Nuclear Velocity Perturbation Theory of Vibrational Circular Dichroism

Solid-state vibrational circular dichroism for pharmaceutical applications: Polymorphs and cocrystal of sofosbuvir

X-ray diffraction is a commonly used technique in the pharmaceutical industry for the determination of the atomic and molecular structure of crystals. However, it is costly, sometimes time-consuming, and it requires a considerable degree of expertise. Vibrational circular dichroism (VCD) spectroscopy resolves these limitations, while also exhibiting substantial sensitivity to subtle modifications in the conformation and molecular packaging in the solid state. This study showcases VCD's ability to differentiate between various crystal structures of the same molecule (polymorphs, cocrystals). We examined the most effective approach for producing high-quality spectra and unveiled the intricate link between structure and spectrum via quantum-chemical computations. We rigorously assessed, using alanine as a model compound, multiple experimental conditions on the resulting VCD spectra, with the aim of proposing an optimal and efficient procedure. The proposed approach, which yields reliable, reproducible, and artifact-free results with maximal signal-to-noise ratio, was then validated using a set comprising of three amino acids (serine, alanine, tyrosine), one hydroxy acid (tartaric acid), and a monosaccharide (ribose) to mimic active pharmaceutical components. Finally, the optimized approach was applied to distinguish three polymorphs of the antiviral drug sofosbuvir and its cocrystal with piperazine. Our results indicate that solid-state VCD is a prompt, cost-effective, and easy-to-use technique to identify crystal structures, demonstrating potential for application in pharmaceuticals. We also adapted the cluster and transfer approach to calculate the spectral properties of molecules in a periodic crystal environment. Our findings demonstrate that this approach reliably produces solid-state VCD spectra of model compounds. Although for large molecules with many atoms per unit cell, such as sofosbuvir, this approach has to be simplified and provides only a qualitative match, spectral calculations, and energy analysis helped us to decipher the observed differences in the experimental spectra of sofosbuvir.

A Phase-Space Electronic Hamiltonian For Vibrational Circular Dichroism

We show empirically that a phase-space non-Born-Oppenheimer electronic Hamiltonian approach to quantum chemistry (where the electronic Hamiltonian is parametrized by both nuclear position and momentum, ĤPS(R,P)) is both a practical and accurate means to recover vibrational circular dichroism spectra. We further hypothesize that such a phase-space approach may lead to very new dynamical physics beyond spectroscopic circular dichroism, with potential implications for understanding chiral induced spin selectivity (CISS), noting that classical phase-space approaches conserve the total nuclear plus electronic momentum, whereas classical Born-Oppenheimer approaches do not (they conserve only the nuclear momentum).

After 50 Years of Vibrational Circular Dichroism Spectroscopy: Challenges and Opportunities of Increasingly Accurate and Complex Experiments and Computations

VCD research continues to thrive, driven by ongoing experimental and theoretical advances. Modern studies deal with increasingly complex samples featuring weak intermolecular interactions and shallow potential energy surfaces. Likewise, the combination of VCD measurements with, for instance, cryo-spectroscopic techniques has significantly increased their sensitivity. The extent to which such modern measurements enhance the informative value of VCD depends significantly on the quality of the theoretical models, which must adequately account for anharmonicity, solvation and molecular dynamics. We herein discuss how experimental advancements engage in a stimulating interplay with recent theoretical developments, pursuing either the static or the dynamic computational route. Both paths have their own strengths and limitations, each addressing fundamentally different problems. We give an outlook on future challenges of VCD research, including the possibility to combine static and dynamic approaches to obtain a full picture of the sample.

Vibrational circular dichroism spectra of proline in water at different pH values

Recording VCD spectra of aqueous solution poses a particular challenge as water is a strong infrared absorber. Likewise, the computational analysis of VCD spectra by means of DFT-based spectral calculations requires the consideration of explicit solvent molecules, thus posing an even greater challenge. Several studies suggested that by modeling the solvent environment with a few water molecules in a micro-solvation approach would be sufficient to describe experimental spectra. For example, using proline at different pH values, we herein show that a change in the relative spatial orientation of a single water molecule in five-fold solvated structures strongly affects the computed VCD spectral signatures and that Boltzmann-weighted spectra do not correctly reproduce the experiment. We thus explored an approach based on molecular dynamics and subsequent DFT-calculations, in which we considered 30 water molecules (about 1.5 solvation shells). Once again, it was found that the Boltzmann-weighted spectra obtained on the basis of several hundred structures did not correctly reproduce experimental signatures, and a simple averaging scheme resulted in well-matching spectra with comparable bandwidths. The rationale behind the procedure was that sampling the configurational space of the solvent molecules is as equally important as the conformational sampling of the solute. For conformationally more flexible molecules, it is assumed that a much larger set of structures will have to be computed in order to properly sample the conformational space of both solute and solvent.

