We present a computational protocol for triplet excited-state energy transfer (TEET) within multistate density functional theory with nonorthogonal state interaction (MSDFT-NOSI). Block-localized excitation, achieved through occupation-constrained orbital optimization, generates fragment-localized singlet and triplet configurations in a minimal active space that captures donor and acceptor states. Well-defined diabatic states, with excitations localized on individual fragments, are obtained via the generalized diabatic-at-construction (GDAC) transformation. This yields diabatic energies and electronic couplings for both Dexter-type and Förster-type transfer in a unified framework. Application to the propenal excimer demonstrates that MSDFT-NOSI reproduces TDDFT-quality excitation energies while providing a chemically transparent picture of the TEET process. MSDFT-NOSI/GDAC offers a practical and insightful method for investigating triplet energy transfer in molecular complexes and photocatalytic systems.

Multistate density functional theory (MSDFT) generalizes Kohn-Sham density functional theory to a finite subspace of interacting states through a Hamiltonian matrix functional of the matrix density D(r). A central challenge is to construct matrix functionals that preserve subspace unitary invariance while encoding nontrivial state coupling. Here we show that any local, unitary-covariant matrix functional of D(r) must be codiagonalizable with D(r), and is therefore completely specified by a scalar generator acting on its eigenvalues. This establishes a one-to-all mapping from a scalar generator to the full matrix functional. As a consequence, the construction of N2 matrix elements is reduced to a single scalar mapping evaluated on the eigenvalue spectrum at each spatial grid point. The formalism is illustrated using a four-state Hubbard model, where exact reconstruction is achieved with a known scalar function, and deviations from this mapping can be systematically corrected within the spectral framework. The results provide a rigorous foundation for constructing local matrix exchange-correlation functionals with computational complexity comparable to Kohn-Sham DFT, and offer a practical route toward scalable MSDFT approximations.

This study investigates the performance of Target State Optimization Density Functional Theory (TSO-DFT) in predicting molecular K-edge X-ray Absorption Spectra (XAS). In contrast to Time-Dependent Density Functional Theory (TDDFT), which systematically underestimates core excitation energies by more than 10 eV, TSO-DFT optimizes wave function for every state to account for orbital relaxation effects and can achieve an accuracy of subelectronvolts. We apply TSO-DFT to predict the K-edge XAS for which is critical for accurate predictions of core excitations. TSO-DFT is applied to predict XAS for CO2, N2O, carbonyl compounds, and radicals. TSO-DFT succeeds in predicting both the main features and core excitation energies. TSO-DFT is also used to predict the angle-dependent XAS of porphyrin and polarized XAS of the uranyl ion. The calculated XAS agrees quite well with experiments and can give details of electronic structure change that cannot be obtained straightforwardly from experiments alone. TSO-DFT is a promising method for studying molecular XAS and is available in the software Qbics, which can be downloaded free of charge.

Multistate density functional theory (MSDFT) provides a rigorous variational framework for the simultaneous description of multiple electronic states through a matrix density, but practical implementations have relied on multiconfigurational many-body wavefunctions. Here, we introduce the Dyson field, ψ(r), an L×N matrix-valued function of the coordinate r that factorizes the matrix density as D(r) = ψ†(r)ψ(r). The elements of ψ(r) = {ψpA(r)} are shown to be Dyson orbitals connecting the n-electron states of interest to (n − 1)-electron ionization channels of size L, providing a direct physical interpretation of the matrix density in terms of electron removal amplitudes. Variational minimization of the MSDFT subspace energy with respect to the Dyson field yields a matrix Fock equation, in which the kinetic and external potential operators act locally, while Hartree and exchange–correlation effects appear as N×N matrix potentials, VH[D](r) and Vxc[D](r), that couple electronic states within the subspace. This formulation defines a quasiparticle reference system for MSDFT that is analogous to the Kohn–Sham orbitals in Hohenberg-Kohn DFT. In appropriate limits, the formalism reduces exactly to Kohn-Sham DFT for N = 1 and to the Tamm-Dancoff approximation of time-dependent DFT within the single-excitation manifold. More generally, the Dyson-field construction transforms MSDFT from a formally exact but wavefunction-dependent framework into an orbital-based theory, opening a practical route to self-consistent, density-based treatments of strongly correlated and electronically coupled states.

