermolecular distance of less than 3 Å. The intermolecular interaction changes the nature of the frontier orbitals leading to a formal double bond between the norcorrole macrocycles.

Geometric Optimization of Restricted-Open and Complete Active Space Self-Consistent Field Wave Functions.

We explore Riemannian optimization methods for Restricted-Open-shell Hartree-Fock (ROHF) and Complete Active Space Self-Consistent Field (CASSCF) methods. After showing that ROHF and CASSCF can be reformulated as optimization problems on so-called "flag manifolds", we review Riemannian optimization basics and their application to these specific problems. We compare these methods to traditional ones and find robust convergence properties without fine-tuning of numerical parameters. Our study suggests that Riemannian optimization is a valuable addition to orbital optimization for ROHF and CASSCF, warranting further investigation.

Cholesky Decomposition in Spin-Free Dirac-Coulomb Coupled-Cluster Calculations.

We present an implementation for the use of Cholesky decomposition (CD) of two-electron integrals within the spin-free Dirac-Coulomb (SFDC) scheme that enables to perform high-accuracy coupled-cluster (CC) calculations at costs almost comparable to those of their nonrelativistic counterparts. While for nonrelativistic CC calculations, atomic-orbital (AO)-based algorithms, due to their significantly reduced disk-space requirements, are the key to efficient large-scale computations, such algorithms are less advantageous in the SFDC case due to their increased computational cost in that case. Here, molecular-orbital (MO)-based algorithms exploiting the CD of the two-electron integrals allow us to reduce disk-space requirements and lead to computational cost in the CC step that is more or less the same as in the nonrelativistic case. The only remaining overhead in a CD-SFDC-CC calculation is due to the need to compute additional two-electron integrals, the somewhat higher cost of the Hartree-Fock calculation in the SFDC case, and additional cost in the transformation of the Cholesky vectors from the AO to the MO representation. However, these additional costs typically amount to less than 5-15% of the total wall time and are thus acceptable. We illustrate the efficiency of our CD scheme for SFDC-CC calculations on a series of illustrative calculations for the X(CO)4 molecules with X = Ni, Pd, Pt.

The OpenMMPol library for polarizable QM/MM calculations of properties and dynamics.

We present a new library designed to provide a simple and straightforward way to implement QM/AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) and other polarizable QM/MM (Molecular Mechanics) methods based on induced point dipoles. The library, herein referred to as OpenMMPol, is free and open-sourced and is engineered to address the increasing demand for accurate and efficient QM/MM simulations. OpenMMPol is specifically designed to allow polarizable QM/MM calculations of ground state energies and gradients and excitation properties. Key features of OpenMMPol include a modular architecture facilitating extensibility, parallel computing capabilities for enhanced performance on modern cluster architectures, a user-friendly interface for intuitive implementation, and a simple and flexible structure for providing input data. To show the capabilities offered by the library, we present an interface with PySCF to perform QM/AMOEBA molecular dynamics, geometry optimization, and excited-state calculation based on (time-dependent) density functional theory.

Assessing Implicit and Explicit Polarizable Solvation Models for Nuclear-Electronic Orbital Systems: Quantum Proton Polarization and Solvation Energetics.

Accurate simulations of many chemical processes require the inclusion of both nuclear quantum effects and a solvent environment. The nuclear-electronic orbital (NEO) approach, which treats electrons and select nuclei quantum mechanically on the same level, combined with a polarizable continuum model (PCM) for the solvent environment, addresses this challenge in a computationally practical manner. In this work, the NEO-PCM approach is extended beyond the IEF-PCM (integral equation formalism PCM) and C-PCM (conductor PCM) approaches to the SS(V)PE (surface and simulation of volume polarization for electrostatics) and ddCOSMO (domain decomposed conductor-like screening model) approaches. IEF-PCM, SS(V)PE, C-PCM, and ddCOSMO all exhibit similar solvation energies as well as comparable nuclear polarization within the NEO framework. The calculations show that the nuclear density does not leak out of the molecular cavity because it is much more localized than the electronic density. Finally, the polarization of quantized protons is analyzed in both continuum solvent and explicit solvent environments described by the polarizable MB-pol model, illustrating the impact of specific hydrogen-bonding interactions captured only by explicit solvation. These calculations highlight the relationship among solvation formalism, nuclear polarization, and energetics.