Chiral Spectroscopy of Bulk Systems with Propagated Localized Orbitals

We present approaches for the simulation of electronic circular dichroism, Raman, and Raman optical activity (ROA) spectra for isolated and periodic systems as well as subsystem analysis thereof. The method is based on the use of time-dependent maximally localized Wannier functions in the CP2K package and accounts for origin dependencies inherent to the Gaussian and plane wave with pseudopotentials approach as well as the origin dependence of the magnetic dipole and electric quadrupole operators. Tests on the H-bonded enantiomers of alanine by harmonic normal-mode analysis and on an aqueous solution of l-alanine by ab initio molecular dynamics obeying periodic boundary conditions (PBCs) are presented as total and subsystem-resolved spectra. To our knowledge, this is the first instance of an ROA spectrum derived from real-time propagation obeying PBCs and the first ROA simulation considering off-, pre-, and on-resonance effects within PBCs.

Vibrational Circular Dichroism Spectroscopy with a Classical Polarizable Force Field: Alanine in the Gas and Condensed Phases

Polarizable force fields are an essential component for the chemically accurate modeling of complex molecular systems with a significant degree of fluxionality, beyond harmonic or perturbative approximations. In this contribution we examine the performance of such an approach for the vibrational spectroscopy of the alanine amino acid, in the gas and condensed phases, from the Fourier transform of appropriate time correlation functions generated along molecular dynamics (MD) trajectories. While the infrared (IR) spectrum only requires the electric dipole moment, the vibrational circular dichroism (VCD) spectrum further requires knowledge of the magnetic dipole moment, for which we provide relevant expressions to be used with polarizable force fields. The AMOEBA force field was employed here to model alanine in the neutral and zwitterionic isolated forms, solvated by water or nitrogen, and as a crystal. Within this framework, comparison of the electric and magnetic dipole moments to those obtained with nuclear velocity perturbation theory based on density-functional theory for the same MD trajectories are found to agree well with one another. The statistical convergence of the IR and VCD spectra is examined and found to be more demanding in the latter case. Comparisons with experimental frequencies are also provided for the condensed phases.

Practical phase-space electronic Hamiltonians for ab initio dynamics

Modern electronic structure theory is built around the Born-Oppenheimer approximation and the construction of an electronic Hamiltonian Ĥel(X) that depends on the nuclear position X (and not the nuclear momentum P). In this article, using the well-known theory of electron translation (Γ') and rotational (Γ″) factors to couple electronic transitions to nuclear motion, we construct a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, ĤPS(X,P). While classical Born-Oppenheimer dynamics that run along the eigensurfaces of the operator Ĥel(X) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of ĤPS(X,P) can better capture both nuclear and electronic properties (including the elusive electronic momentum studied by Nafie). Moreover, only the latter (as opposed to the former) conserves the total linear and angular momentum in general.

Diagonalizing the Born-Oppenheimer Hamiltonian via Moyal perturbation theory, nonadiabatic corrections, and translational degrees of freedom

This article describes a method for calculating higher order or nonadiabatic corrections in Born-Oppenheimer theory and its interaction with the translational degrees of freedom. The method uses the Wigner-Weyl correspondence to map nuclear operators into functions on the classical phase space and the Moyal star product to represent operator multiplication on those functions. These are explained in the body of the paper. The result is a power series in κ2, where κ = (m/M)1/4 is the usual Born-Oppenheimer parameter. The lowest order term is the usual Born-Oppenheimer approximation, while higher order terms are nonadiabatic corrections. These are needed in calculations of electronic currents, momenta, and densities. The separation of nuclear and electronic degrees of freedom takes place in the context of the exact symmetries (for an isolated molecule) of translations and rotations, and these, especially translations, are explicitly incorporated into our discussion. This article presents an independent derivation of the Moyal expansion in molecular Born-Oppenheimer theory. We show how electronic currents and momenta can be calculated within the framework of Moyal perturbation theory; we derive the transformation laws of the electronic Hamiltonian, the electronic eigenstates, and the derivative couplings under translations; we discuss in detail the rectilinear motion of the molecular center of mass in the Born-Oppenheimer representation; and we show how the elimination of the translational components of the derivative couplings leads to a unitary transformation that has the effect of exactly separating the translational degrees of freedom.

