Gradient-based direct normal-mode analysis

Quantum harmonic free energies for biomolecules and nanomaterials

Obtaining the free energy of large molecules from quantum mechanical energy functions is a long-standing challenge. We describe a method that allows us to estimate, at the quantum mechanical level, the harmonic contributions to the thermodynamics of molecular systems of large size, with modest cost. Using this approach, we compute the vibrational thermodynamics of a series of diamond nanocrystals, and show that the error per atom decreases with system size in the limit of large systems. We further show that we can obtain the vibrational contributions to the binding free energies of prototypical protein-ligand complexes where exact computation is too expensive to be practical. Our work raises the possibility of routine quantum mechanical estimates of thermodynamic quantities in complex systems.

A matrix completion algorithm for efficient calculation of quantum and variational effects in chemical reactions

This work examines the viability of matrix completion methods as cost-effective alternatives to full nuclear Hessians for calculating quantum and variational effects in chemical reactions. The harmonic variety-based matrix completion (HVMC) algorithm, developed in a previous study [S. J. Quiton et al., J. Chem. Phys. 153, 054122 (2020)], exploits the low-rank character of the polynomial expansion of potential energy to recover vibrational frequencies (square roots of eigenvalues of nuclear Hessians) constituting the reaction path using a small sample of its entities. These frequencies are essential for calculating rate coefficients using variational transition state theory with multidimensional tunneling (VTST-MT). HVMC performance is examined for four S_N2 reactions and five hydrogen transfer reactions, with each H-transfer reaction consisting of at least one vibrational mode strongly coupled to the reaction coordinate. HVMC is robust and captures zero-point energies, vibrational free energies, zero-curvature tunneling, and adiabatic ground state and free energy barriers as well as their positions on the reaction coordinate. For medium to large reactions involving H-transfer, with the sole exception of the most complex Ir catalysis system, less than 35% of total eigenvalue information is necessary for accurate recovery of key VTST-MT observables.

A matrix completion algorithm to recover modes orthogonal to the minimum energy path in chemical reactions

Structured statistical methods are promising for recovering or completing information from noisy and incomplete data with high fidelity. In particular, matrix completion exploits underlying structural properties such as rank or sparsity. Our objective is to employ matrix completion to reduce computational effort associated with the calculation of multiple quantum chemical Hessians, which are necessary for identification of temperature-dependent free energy maxima under canonical variational transition state theory (VTST). We demonstrate proof-of-principle of an algebraic variety-based matrix completion method for recovering missing elements in a matrix of transverse Hessian eigenvalues constituting the minimum energy path (MEP) of a reaction. The algorithm, named harmonic variety-based matrix completion (HVMC), utilizes the fact that the points lying on the MEP of a reaction step constitute an algebraic variety in the reaction path Hamiltonian representation. We demonstrate that, with as low as 30% random sampling of matrix elements for the largest system in our test set (46 atoms), the complete matrix of eigenvalues can be recovered. We further establish algorithm performance for VTST rate calculations by quantifying errors in zero-point energies and vibrational free energies. Motivated by this success, we outline next steps toward developing a practical HVMC algorithm, which utilizes a gradient-based sampling protocol for low-cost VTST rate computations.

Excited State Orbital Optimization via Minimizing the Square of the Gradient: General Approach and Application to Singly and Doubly Excited States via Density Functional Theory

We present a general approach to converge excited state solutions to any quantum chemistry orbital optimization process, without the risk of variational collapse. The resulting square gradient minimization (SGM) approach only requires analytic energy/Lagrangian orbital gradients and merely costs 3 times as much as ground state orbital optimization (per iteration), when implemented via a finite difference approach. SGM is applied to both single determinant ΔSCF and spin-purified restricted open-shell Kohn-Sham (ROKS) approaches to study the accuracy of orbital optimized DFT excited states. It is found that SGM can converge challenging states where the maximum overlap method (MOM) or analogues either collapse to the ground state or fail to converge. We also report that ΔSCF/ROKS predict highly accurate excitation energies for doubly excited states (which are inaccessible via TDDFT). Singly excited states obtained via ROKS are also found to be quite accurate, especially for Rydberg states that frustrate (semi)local TDDFT. Our results suggest that orbital optimized excited state DFT methods can be used to push past the limitations of TDDFT to doubly excited, charge-transfer, or Rydberg states, making them a useful tool for the practical quantum chemist's toolbox for studying excited states in large systems.

Selective calculation of high-intensity vibrations in molecular resonance Raman spectra

We present an intensity-driven approach for the selective calculation of vibrational modes in molecular resonance Raman spectra. The method exploits the ideas of the mode-tracking algorithm [M. Reiher and J. Neugebauer, J. Chem. Phys. 118, 1634 (2003)] for the calculation of preselected molecular vibrations and of Heller's gradient approximation [Heller et al., J. Phys. Chem. 86, 1822 (1982)] for the estimation of resonance Raman intensities. The gradient approximation allows us to construct a basis vector for the subspace iteration carried out in the mode-tracking calculation, which corresponds to an artificial collective motion of the molecule that contains the entire intensity in the resonance Raman spectrum. Subsequently, the algorithm generates new basis vectors from which normal mode approximations are obtained. It is then possible to provide estimates for (i) the accuracy of the normal mode approximations and (ii) the intensity of these modes in the final resonance Raman spectrum. This approach is tested for the examples of uracil and a structural motif from the E colicin binding immunity protein Im7, in which a few aromatic amino acids dominate the resonance Raman spectrum at wavelengths larger than 240 nm.

Can Raman Optical Activity Separate Axial from Local Chirality? A Theoretical Study of Helical Deca-Alanine

Motivated by experimental work on the distinction of protein secondary structure motifs by Raman optical activity (ROA) spectroscopy, we demonstrate using density functional theory that axial chirality in structures with different local chirality can be filtered out by ROA spectroscopy. To this purpose, two diastereomers of right-handed helical deca-alanine, the (all-S) and the (R,S,R,S,R,S,R,S,R,S) form, are compared. Furthermore, we suggest to interpret calculated ROA spectra of large molecules in terms of vibrational bands rather than individual peaks. This is due to the non-homogeneous effect of the harmonic approximation as well as of the chosen electronic structure method onto the vibrational frequencies, which in a dense region of many vibrations will strongly determine the shape of the spectrum. In addition, the calculated ROA spectrum of (all-S)-deca-alanine is compared to the experimental spectrum of poly-(L)-alanine in solution.