Grassmann Extrapolation of Density Matrices for Born-Oppenheimer Molecular Dynamics

Second-Order Mass-Weighting Scheme for Atom-Centered Density Matrix Propagation Molecular Dynamics

The atom-centered density matrix propagation (ADMP) method is an extended Lagrangian approach to ab initio molecular dynamics, which includes the density matrix in an orthonormalized atom-centered Gaussian basis as additional, fictitious, electronic degrees of freedom, classically propagated along with the nuclear ones. A high adiabaticity between the nuclear and electronic subsystems is mandatory in order to keep the trajectory close to the Born-Oppenheimer (BO) surface. In this regard, the fictitious electronic mass μ, being a symmetric, nondiagonal matrix in its most general form, represents a free parameter, exploitable to optimize the propagation of the electronic density. Although mass-weighting schemes in ADMP exist, a systematic procedure to define an optimal value of the fictitious masses is not available yet. In this work, in order to rationally evaluate the electronic mass, fictitious electronic normal modes are defined through the diagonalization of the Hessian of the electronic density matrix. If the same frequency is imposed on all such modes (compatible with the chosen integration time step), then the corresponding μ matrix can be calculated and then employed for the following propagation. Analysis of several ADMP test simulations reveals that such Hessian-based mass-weighting approach is able to ensure, together with a 0.1/0.2 fs time steps, a high separation between the (real) nuclear and the (fictitious) electronic frequencies, which determines a high adiabaticity. This high, unprecedented, accuracy in the propagation leads, in turn, to low errors in the estimated nuclear vibrational frequencies, making the ADMP method totally comparable to a fully converged BO molecular dynamics simulation but more computationally efficient. This work, therefore, contributes to a further development of the ADMP ab initio molecular dynamics method, aimed at improving its accuracy through a more rational evaluation of the fictitious electronic mass parameter.

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.

Mapping spin contamination-free potential energy surfaces using restricted open-shell methods with Grassmannians

The Lagrange-based Grassmann interpolation (G-Int) method has been extended for open-shell systems using restricted open-shell (RO) methods. The performance of this method was assessed in constructing potential energy surfaces (PESs) for vanadium(II) oxide, benzyl radical, and methanesulfenyl chloride radical cation. The density matrices generated by G-Int when used as initial guesses for self-consistent field (SCF) calculations, exhibit superior performance compared to other traditional SCF initial guess schemes, such as SADMO, GWH, and CORE. Additionally, the energy obtained from the G-Int scheme satisfies the variational principle and outperforms the direct energy-based Lagrange interpolation approach. In the case of methanesulfenyl chloride radical cation, a unique example with a flat PES at the end region along the H-C-S-Cl dihedral angle, the use of an equally-spaced grid sampling leads to significant oscillations near the end of the interval due to the effects of Runge's phenomenon. Introducing an unequally-spaced grid sampling based on a scaled Gauss-Chebyshev quadrature effectively mitigated the Runge's phenomenon, making it suitable for combining with G-Int in constructing PESs for general applications. Thus, G-Int provides an efficient and robust strategy for building spin contamination-free PESs with consistent accuracy.

A Quasi Time-Reversible Scheme Based on Density Matrix Extrapolation on the Grassmann Manifold for Born-Oppenheimer Molecular Dynamics

This Letter introduces the so-called Quasi Time-Reversible scheme based on Grassmann extrapolation (QTR G-Ext) of density matrices for an accurate calculation of initial guesses in Born-Oppenheimer Molecular Dynamics (BOMD) simulations. The method shows excellent results on four large molecular systems that are representative of real-life production applications, ranging from 21 to 94 atoms simulated with Kohn-Sham (KS) density functional theory surrounded with a classical environment with 6k to 16k atoms. Namely, it clearly reduces the number of self-consistent field iterations while at the same time achieving energy-conserving simulations, resulting in a considerable speed-up of BOMD simulations even when tight convergence of the KS equations is required.

Fast Method for Excited-State Dynamics in Complex Systems and Its Application to the Photoactivation of a Blue Light Using Flavin Photoreceptor

The excited-state dynamics of molecules embedded in complex (bio)matrices is still a challenging goal for quantum chemical models. Hybrid QM/MM models have proven to be an effective strategy, but an optimal combination of accuracy and computational cost still has to be found. Here, we present a method which combines the accuracy of a polarizable embedding QM/MM approach with the computational efficiency of an excited-state self-consistent field method. The newly implemented method is applied to the photoactivation of the blue-light-using flavin (BLUF) domain of the AppA protein. We show that the proton-coupled electron transfer (PCET) process suggested for other BLUF proteins is still valid also for AppA.

Generating accurate density matrices on the tangent space of a Grassmann manifold

Interpolating a density matrix from a set of known density matrices is not a trivial task. This is because a linear combination of density matrices does not necessarily correspond to another density matrix. In this Communication, density matrices are examined as objects of a Grassmann manifold. Although this manifold is not a vector space, its tangent space is a vector space. As a result, one can map the density matrices on this manifold to their corresponding vectors in the tangent space and then perform interpolations on that tangent space. The resulting interpolated vector can be mapped back to the Grassmann manifold, which can then be utilized (1) as an optimal initial guess for a self-consistent field (SCF) calculation or (2) to derive energy directly without time-consuming SCF iterations. Such a promising approach is denoted as Grassmann interpolation (G-Int). The hydrogen molecule has been used to illustrate that the described interpolated method in this work preserves the essential attributes of a density matrix. For phosphorus mononitride and ferrocene, it was demonstrated numerically that reference points for the definition of the corresponding tangent spaces can be chosen arbitrarily. In addition, the interpolated density matrices provide a superior and essentially converged initial guess for an SCF calculation to make the SCF procedure itself unnecessary. Finally, this accurate, efficient, robust, and systematically improved G-Int strategy has been used for the first time to generate highly accurate potential energy surfaces with fine details for the difficult case, ferrocene.

Geometric interpretation for coupled-cluster theory. A comparison of accuracy with the corresponding configuration interaction model

Although coupled-cluster theory is well-known for its accuracy, the geometry associated to the manifold of wave functions reached by the coupled-cluster ansatz has not been deeply explored. In this article we look for an interpretation for the high accuracy of coupled-cluster theory based on how the manifold of coupled-cluster wave functions is embedded within the space of n-electron wave functions. We define the coupled-cluster and configuration interaction manifolds and measure the distances from the full configuration interaction (FCI) wave function to these manifolds. We clearly observe that the FCI wave function is closer to the coupled-cluster manifold, that is curved, than to the configuration interaction manifold, that is flat, for the selected systems studied in this work. Furthermore, the decomposition of the distances among these manifolds and wave functions into excitation ranks gives insights on the failure of the coupled-cluster approach for multireference systems. The present results show a new interpretation for the quality of the coupled-cluster method, as contrasted to the truncated configuration interaction approach, besides the well-established argument based on size-extensivity. Furthermore, we show how a geometric description of wave function methods can be used in electronic structure theory.