A novel coupled-cluster singles and doubles implementation that combines the exploitation of point-group symmetry and Cholesky decomposition of the two-electron integrals.

A novel implementation of the coupled-cluster singles and doubles (CCSD) approach is presented that is specifically tailored for the treatment of large symmetric systems. It fully exploits Abelian point-group symmetry and the use of the Cholesky decomposition of the two-electron repulsion integrals. In accordance with modern CCSD algorithms, we propose two alternative strategies for the computation of the so-called particle-particle ladder term. The code is driven toward the optimal choice depending on the available hardware resources. As a large-scale application, we computed the frozen-core correlation energy of buckminsterfullerene (C60) with a polarized valence triple-zeta basis set (240 correlated electrons in 1740 orbitals).

Electronic Circular Dichroism Imaging (ECDi) Casts a New Light on the Origin of Solid-State Chiroptical Properties.

Solid-state ECD (ss-ECD) spectra of a model microcrystalline solid, finasteride, dispersed into a KCl pellet were recorded by using the synchrotron radiation source at the Diamond B23 beamline. Scanning a surface of 36 mm2 with a step of 0.5 mm, we measured a set of ECD imaging (ECDi) spectra very different from each other and from the ss-ECD recorded with a bench-top instrument (1 cm2 area). This is due to the anisotropic part of the ECD (ACD), which averages to zero in solution or on a large number of randomly oriented crystallites, but can otherwise be extremely large. Two-way singular value decomposition (SVD) analysis, through experimental and simulated TDDFT spectra, disclosed that the measured and theoretical principal components are in line with each other. This finding demonstrates that the observed isotropic ss-ECD spectrum is governed by the anisotropy of locally oriented crystals. It also introduces a new quality for ss-ECD measurements and opens a new future for probing and mapping chiral materials in the solid state such as active pharmaceutical ingredients (APIs).

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.

A Unique and Stable Polyproline I Helix Sorted out from Conformational Equilibrium by Solvent Polarity.

Polyproline I helical structures are often considered as the hidden face of their most famous geminal sibling, Polyproline II, as PPI is generally spotted only within a conformational equilibrium. We designed and synthesized a stable Polyproline I structure exploiting the striking tendency of (S)-indoline-2-carboxylic acid to drive the peptide bond conformation toward the cis amide isomer, when dissolved in polar solvents. The cooperative effect of only four amino acidic units is sufficient to form a preferential structure in solution. We shed light on this rare secondary structure with a thorough analysis of the spectroscopic and chiroptical properties of the tetramer, supported by X-ray crystallography and computational studies.

Probing aqueous ions with non-local Auger relaxation.

Non-local analogues of Auger decay are increasingly recognized as important relaxation processes in the condensed phase. Here, we explore non-local autoionization, specifically Intermolecular Coulombic Decay (ICD), of a series of aqueous-phase isoelectronic cations following 1s core-level ionization. In particular, we focus on Na+, Mg2+, and Al3+ ions. We unambiguously identify the ICD contribution to the K-edge Auger spectrum. The different strength of the ion-water interactions is manifested by varying intensities of the respective signals: the ICD signal intensity is greatest for the Al3+ case, weaker for Mg2+, and absent for weakly-solvent-bound Na+. With the assistance of ab initio calculations and molecular dynamics simulations, we provide a microscopic understanding of the non-local decay processes. We assign the ICD signals to decay processes ending in two-hole states, delocalized between the central ion and neighbouring water. Importantly, these processes are shown to be highly selective with respect to the promoted water solvent ionization channels. Furthermore, using a core-hole-clock analysis, the associated ICD timescales are estimated to be around 76 fs for Mg2+ and 34 fs for Al3+. Building on these results, we argue that Auger and ICD spectroscopy represents a unique tool for the exploration of intra- and inter-molecular structure in the liquid phase, simultaneously providing both structural and electronic information.