Influence of microsolvation on vibrational circular dichroism spectra in dimethyl sulfoxide solvent: A Bottom-Up approach using Quantum cluster growth

Chiroptical spectroscopic measurements serve as routine methods to assign the absolute configuration of chiral compounds and interpret their conformational behavior in solution. One common challenge is the use of strongly hydrogen-bonding solvents, which can significantly bias the conformational ensemble and affect the vibrational circular dichroism (VCD) active bands in solution. One such solvent is dimethyl sulfoxide (DMSO)-an excellent solvent for stubborn compounds-that must be explicitly considered in VCD analysis. Explicit consideration of solvent remains a critical challenge in chiroptical spectroscopy due to the need to explore solute-solvent conformational space and the computational expense in modeling these clusters. Interested in the recent development of the Quantum Cluster Growth (QCG) program by the Grimme lab, we set out to model and interpret previously reported VCD spectra for several molecules using their efficient program. Our purposes are two-fold: (1) to investigate the applicability of the QCG program to the problem of reproducing VCD spectra in DMSO solvent and (2) to identify limitations in using this approach. We find that we can conveniently model and analyze the VCD spectra of investigated molecules in DMSO. However, the final set of conformers used for VCD calculations are functional dependent and different sets of conformers can provide satisfactory quantitative agreement between experimental and predicted VCD spectra. We hope that this study provides guidance for future chiroptical studies in the challenging DMSO solvent.

Modelling solute-solvent interactions in VCD spectra analysis with the micro-solvation approach

Vibrational circular dichroism (VCD) spectroscopy has become an important part of the (stereo-)chemists' toolbox as a reliable method for the determination of absolute configurations. Being the chiroptical version of infrared spectroscopy, it has also been recognized as being very sensitive to conformational changes and intermolecular interactions. This sensitivity originates from the fact that the VCD spectra of individual conformers are often more different than their IR spectra, so that changes in conformational distributions or band positions and intensities become more pronounced. What is an advantage for studies focussing on intermolecular interactions can, however, quickly turn into a major obstacle during AC determinations: solute-solvent interactions can have a strong influence on spectral signatures and they must be accurately treated when simulating VCD and IR spectra. In this perspective, we showcase selected examples which exhibit particularly pronounced solvent effects. It is demonstrated that it is typically sufficient to model solute-solvent interactions by placing single solvent molecules near hydrogen bonding sites of the solute and subsequently use the optimized structures for spectra simulations. This micro-solvation approach works reasonably well for medium-sized, not too conformationally flexible molecules. We thus also discuss its limitations and outline the next steps that method development needs to take in order to further improve the workflows for VCD spectra predictions.

Vibrational Circular Dichroism Spectroscopy of Chiral Molecular Crystals: Insights from Theory

Chirality is a curious phenomenon that appears in various forms. While the concept of molecular (RS-)chirality is ubiquitous in chemistry, there are also more intricate forms of structural chirality. One of them is the enantiomorphism of crystals, especially molecular crystals, that describes the lack of mirror symmetry in the unit cell. Its relation to molecular chirality is not obvious, but still an open question, which can be addressed with chiroptical tools. Vibrational circular dichroism (VCD) denotes chiral infrared (IR) spectroscopy that is susceptible to both, the molecular as well as the intermolecular space by means of vibrational transitions. When carried out in the solid state, VCD delivers a very rich set of non-local contributions that are determined by crystal packing and collective motion. Since its discovery in the 1970s, VCD has become the method of choice for the determination of absolute configurations, but its applicability reaches beyond towards the study of different crystal forms and polymorphism. This brief review summarises the theoretical concepts of crystal chirality and how computations of solid-state VCD can shed light into the intimate connection of chiral structure and vibrational optical activity.