A covariant local matrix density approximation (LMDA) is introduced within multistate density functional theory based on subspace invariance and the spectral decomposition of the matrix containing state and transition densities. The exchange correlation matrix functional is constructed through spectral reconstruction of this matrix density, whereby conventional local exchange-correlation functionals are incorporated as spectral-channel functionals within a covariant matrix-functional formalism. The resulting formulation preserves exact normalization of the exchange-correlation matrix hole, recovers Kohn-Sham density functional theory in the single-state limit, and preserves spin-multiplet degeneracy through covariance of the spin matrix functional under spin rotations. Combined with multistate self-consistent-field (MSSCF) optimization, the present framework enables fully variational calculations of interacting ground and excited states. Applications to atomic excitations, H2 dissociation, ethylene torsion and cyclobutadiene automerization reveals that the resulting MSDFT/LMDA approach captures essential multistate and strong-correlation physics, including static correlation and spin symmetry. The key insight is that the central obstacle in extending density functional theory to coupled electronic states is not necessarily the lack of appropriate scalar exchange-correlation approximations, but the lack of a covariant matrix-functional formalism in which such functionals can operate. The present MSDFT/LMDA provides a direct realization of this matrix-functional formalism.

We present a tutorial review of the theoretical background and a step-by-step computational procedure for determining kinetic isotope effects (KIE) of chemical reactions in aqueous solution. The method combines path integral and free energy perturbation (PI-FEP) simulations to directly yield the ratio of the partition functions between different isotopic reactions. This review is the result from a collaborative work in a Computational Chemistry course at the University of Minnesota, where two intramolecular proton transfer reactions were given as classroom exercises. Through this study, we wish to accomplish three main goals: (i) determination of nuclear quantum effects and quantum-mechanical potentials of mean force (QM-PMF), (ii) computation of primary KIE using PI-FEP simulations, and (iii) an understanding of solvent effects on proton transfer reactions in water. Analyses of computational results provide insights into substituent effects on chemical reactivity, solvent effects on reaction rate, nuclear quantum effects on free energy barrier, and kinetic isotope effects on transition state. The theory and computational procedure for determining KIE can be directly used to study chemical reactions in solutions and enzymatic processes with two publicly available software packages (CHARMM and QBICS).

The interaction between excited states of a closed-shell chromophore and a nearby free radical species gives rise to spin-coupled doublet states, namely singdoublet and tripdoublet, as well as a quartet state. This coupling facilitates transitions that are otherwise spin-forbidden, thereby enhancing intersystem crossing and influencing luminescence and non-radiative decay pathways. In this chapter, we explore these interactions using multistate density functional theory (MSDFT). By employing a minimal active space (MAS) comprising just ten determinant configurations, MSDFT effectively captures local and charge-transfer excitations with inclusion of correlation effects. MSDFT extends the Hohenberg-Kohn density functional theory from the ground state to encompass all electronic states, underscoring the potential for developing computationally efficient methods to study excited states. Numerical results demonstrate that MSDFT accurately reproduces both qualitative trends and quantitative excited-state energies, in accord with previous studies using extended multistate complete-active-space second-order perturbation theory (XMS-CASPT2). The work explores energy changes along a reaction path from the D_0/D_1 minimum energy crossing intersection to the D_2/D_3 crossing in the exciplex formed by 10-methylphenothiazine and a dicarboximide electron acceptor linked to the stable free radical 2,2,6,6-tetramethylpiperidin-1-oxyl (TEMPO).

A quantum theory of density functionals and its applications is presented. By introducing a matrix density D ( r ) of rank N as the fundamental variable, a one-to-one correspondence has been established between D ( r ) and the Hamiltonian matrix representing N electronic states-that is, a matrix density functional ℋ [ D ] . Moreover, no more than N 2 Slater determinants are sufficient to represent D ( r ) exactly, giving rise to the concept of minimal active space (MAS). The use of a MAS naturally leads to the definition of correlation matrix functional ℰ c [ D ] , the multi-state extension of the exchange-correlation functional in Kohn-Sham DFT. Variational minimization of the multistate energy, which is defined as the trace of the Hamiltonian matrix functional, yields the exact energies and densities of the lowest N eigenstates. A nonorthogonal state interaction (NOSI) algorithm has been developed to optimize the orbitals associated with D ( r ) and to approximate the correlation matrix functional. The MSDFT-NOSI method is demonstrated across a range of applications, particularly in cases where KS-DFT and linear-response time-dependent DFT fail, with its accuracy validated through comparison with high-level multiconfigurational wave function theory.