Trajectory Surface Hopping for a Polarizable Embedding QM/MM Formulation.

We present the implementation of trajectory surface-hopping nonadiabatic dynamics for a polarizable embedding QM/MM formulation. Time-dependent density functional theory was used at the quantum mechanical level of theory, whereas the molecular mechanics description involved the polarizable AMOEBA force field. This implementation has been obtained by integrating the surface-hopping program Newton-X NS with an interface between the Gaussian 16 and the Tinker suites of codes to calculate QM/AMOEBA energies and forces. The implementation has been tested on a photoinduced electron-driven proton-transfer reaction involving pyrimidine and a hydrogen-bonded water surrounded by a small cluster of water molecules and within a large water droplet.

Computation of NMR shieldings at the CASSCF level using gauge-including atomic orbitals and Cholesky decomposition.

We present an implementation of coupled-perturbed complete active space self-consistent field (CP-CASSCF) theory for the computation of nuclear magnetic resonance chemical shifts using gauge-including atomic orbitals and Cholesky decomposed two-electron integrals. The CP-CASSCF equations are solved using a direct algorithm where the magnetic Hessian matrix-vector product is expressed in terms of one-index transformed quantities. Numerical tests on systems with up to about 1300 basis functions provide information regarding both the computational efficiency and limitations of our implementation.

The He-H3 + complex. I. Vibration-rotation-tunneling states and transition probabilities.

With a He-H3 + interaction potential obtained from advanced electronic structure calculations, we computed the vibration-rotation-tunneling (VRT) states of this complex for total angular momenta J from 0 to 9, both for the vibrational ground state and for the twofold degenerate v2 = 1 excited state of H3 +. The potential has three equivalent global minima with depth De = 455.3 cm-1 for He in the plane of H3 +, three equatorial saddle points that separate these minima with barriers of 159.5 cm-1, and two axial saddle points with energies of 243.1 cm-1 above the minima. The dissociation energies calculated for the complexes of He with ortho-H3 + (oH3 +) and para-H3 + (pH3 +) are D0 = 234.5 and 236.3 cm-1, respectively. Wave function plots of the VRT states show that they may be characterized as weakly hindered internal rotor states, delocalized over the three minima in the potential and with considerable amplitude at the barriers. Most of them are dominated by the jk = 10 and 11 rotational ground states of oH3 + and pH3 +, with the intermolecular stretching mode excited up to v = 4 inclusive. However, we also found excited internal rotor states: 33 in He-oH3 +, and 22 and 21 in He-pH3 +. The VRT levels and wave functions were used to calculate the frequencies and line strengths of all allowed v2 = 0 → 1 rovibrational transitions in the complex. Theoretical spectra generated with these results are compared with the experimental spectra in Paper II [Salomon et al., J. Chem. Phys. 156, 144308 (2022)] and are extremely helpful in assigning these spectra. This comparison shows that the theoretical energy levels and spectra agree very well with the measured ones, which confirms the high accuracy of our ab initio He-H3 + interaction potential and of the ensuing calculations of the VRT states.

The He-H3 + complex. II. Infrared predissociation spectrum and energy term diagram.

The rotationally resolved infrared (IR) spectrum of the He-H3 + complex has been measured in a cryogenic ion trap experiment at a nominal temperature of 4 K. Predissociation of the stored complex has been invoked by excitation of the degenerate ν2 mode of the H3 + sub-unit using a pulsed optical parametric oscillator system. An assignment of the experimental spectrum became possible through one-to-one correlations with bands of the spectrum theoretically predicted in Paper I [Harding et al., J. Chem. Phys. 156, 144307 (2022)]. 19 bands have been assigned and analyzed, and the energy term diagram of the lower states of this floppy molecular complex has been derived from combination differences (CDs) in the experimental spectrum. Ground state combination differences (GSCDs) reveal a large part of the energy term diagram for the He-H3 + complex in its vibrational ground state, v = 0. Experimental and theoretical term energies agree within experimental accuracy for the rotational fine structure associated with the total angular momentum quantum number J and the parity e/f as well as for the coarse spacing of the lowest K states of the complex. This favorable comparison shows that the potential energy surface (PES) calculated in Paper I is accurate. The barriers between the three equivalent global minima in this PES are relatively low and the He-H3 + complex is extremely floppy, with nearly unhindered internal rotation of the H3 + sub-unit. The resulting Coriolis interactions couple the internal and end-over-end rotation of the complex and contribute significantly to the energy terms. They are observed both in experiment and theory and are, e.g., the origin of different rotational constants for states of e and f parity. Also in this respect, experiment and theory agree very well. Despite the assignment and analysis of many bands of the extremely rich IR spectrum of He-H3 +, higher levels of excitation, including the complex stretching mode, need further attention.