Vibrational circular dichroism spectra of natural products by means of the nuclear velocity perturbation theory

We present the application of the recently implemented nuclear velocity perturbation theory, using the combined Gaussian and plane waves approach in CP2K, to the vibrational circular dichroism (VCD) spectra of a set of natural products. Even though the calculations were carried out for isolated molecules in the gas-phase limit, neglecting inter-molecular interactions and anharmonic effects, the match between simulated and experimental spectra is reasonable. We also study the influence of different density functionals on the conformational search and the resulting VCD spectra via group coupling matrices (GCMs). The GCM analysis reveals that the VCD signal can in some cases arise from moieties which are close to each other and in other cases from moieties far from each other. Differences in spectra obtained using different exchange-correlation density functionals can be attributed to interaction terms between different moieties in the molecules changing their sign.

How Crystal Symmetry Dictates Non-Local Vibrational Circular Dichroism in the Solid State

Solid-State Vibrational Circular Dichroism (VCD) can be used to determine the absolute structure of chiral crystals, but its interpretation remains a challenge in modern spectroscopy. In this work, we investigate the effect of a twofold screw axis on the solid-state VCD spectrum in a combined experimental and theoretical analysis of P2₁ crystals of (S)-(+)-1-indanol. Even though the space group is achiral, a single proper symmetry operation has an important impact on the VCD spectrum, which reflects the supramolecular chirality of the crystal. Distinguishing between contributions originating from molecular chirality and from chiral crystal packing, we find that while IR absorption hardly depends on the symmetry of the space group, the situation is different for VCD, where completely new non-local patterns emerge. Understanding the two underlying mechanisms, namely gauge transport and direct coupling, will help to use VCD to distinguish polymorphic forms.

Exact Factorization Adventures: A Promising Approach for Non-Bound States

Modeling the dynamics of non-bound states in molecules requires an accurate description of how electronic motion affects nuclear motion and vice-versa. The exact factorization (XF) approach offers a unique perspective, in that it provides potentials that act on the nuclear subsystem or electronic subsystem, which contain the effects of the coupling to the other subsystem in an exact way. We briefly review the various applications of the XF idea in different realms, and how features of these potentials aid in the interpretation of two different laser-driven dissociation mechanisms. We present a detailed study of the different ways the coupling terms in recently-developed XF-based mixed quantum-classical approximations are evaluated, where either truly coupled trajectories, or auxiliary trajectories that mimic the coupling are used, and discuss their effect in both a surface-hopping framework as well as the rigorously-derived coupled-trajectory mixed quantum-classical approach.

Implementation of Nuclear Velocity Perturbation and Magnetic Field Perturbation Theory in CP2K and Their Application to Vibrational Circular Dichroism

We present the implementation of nuclear velocity perturbation theory (NVPT), using a pioneering combination of atom-centered (velocity-dependent) Gaussian basis functions and plane waves in the CP2K package. The atomic polar tensors (APTs) and atomic axial tensors (AATs) are evaluated in the velocity representation using efficient density functional perturbation theory. The presence of nonlocal pseudopotentials, the representation of potentials on numerical integration grids, and effects arising from the basis functions being centered on the atoms have been considered in the implementation. The Magnetic Field Perturbation Theory (MFPT) using gauge-including atomic orbitals is implemented in the same code and compared to the NVPT. Our implementation is the first to compare both approaches (MFPT and NVPT) in the same code. The implementation has been verified via sum rules and by investigating the gauge origin dependence of the AATs for a set of small molecules, oxirane, and fluoro-oxirane. We also present vibrational circular dichroism spectra that are related to the APTs and AATs, applying both theories.

Competition between inter and intramolecular hydrogen bond evidenced by vibrational circular dichroism spectroscopy: The case of (1S,2R)-(-)-cis-1-amino-2-indanol

The infrared (IR) absorption and vibrational circular dichroism (VCD) spectra of an intramolecularly hydrogen-bonded chiral amino-alcohol, (1S,2R)-(-)-cis-1-amino-2-indanol, are studied in DMSO-d₆ . The spectra are simulated at the density functional theory (DFT) level within the frame of the cluster-in-the-liquid model. Both IR and VCD spectra show a clear signature of the formation of intermolecular hydrogen bonds at the detriment of the intramolecular OH … N interaction present in the isolated molecule. Two solvent molecules are necessary to reproduce the experimental spectra. Whereas the first DMSO molecule captures the main spectral modifications due to hydrogen bond formation between the solute and the solvent, the second DMSO molecule is necessary for a good description of the Boltzmann contribution of the different complexes, based on their Gibbs free energy.