Regulating the coordination environment of active sites has proved powerful for tapping into their catalytic activity and selectivity in homogeneous catalysis, yet the heterogeneous nature of copper single-atom catalysts (SACs) makes it challenging. This work reports a bottom-up approach to construct a SAC (rGO@Cu−N(H x )−C) by inlaying preformed amine coordinated Cu 2+ units into reduced graphene oxide (rGO), permitting molecular level revelation on how the proximal N-site functional groups (N−H or N−CH 3 ) impact on the carbon dioxide reduction reaction (CO 2 RR). It is demonstrated that the N−H moiety of rGO@Cu−NH x −C can serve as an in situ protonation agent to accelerate the CO 2 -to-methane reduction kinetics, delivering a methane current density (163 mA/cm 2 ) 2.42-times that with the -CH 3 substituted counterpart rGO@Cu−N−C. Operando spectroscopic studies and theoretical calculations elucidate that the high methane faradaic efficiency (77.1 %) achieved here is enabled by opening up the energetically favorable formyl pathway (*OCHO pathway) against the traditional *CO pathway that normally leads to various CO 2 RR products other than methane. Our strategy sets the stage to precisely modulate single-atom catalysts for efficient and selective electrochemical CO 2 reduction.

In the Big Data era, a change of paradigm in the use of molecular dynamics is required. Trajectories should be stored under FAIR (findable, accessible, interoperable and reusable) requirements to favor its reuse by the community under an open science paradigm.

Excited-state energy decomposition analysis (EDA) provides a useful framework to dissect the physical interactions that stabilize molecular complexes in electronically excited states. While ground-state EDA has been widely applied to understand noncovalent interactions and chemical bonding, excited states introduce qualitatively new contributions, including photoexcitation, exciton resonance, and charge-transfer excitations. Recent developments in multistate density functional theory (MSDFT) extends the interpretability of EDA into the excited-state domain, offering mechanistic insight into photophysical and photochemical phenomena. This report summarizes the theoretical foundation of multistate EDA (MS-EDA), defines its key energetic terms, and illustrates its application to several groups of excited-state complexes. It is hoped that MS-EDA can provide interpretable understanding of excited state energies in terms of exciton resonance, superexchange stabilization and orbital and configuraiton delocalization.

On the basis of recent advancements in the Hamiltonian matrix density functional for multiple electronic eigenstates, this study delves into the mathematical foundation of the multistate density functional theory (MSDFT). We extend a number of physical concepts at the core of Kohn-Sham DFT, such as density representability, to the matrix density functional. In this work, we establish the existence of the universal matrix functional for many states as a proper generalization of the Lieb universal functional for the ground state. Consequently, the variation principle of MSDFT can be rigorously defined within an appropriate domain of matrix densities, thereby providing a solid framework for DFT of both the ground state and excited states. We further show that the analytical structure of the Hamiltonian matrix functional is considerably constrained by the subspace symmetry and invariance properties, requiring and ensuring that all elements of the Hamiltonian matrix functional are variationally optimized in a coherent manner until the Hamiltonian matrix within the subspace spanned by the lowest eigenstates is obtained. This work solidifies the theoretical foundation to treat multiple electronic states using density functional theory.

In reactive molecular dynamics (MD) simulations, such as those used to model combustion, filtering noisy data from reactive trajectories is crucial for accurately constructing reaction networks and elucidating macroscopic mechanisms. To address this challenge, we introduce a graph algorithm-based explicit denoising approach that defines user-controlled operations for removing oscillatory reaction patterns, including combination and separation, isomerization, and node contraction. This algorithm is implemented in ReaxANA, a parallel Python package designed to extract reaction mechanisms from both heterogeneous and homogeneous reactive MD trajectories. ReaxANA operates solely on atomic position data, enabling its easy integration with various simulation platforms. We demonstrate its capabilities through the analysis of the TNT (trinitrotoluene) explosion system generated by using molecular dynamics simulations with the ReaxFF force field. ReaxANA effectively distinguishes structural isomers, facilitating a comprehensive examination of reaction networks. Our findings reveal that the primary decomposition pathway of TNT involves pyrolysis of the ortho nitro group (-NO2), followed by further decomposition that leads to a five-membered ring compound. ReaxANA is an open-source software and packaged in a Docker container for cross-platform compatibility, providing insights and advanced analytical capabilities.