A Proline Mimetic for the Design of New Stable Secondary Structures: Solvent-Dependent Amide Bond Isomerization of (S)-Indoline-2-carboxylic Acid Derivatives.

A thorough experimental and computational study on the conformational properties of (S)-indoline-2-carboxylic acid derivatives has been conducted. Methyl (S)-1-acetylindoline-2-carboxylate, both a mimetic of proline and phenylalanine, shows a remarkable tendency toward the cis amide isomer when dissolved in polar solvents. This behavior is opposite to the general preference of proline for the trans isomer, making indoline-2-carboxylic acid a good candidate for the design of different secondary structures and new materials.

NMR chemical shift computations at second-order Møller-Plesset perturbation theory using gauge-including atomic orbitals and Cholesky-decomposed two-electron integrals.

We report on a formulation and implementation of a scheme to compute nuclear magnetic resonance (NMR) shieldings at second-order Møller-Plesset (MP2) perturbation theory using gauge-including atomic orbitals (GIAOs) to ensure gauge-origin independence and Cholesky decomposition (CD) to handle unperturbed and perturbed two-electron integrals. We investigate the accuracy of the CD for the derivatives of the two-electron integrals with respect to an external magnetic field and for the computed NMR shieldings, before we illustrate the applicability of our CD-based GIAO-MP2 scheme in calculations involving up to about 100 atoms and more than 1000 basis functions.

An enhanced sampling QM/AMOEBA approach: The case of the excited state intramolecular proton transfer in solvated 3-hydroxyflavone.

We present an extension of the polarizable quantum mechanical (QM)/AMOEBA approach to enhanced sampling techniques. This is achieved by connecting the enhanced sampling PLUMED library to the machinery based on the interface of Gaussian and Tinker to perform QM/AMOEBA molecular dynamics. As an application, we study the excited state intramolecular proton transfer of 3-hydroxyflavone in two solvents: methanol and methylcyclohexane. By using a combination of molecular dynamics and umbrella sampling, we find an ultrafast component of the transfer, which is common to the two solvents, and a much slower component, which is active in the protic solvent only. The mechanisms of the two components are explained in terms of intramolecular vibrational redistribution and intermolecular hydrogen-bonding, respectively. Ground and excited state free energies along an effective reaction coordinate are finally obtained allowing for a detailed analysis of the solvent mediated mechanism.

How accurate are EOM-CC4 vertical excitation energies?

We report the first investigation of the performance of EOM-CC4-an approximate equation-of-motion coupled-cluster model, which includes iterative quadruple excitations-for vertical excitation energies in molecular systems. By considering a set of 28 excited states in 10 small molecules for which we have computed CC with singles, doubles, triples, quadruples, and pentuples and full configuration interaction reference energies, we show that, in the case of excited states with a dominant contribution from the single excitations, CC4 yields excitation energies with sub-kJ mol-1 accuracy (i.e., error below 0.01 eV), in very close agreement with its more expensive CC with singles, doubles, triples, and quadruples parent. Therefore, if one aims at high accuracy, CC4 stands as a highly competitive approximate method to model molecular excited states, with a significant improvement over both CC3 and CC with singles, doubles, and triples. Our results also evidence that, although the same qualitative conclusions hold, one cannot reach the same level of accuracy for transitions with a dominant contribution from the double excitations.