The important role of non-covalent interactions for the vibrational circular dichroism of lactic acid in aqueous solution

We present a computational study of vibrational circular dichroism (VCD) in solutions of (S)-lactic acid, relying on ab initio molecular dynamics (AIMD) and full solvation with bulk water. We discuss the effect of the hydrogen bond network on the aggregation behaviour of the acid: while aggregates of the solute represent conditions encountered in a weakly interacting solvent, the presence of water drastically interferes with the clusters - more strongly than originally anticipated. For both scenarios we computed the VCD spectra by means of nuclear velocity perturbation theory (NVPT). The comparison with experimental data allows us to establish a VCD-structure relationship that includes the solvent network around the chiral solute. We suggest that fundamental modes with strong polarisation such as the carbonyl stretching vibration can borrow VCD from the chirally restructured solvent cage, which extends the common explanatory models of VCD generation in aqueous solution.

Computation of Solid-State Vibrational Circular Dichroism in the Periodic Gauge

We introduce a new theoretical formalism to compute solid-state vibrational circular dichroism (VCD) spectra from molecular dynamics simulations. Having solved the origin-dependence problem of the periodic magnetic gauge, we present IR and VCD spectra of (1S,2S)-trans-1,2-cyclohexanediol obtained from first-principles molecular dynamics calculations and nuclear velocity perturbation theory, along with the experimental results. Because the structure model imposes periodic boundary conditions, the common origin of the rotational strength has hitherto been ill-defined and was approximated by means of averaging multiple origins. The new formalism reconnects the periodic model with the finite physical system and restores gauge freedom. It nevertheless fully accounts for nonlocal spatial couplings from the gauge transport term. We show that even for small simulation cells the rich nature of solid-state VCD spectra found in experiments can be reproduced to a very satisfactory level.

Theory and algorithms for chiroptical properties and spectroscopies of aqueous systems

Chiroptical properties and spectroscopies are valuable tools to study chiral molecules and assign absolute configurations. The spectra that result from chiroptical measurements may be very rich and complex, and hide much of their information content. For this reason, the interplay between experiments and calculations is especially useful, provided that all relevant physico-chemical interactions that are present in the experimental sample are accurately modelled. The inherent difficulty associated to the calculation of chiral signals of systems in aqueous solutions requires the development of specific tools, able to account for the peculiarities of water-solute interactions, and especially its ability to form hydrogen bonds. In this perspective we discuss a multiscale approach, which we have developed and challenged to model the most used chiroptical techniques.

Vibrational optical activity for structural characterization of natural products

This review presents the recent progress towards elucidating the structures of chiral natural products and applications using vibrational optical activity (VOA) spectroscopy.

Assessing cluster models of solvation for the description of vibrational circular dichroism spectra: synergy between static and dynamic approaches

Solvation effects are essential for defining the shape of vibrational circular dichroism (VCD) spectra.

Chiral Molecular Structures of Substituted Indans: Ring Puckering, Rotatable Substituents, and Vibrational Circular Dichroism

The chiral molecular structures of four different substituted indans, namely, (S)-1-methylindan, (R)-1-methylindan-1-d, (R)-1-aminoindan, and (S)-1-indanol, were investigated using experimental vibrational absorption and vibrational circular dichroism spectra and corresponding spectra predicted using quantum chemical (QC) calculations. All of these molecules possess two ring puckering conformations, with ring puckering leading to the pseudoequatorial substituent being approximately four times more abundant over that leading to the pseudoaxial substituent. The amino group in 1-aminoindan has three conformations arising from the rotation of NH₂ group, for each ring puckering conformation, resulting in a total of six conformations. Whereas 1-indanol in the nonhydrogen-bonding solvent CCl₄ also has six conformations similar to those of 1-aminoindan, 1-indanol in the hydrogen-bonding solvent DMSO-d ₆ adopts numerous conformations, of which 30 conformers are considered to have at least ∼1% or more population. In DMSO solution, ring puckering leading to pseudoequatorial substituent accounts for 77% population and 23% for pseudoaxial substituent. The QC spectra predicted for the geometry optimized conformers are found to be in excellent quantitative agreement with corresponding experimental spectra in all of the molecules considered. The procedures suggested in this work are hoped to provide successful pathways for future chiral molecular structural analyses.