We present a tutorial to carry out umbrella-sampling free-energy simulations with a combined quantum mechanical and molecular mechanical (QM/MM) potential, which may also be used in a computational or biophysical chemistry curriculum for first-year graduate and undergraduate students. In this article, we choose the Type II S(N)2 Menshutkin reaction between ammonia and chloromethane to construct the potential of mean force (PMF) for the reaction in aqueous solution. In this exercise, we wish to accomplish three tasks: (1) an understanding of the concept of PMF and the umbrella-sampling free-energy simulation method, (2) the use of a combined QM/MM potential in molecular dynamics simulation of chemical reactions, and (3) an understanding of solvent effects and intermolecular interactions on chemical reactions through comparison with gas-phase results. Analysis of the simulation results allows students to appreciate the difference between the transition state along a PMF from statistical simulations versus the optimized saddle point in the gas phase, the shift of transition state with respect to solvation, and the significance of electronic polarization. Through this tutorial, students will gain the necessary skills to carry out free energy simulations of chemical reactions in solution and in enzymes both in a classroom and in the laboratory.

Since its inception nearly a half century ago, CHARMM has been playing a central role in computational biochemistry and biophysics. Commensurate with the developments in experimental research and advances in computer hardware, the range of methods and applicability of CHARMM have also grown. This review summarizes major developments that occurred after 2009 when the last review of CHARMM was published. They include the following: new faster simulation engines, accessible user interfaces for convenient workflows, and a vast array of simulation and analysis methods that encompass quantum mechanical, atomistic, and coarse-grained levels, as well as extensive coverage of force fields. In addition to providing the current snapshot of the CHARMM development, this review may serve as a starting point for exploring relevant theories and computational methods for tackling contemporary and emerging problems in biomolecular systems. CHARMM is freely available for academic and nonprofit research at https://academiccharmm.org/program.

The nitrile (C≡N) stretching vibration is widely used as a site-specific environmental probe of proteins and, as such, many computational studies have been used to investigate the factors that affect its frequency (νCN). These studies, most of which were carried out in the ground electronic state of the molecule of interest, revealed that the formation of a normal or linear hydrogen bond (H-bond) with the nitrile group results in a blueshift in its νCN. Recently, however, several experimental studies showed that for certain aromatic nitriles, solvent relaxations in their excited electronic state(s) induce a redshift (blueshift) in νCN in protic (aprotic) solvents, suggesting that the effect of hydrogen-bonding (H-bonding) interactions on νCN may depend on the electronic state of the molecule. To test this possibility, herein we combine molecular dynamics simulations and quantum mechanical calculations to assess the effect of H-bonding interactions on the νCN of 5-cyanoindole (5-CNI) in its different electronic states. We find that its C≡N group can form either one H-bond (single-H-bond) or two H-bonds (d-H-bonds) with the solvent molecules and that in the ground electronic state, a single-H-bond can lead νCN to shift either to a higher or lower frequency, depending on its angle, which is consistent with previous studies, whereas the d-H-bonds cause νCN to redshift. However, in its lowest-lying excited electronic state (i.e., S1), which has the characteristics of a charge-transfer state, all H-bonds induce a redshift in νCN, with the d-H-bonds being most effective in this regard.

Allosteric cooperativity between ATP and substrates is a prominent characteristic of the cAMP-dependent catalytic subunit of protein kinase A (PKA-C). This long-range synergistic action is involved in substrate recognition and fidelity, and it may also regulate PKA’s association with regulatory subunits and other binding partners. To date, a complete understanding of this intramolecular mechanism is still lacking. Here, we integrated NMR(Nuclear Magnetic Resonance)-restrained molecular dynamics simulations and a Markov State Model to characterize the free energy landscape and conformational transitions of PKA-C. We found that the apoenzyme populates a broad free energy basin featuring a conformational ensemble of the active state of PKA-C (ground state) and other basins with lower populations (excited states). The first excited state corresponds to a previously characterized inactive state of PKA-C with the αC helix swinging outward. The second excited state displays a disrupted hydrophobic packing around the regulatory (R) spine, with a flipped configuration of the F100 and F102 residues at the αC-β4 loop. We validated the second excited state by analyzing the F100A mutant of PKA-C, assessing its structural response to ATP and substrate binding. While PKA-C F100A preserves its catalytic efficiency with Kemptide, this mutation rearranges the αC-β4 loop conformation, interrupting the coupling of the two lobes and abolishing the allosteric binding cooperativity. The highly conserved αC-β4 loop emerges as a pivotal element to control the synergistic binding of nucleotide and substrate, explaining how mutations or insertions near or within this motif affect the function and drug sensitivity in homologous kinases.

In this paper, we combine an energy decomposition analysis (EDA) scheme with many-body expansion (MBE) to develop a MB-EDA method to study the cooperative and anti-cooperative effects in molecular cluster systems.