Analytic gradient routines are a desirable feature for quantum mechanical methods, allowing for efficient determination of equilibrium and transition state structures and several other molecular properties. In this work, we present analytical gradients for multiconfiguration pair-density functional theory (MC-PDFT) when used with a state-specific complete active space self-consistent field reference wave function. Our approach constructs a Lagrangian that is variational in all wave function parameters.We find that MC-PDFT locates equilibrium geometries for several small-to mediumsized organic molecules that are similar to those located by complete active space second-order perturbation theory but that are obtained with decreased computational cost.

The success of any physical model critically depends upon adopting an appropriate representation for the phenomenon of interest. Unfortunately, it remains generally challenging to identify the essential degrees of freedom or, equivalently, the proper order parameters for describing complex phenomena. Here we develop a statistical physics framework for exploring and quantitatively characterizing the space of order parameters for representing physical systems. Specifically, we examine the space of low-resolution representations that correspond to particle-based coarse-grained (CG) models for a simple microscopic model of protein fluctuations. We employ Monte Carlo (MC) methods to sample this space and determine the density of states for CG representations as a function of their ability to preserve the configurational information, I, and large-scale fluctuations, Q, of the microscopic model. These two metrics are uncorrelated in high-resolution representations but become anticorrelated at lower resolutions. Moreover, our MC simulations suggest an emergent length scale for coarse-graining proteins, as well as a qualitative distinction between good and bad representations of proteins. Finally, we relate our work to recent approaches for clustering graphs and detecting communities in networks.

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The accurate description of reaction barrier heights is challenging for quantum mechanical methods due to the need for a balanced treatment of dynamic and static correlation energies because their importance varies during the course of a chemical reaction. While some regions of potential energy surfaces are well-described by a single-reference wave function or by Kohn–Sham density functional theory, in other cases a multireference treatment is needed. For systems with many active electrons, most accurate multireference methods have prohibitive computational scalings with system size. Multiconfiguration pair-density functional theory, MC-PDFT, is a more affordable multireference approach that computes the total electron correlation energy in a single step by using the multiconfiguration kinetic energy, density, and on-top pair density and an on-top density functional. In this work, we apply MC-PDFT to a benchmark database (DBH24/18) of 24 diverse reaction barrier heights. We explore the role of active space and basis set selection on the performance of MC-PDFT. We find that MC-PDFT is able to calculate reaction barrier heights with a similar accuracy to complete active space second order perturbation theory, CASPT2, but at a lower computational cost, and we find that MC-PDFT is less dependent on basis set selection than CASPT2.

Rate constants for overall decomposition (kd) for a series of exo‐7‐alkylbicyclo[3.2.0]hept‐2‐enes are relatively invariant. For the alkyl substituents ethyl, propyl, butyl, isopropyl, and t‐butyl, the ratio of the rate constant for [1,3] sigmatropic rearrangement to the rate constant for fragmentation, k13/kf, is significantly lower than k13/kf = 150 observed for exo‐7‐methylbicyclo[3.2.0]hept‐2‐ene. Regardless of the size and mass of the alkyl group, the stereoselectivity of the [1,3] carbon migration appears to be quite stable at 80% to 89% suprafacial inversion (si), an observation consistent with conservation of angular momentum but not conservation of orbital symmetry. This global result comports with the phenomenon of “dynamic matching” espoused by Carpenter and collaborators for [1,3] sigmatropic rearrangements in general.