Beyond the Rosenfeld Equation: Computation of Vibrational Circular Dichroism Spectra for Anisotropic Solutions

The difference in absorption of left and right circularly polarized light by chiral molecules can be described by the Rosenfeld equation for isotropic samples. It allows the assignment of the absolute stereochemistry by comparing experimental and computationally derived spectra. Despite the simple form of the Rosenfeld equation, its evaluation in the infrared regime remained challenging, as the contribution from the magnetic dipole operator is zero within the Born-Oppenheimer (BO) approximation. In order to resolve this issue, "beyond BO" theories had to be developed, among which Stephen's magnetic field perturbation (MFP) approach offers a computationally easily accessible form. In this work, optical activity is discussed for cylindrically symmetric solutions, which cannot be described anymore by Rosenfeld's equation due to broken spherical symmetry. Mathematical properties of natural and electric-field induced anisotropies are discussed on the basis of the gauge-independent theoretical framework of Buckingham and Dunn. The issue of achiral noise arising from external field perturbations is considered, and potential remedies are introduced. Natural anisotropic vibrational circular dichroism (VCD) equations are solved numerically by applying the MFP approach within the Hartree-Fock (HF) formalism. Properties of anisotropic VCD spectra are discussed for R-(+)-methyloxirane and (1 S,2 S)-cyclopropane-1,2-dicarbonitrile. In particular, by using a group theoretical argument, a gauge-independent lower bound for the quadrupole contribution of C₂-symmetric molecules can be identified, which allows the importance of additional quadrupole terms in anisotropic VCD spectra calculation to be assessed.

Effect of puckering motion and hydrogen bond formation on the vibrational circular dichroism spectrum of a flexible molecule: the case of (S)-1-indanol

Vibrational circular dichroism spectra of (S)-1-indanol in DMSO and CCl₄ are described by cluster-in-the-bulk static calculations and first principles molecular dynamics.

Effective computational route towards vibrational optical activity spectra of chiral molecules in aqueous solution

A polarizable QM/MM approach to accurately compute the Vibrational Optical Activity (VOA) spectra of chiral systems is proposed and applied to aqueous solutions of (l)-methyl lactate and (S)-glycidol.

Computing Bulk Phase Raman Optical Activity Spectra from ab initio Molecular Dynamics Simulations

We present our novel methodology for computing Raman optical activity (ROA) spectra of liquid systems from ab initio molecular dynamics (AIMD) simulations. The method is built upon the recent developments to obtain magnetic dipole moments from AIMD and to integrate molecular properties by using radical Voronoi tessellation. These techniques are used to calculate optical activity tensors for large and complex periodic bulk phase systems. Only AIMD simulations are required as input, and no time-consuming perturbation theory is involved. The approach relies only on the total electron density in each time step and can readily be combined with a wide range of electronic structure methods. To the best of our knowledge, these are the first computed ROA spectra for a periodic bulk phase system. As an example, the experimental ROA spectrum of liquid (R)-propylene oxide is reproduced very well.

Classical Magnetic Dipole Moments for the Simulation of Vibrational Circular Dichroism by ab Initio Molecular Dynamics

We present a new approach for calculating vibrational circular dichroism spectra by ab initio molecular dynamics. In the context of molecular dynamics, these spectra are given by the Fourier transform of the cross-correlation function of magnetic dipole moment and electric dipole moment. We obtain the magnetic dipole moment from the electric current density according to the classical definition. The electric current density is computed by solving a partial differential equation derived from the continuity equation and the condition that eddy currents should be absent. In combination with a radical Voronoi tessellation, this yields an individual magnetic dipole moment for each molecule in a bulk phase simulation. Using the chiral alcohol 2-butanol as an example, we show that experimental spectra are reproduced very well. Our approach requires knowing only the electron density in each simulation step, and it is not restricted to any particular electronic structure method.