Positivity preserving density matrix minimization at finite temperatures via square root

We present a Wave Operator Minimization (WOM) method for calculating the Fermi-Dirac density matrix for electronic structure problems at finite temperature while preserving physicality by construction using the wave operator, i.e., the square root of the density matrix. WOM models cooling a state initially at infinite temperature down to the desired finite temperature. We consider both the grand canonical (constant chemical potential) and canonical (constant number of electrons) ensembles. Additionally, we show that the number of steps required for convergence is independent of the number of atoms in the system. We hope that the discussion and results presented in this article reinvigorate interest in density matrix minimization methods.

Theoretical Advances in Polariton Chemistry and Molecular Cavity Quantum Electrodynamics

When molecules are coupled to an optical cavity, new light-matter hybrid states, so-called polaritons, are formed due to quantum light-matter interactions. With the experimental demonstrations of modifying chemical reactivities by forming polaritons under strong light-matter interactions, theorists have been encouraged to develop new methods to simulate these systems and discover new strategies to tune and control reactions. This review summarizes some of these exciting theoretical advances in polariton chemistry, in methods ranging from the fundamental framework to computational techniques and applications spanning from photochemistry to vibrational strong coupling. Even though the theory of quantum light-matter interactions goes back to the midtwentieth century, the gaps in the knowledge of molecular quantum electrodynamics (QED) have only recently been filled. We review recent advances made in resolving gauge ambiguities, the correct form of different QED Hamiltonians under different gauges, and their connections to various quantum optics models. Then, we review recently developed ab initio QED approaches which can accurately describe polariton states in a realistic molecule-cavity hybrid system. We then discuss applications using these method advancements. We review advancements in polariton photochemistry where the cavity is made resonant to electronic transitions to control molecular nonadiabatic excited state dynamics and enable new photochemical reactivities. When the cavity resonance is tuned to the molecular vibrations instead, ground-state chemical reaction modifications have been demonstrated experimentally, though its mechanistic principle remains unclear. We present some recent theoretical progress in resolving this mystery. Finally, we review the recent advances in understanding the collective coupling regime between light and matter, where many molecules can collectively couple to a single cavity mode or many cavity modes. We also lay out the current challenges in theory to explain the observed experimental results. We hope that this review will serve as a useful document for anyone who wants to become familiar with the context of polariton chemistry and molecular cavity QED and thus significantly benefit the entire community.

Biochemical and Phylogenetic Analysis of Italian Phaseolus vulgaris Cultivars as Sources of α-Amylase and α-Glucosidase Inhibitors

Phaseolus vulgaris α-amylase inhibitor (α-AI) is a protein that has recently gained commercial interest, as it inhibits mammalian α-amylase activity, reducing the absorption of dietary carbohydrates. Numerous studies have reported the efficacy of preparations based on this protein on the control of glycaemic peaks in type-2 diabetes patients and in overweight subjects. A positive influence on microbiota regulation has also been described. In this work, ten insufficiently studied Italian P. vulgaris cultivars were screened for α-amylase- and α-glucosidase-inhibiting activity, as well as for the absence of antinutritional compounds, such as phytohemagglutinin (PHA). All the cultivars presented α-glucosidase-inhibitor activity, while α-AI was missing in two of them. Only the Nieddone cultivar (ACC177) had no haemagglutination activity. In addition, the partial nucleotide sequence of the α-AI gene was identified with the degenerate hybrid oligonucleotide primer (CODEHOP) strategy to identify genetic variability, possibly linked to functional α-AI differences, expression of the α-AI gene, and phylogenetic relationships. Molecular studies showed that α-AI was expressed in all the cultivars, and a close similarity between the Pisu Grogu and Fasolu cultivars' α-AI and α-AI-4 isoform emerged from the comparison of the partially reconstructed primary structures. Moreover, mechanistic models revealed the interaction network that connects α-AI with the α-amylase enzyme characterized by two interaction hotspots (Asp38 and Tyr186), providing some insights for the analysis of the α-AI primary structure from the different cultivars, particularly regarding the structure-activity relationship. This study can broaden the knowledge about this class of proteins, fuelling the valorisation of Italian agronomic biodiversity through the development of commercial preparations from legume cultivars.

Tensor Hypercontraction Form of the Perturbative Triples Energy in Coupled-Cluster Theory

We present the working equations for a reduced-scaling method of evaluating the perturbative triples (T) energy in coupled-cluster theory, through the tensor hypercontraction (THC) of the triples amplitudes (t_ijk^abc). Through our method, we can reduce the scaling of the (T) energy from the traditional O(N7) to a more modest O(N5). We also discuss implementation details to aid future research, development, and software realization of this method. Additionally, we show that this method yields submillihartree (mEh) differences from CCSD(T) when evaluating absolute energies and sub-0.1 kcal/mol energy differences when evaluating relative energies. Finally, we demonstrate that this method converges to the true CCSD(T) energy through the systematic increasing of the rank or eigenvalue tolerance of the orthogonal projector, as well as exhibiting sublinear to linear error growth with respect to system size.

Absorption Properties of Large Complex Molecular Systems: The DFTB/Fluctuating Charge Approach

We report on the first formulation of a novel polarizable QM/MM approach, where the density functional tight binding (DFTB) is coupled to the fluctuating charge (FQ) force field. The resulting method (DFTB/FQ) is then extended to the linear response within the TD-DFTB framework and challenged to study absorption spectra of large condensed-phase systems.