Efficient representation of the linear density-density response function.

We present a thorough derivation of the mathematical foundations of the representation of the molecular linear electronic density-density response function in terms of a computationally highly efficient moment expansion. Our new representation avoids the necessities of computing and storing numerous eigenfunctions of the response kernel by means of a considerable dimensionality reduction about from 103 to 101 . As the scheme is applicable to any compact, self-adjoint, and positive definite linear operator, we present a general formulation, which can be transferred to other applications with little effort. We also present an explicit application, which illustrates the actual procedure for applying the moment expansion of the linear density-density response function to a water molecule that is subject to a varying external perturbation potential. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.

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

The influence of flexibility and hydrogen bond formation on the IR absorption and vibrational circular dichroism (VCD) spectrum of a floppy protic molecule, namely, (S)-1-indanol, is studied in both non-polar CCl4 and polar DMSO solvents. The experimental IR absorption and VCD spectra obtained by Fourier transform spectroscopy are interpreted using both static density functional theory (DFT) calculations and first principles molecular dynamics (FPMD) within DFT, using the nuclear velocity perturbation theory (NVPT). Simulation of the spectra based on static optimised geometries is not sufficient in CCl4 and going beyond static calculations is mandatory for satisfactorily reproducing the VCD spectra. The FPMD results obtained in DMSO indicate that (S)-1-indanol is hydrogen-bonded to one DMSO molecule. As a result, static "cluster-in-the-bulk" DFT calculations in which the solute-solvent interaction is modeled as the most stable (S)-1-indanol:DMSO complexes in a DMSO continuum yield satisfactory agreement with the experiment. Correspondence between experimental and simulated spectra is slightly improved when the VCD spectrum is calculated as the summed contributions of snapshots extracted from FPMD trajectories, due to better sampling of the potential-energy surface. Finally, NVPT calculations further improve the description of experimental spectra by taking into account higher-energy structures, which are not necessary local minima.

Chiral Crystal Packing Induces Enhancement of Vibrational Circular Dichroism.

We demonstrate that molecular vibrations with originally low or zero intensity in a vibrational circular dichroism (VCD) spectrum attain chirality in molecular crystals by coordinated motion of the atoms. Ab initio molecular dynamics simulations of anharmonic solid-state VCD spectra of l-alanine crystals reveal how coherent vibrational modes exploit the space group's chirality, leading to non-local, enhanced VCD features, most significantly in the carbonyl region of the spectrum. The VCD-enhanced signal is ascribed to a helical arrangement of the oscillators in the crystal layers. No structural irregularities need to be considered to explain the amplification, but a crucial point lies in the polarization of charge, which requires an accurate description of the electronic structure. Delivering a quantitative atomic conception of supramolecular chirality induction, our ab initio scheme is applicable well beyond molecular crystals, for example, to address VCD in proteins and related compounds.

Moment expansion of the linear density-density response function.

We present a low rank moment expansion of the linear density-density response function. The general interacting (fully nonlocal) density-density response function is calculated by means of its spectral decomposition via an iterative Lanczos diagonalization technique within linear density functional perturbation theory. We derive a unitary transformation in the space of the eigenfunctions yielding subspaces with well-defined moments. This transformation generates the irreducible representations of the density-density response function with respect to rotations within SO(3). This allows to separate the contributions to the electronic response density from different multipole moments of the perturbation. Our representation maximally condenses the physically relevant information of the density-density response function required for intermolecular interactions, yielding a considerable reduction in dimensionality. We illustrate the performance and accuracy of our scheme by computing the electronic response density of a water molecule to a complex interaction potential. © 2015 Wiley Periodicals, Inc.

Vibrational circular dichroism from ab initio molecular dynamics and nuclear velocity perturbation theory in the liquid phase.

We report the first fully ab initio calculation of dynamical vibrational circular dichroism spectra in the liquid phase using nuclear velocity perturbation theory (NVPT) derived electronic currents. Our approach is rigorous and general and thus capable of treating weak interactions of chiral molecules as, e.g., chirality transfer from a chiral molecule to an achiral solvent. We use an implementation of the NVPT that is projected along the dynamics to obtain the current and magnetic dipole moments required for accurate intensities. The gauge problem in the liquid phase is resolved in a twofold approach. The electronic expectation values are evaluated in a distributed origin gauge, employing maximally localized Wannier orbitals. In a second step, the gauge invariant spectrum is obtained in terms of a scaled molecular moments, which allows to systematically include solvent effects while keeping a significant signal-to-noise ratio. We give a thorough analysis and discussion of this choice of gauge for the liquid phase. At low temperatures, we recover the established double harmonic approximation. The methodology is applied to chiral molecules ((S)-d2-oxirane and (R)-propylene-oxide) in the gas phase and in solution. We find an excellent agreement with the theoretical and experimental references, including the emergence of signals due to chirality transfer from the solute to the (achiral) solvent.

Generalization of the electronic susceptibility for arbitrary molecular geometries.

We generalize the explicit representation of the electronic susceptibility χ[R](r, r') for arbitrary molecular geometries R. The electronic susceptibility is a response function that yields the response of the molecular electronic charge density at linear order to an arbitrary external perturbation. We address the dependence of this response function on the molecular geometry. The explicit representation of the molecular geometry dependence is achieved by means of a Taylor expansion in the nuclear coordinates. Our approach relies on a recently developed low-rank representation of the response function χ[R](r, r') which allows a highly condensed storage of the expansion and an efficient application within dynamical chemical environments. We illustrate the performance and accuracy of our scheme by computing the vibrationally induced variations of the response function of a water molecule and its resulting Raman spectrum.

Nuclear velocity perturbation theory for vibrational circular dichroism: An approach based on the exact factorization of the electron-nuclear wave function.

The nuclear velocity perturbation theory (NVPT) for vibrational circular dichroism (VCD) is derived from the exact factorization of the electron-nuclear wave function. This new formalism offers an exact starting point to include correction terms to the Born-Oppenheimer (BO) form of the molecular wave function, similar to the complete-adiabatic approximation. The corrections depend on a small parameter that, in a classical treatment of the nuclei, is identified as the nuclear velocity. Apart from proposing a rigorous basis for the NVPT, we show that the rotational strengths, related to the intensity of the VCD signal, contain a new contribution beyond-BO that can be evaluated with the NVPT and that only arises when the exact factorization approach is employed. Numerical results are presented for chiral and non-chiral systems to test the validity of the approach.

Electronic density response to molecular geometric changes from explicit electronic susceptibility calculations.

We present a first principles approach to compute the response of the molecular electronic charge distribution to a geometric distortion. The scheme is based on an explicit representation of the linear electronic susceptibility. The linear electronic susceptibility is a tensor quantity which directly links the first-order electronic response density to the perturbation potential, without requiring self-consistency. We first show that the electronic susceptibility is almost invariant to small changes in the molecular geometry. We then compute the dipole moments from the response density induced by the geometrical changes. We verify the accuracy by comparing the results to the corresponding values obtained from the self-consistent calculations of the ground-state densities in both geometries.