arXiv subjects

Christopher J. Stein

Publications and source records attributed to Christopher J. Stein.

At least 19 recordsLinked to original sources

arXiv2026

An embedding method with constant potential boundary conditions

We present a self-consistent field framework for finite embedded quantum-chemical clusters with constant potential boundary conditions. The coupling is realized through an energy-independent self-energy commonly employed in quantum-transport calculations within the wide-band approximation. Starting from the corresponding non-equilibrium Green's function formalism, we derive an analytic expression for the one-particle density matrix update that can be incorporated into conventional Hartree--Fock and density functional theory. The resulting non-Hermitian self-consistent field equations are solved using adapted Pulay-type mixing schemes. Applications to a quasi-periodic hydrogen ring demonstrate that a finite fragment coupled through an optimized self-energy accurately reproduces the polarization response of the extended system, while calculations on a lithium cluster capture metallic charge transfer and fractional occupations under open-boundary conditions. The proposed framework establishes practical grand-canonical boundary conditions for finite quantum-chemical clusters and lays the methodological foundation for quantum embedding methods for electrochemical systems.

physics.chem-ph↗

arXiv2026

Exact and variational identities for free energy differences in strongly coupled open systems

We derive exact identities for open systems connecting two equilibrium endpoints without imposing microscopic reversibility, detailed balance (DB), fluctuation-dissipation structure, or local detailed balance (LDB) on the driven dynamics. The identities express the Hamiltonian of mean force (HMF) free energy differences through exponential moments and an explicit chi-squared overlap between the endpoint marginals. In the frozen-coupling regime, the HMF shift reduces to a bare-system increment and admits a trajectory-level heat-work-reference decomposition. The exact relations then reduce the problem to a scalar-action law. A maximum-entropy construction gives a Bessel-form scalar-action law, independent of the microscopic system, environment, and number of degrees of freedom at the level of the variational reconstruction. This law provides three outputs from the same sampled configurations: the HMF free energy difference, the endpoint-overlap burden, and a Hessian uncertainty estimate. Since many systems in biology, chemistry, physics and engineering violate the underlying assumptions of the standard Jarzynski identity, we validate the framework on a reduced-dimensional model with a non-Liouvillian, phase-space-compressing ramp followed by underdamped Langevin relaxation. The standard Jarzynski work estimator fails for this ramp because phase-space preservation is broken and no compensating Jacobian correction is included, whereas the present endpoint identities recover the exact HMF free energy difference, and the variational construction reproduces it within its local uncertainty.

cond-mat.stat-mech↗

arXiv2026

The BOS-TMC Dataset: DFT Properties of 159k Experimentally Characterized Transition Metal Complexes Spanning Multiple Charge and Spin States

We present the Boston Open-Shell Transition Metal Complex (BOS-TMC) dataset, a set of density functional theory (DFT) properties for 159k experimentally characterized mononuclear transition metal complexes (TMCs) in multiple spin states with a range of formal charges derived from the Cambridge Structural Database (CSD). To curate this set, we carried out an iterative procedure to confidently assign overall TMC charge. From this information, we then obtained properties in up to three spin states, i.e., low-, intermediate-, and high-spin for 3d metals and low- and intermediate-spin for 4d and 5d metals, depending on compatibility with the metal electron configuration, for a total of 343.8k TMC/spin combinations. At odds with prior sets, we preserved experimental heavy-atom coordinates in these structures during optimization. We report all properties using PBE0/def2-TZVP single-point energies on these structures. We introduce a scheme for computing metal-spin-dependent atomization energies, which we report for each TMC. Alongside electronic energies, we report up to seven additional properties including: HOMO, LUMO, HOMO-LUMO gap, atomic partial charges, dipole moments, atomization energies, and spin-splitting energies for a total of over 2.9M TMC-associated properties. For a representative subset of over 10k complexes chosen based on size, we evaluate the sensitivity of computed properties to exchange-correlation (xc) functional choice from a set of twelve xcs spanning rungs of "Jacob's ladder", highlighting hotspots of TMC space that have the greatest uncertainty. In comparison to prior transition-metal datasets, BOS-TMC is both larger and more diverse in terms of charge and spin configurations and, as a result, more diverse in its range of properties. This dataset is expected to provide a high-fidelity foundation for machine-learning model development, DFT benchmarking, and exploration.

physics.chem-ph↗

arXiv2026

Investigating the Electrochemical Double Layer with Quantum-Chemical Simulations and Implicit Solvation Models

We assess the dielectrically consistent reference interaction site model (DRISM) as an implicit electrolyte framework for modeling the electrochemical double layer, and compare it with the Poisson-Boltzmann model and explicit molecular dynamics results from the literature. We use the gold-electrolyte interface as the main test case and analyze solvent and ionic density profiles, the differential capacitance, and the solvation contribution to CO adsorption. The results show a strong sensitivity to the Lennard-Jones parametrization of metal-ion and metal-water interactions. In particular, we find that the default Lorentz-Berthelot mixing rules to be inadequate and lead to excessive Na+ accumulation at the interface, which results in an increase of the differential capacitance at negative electrode potentials. We demonstrate that introducing pair-specific metal-ion parameters yields more symmetric charging behavior and provides greater flexibility. Our findings suggest that using pair-specific parameters, rather than relying on Lorentz-Berthelot mixing rules, improves the accuracy of the model and opens the way for future studies with this improved yet equally performant model.

physics.chem-ph↗

arXiv2025

Exact fluctuation relation for open systems beyond the Zwanzig FEP equation

We develop a fluctuation framework to quantify the free energy difference between two equilibrium states connected by nonequilibrium processes under arbitrary dynamics and system-environment coupling. For an open system described by the Hamiltonian of mean force (HMF), we show that the equilibrium free energy difference between two canonical endpoints can be written as exponential averages of the HMF shift, divided by an explicit factor built from the chi-squared divergence between the initial and final system marginals. These relations hold at the endpoint level and, under an asymptotic equilibration postulate, admit trajectory representations for general driving and coupling protocols. A decomposition of the HMF increment along each trajectory separates the work-like contributions associated with changes in $λ(t)$ and $C(t)$, the heat-like exchange with the environment, and a feedback-like functional defined with respect to the initial protocol. In the frozen-driving regime with a noninteracting reference, the equalities reduce to new FEP-like expressions involving an environment functional and an explicit overlap correction, with the Zwanzig formula recovered as a limiting case. We validate the approach on an open system coupled to an environment and evolved under overdamped Langevin dynamics, where conventional Zwanzig FEP suffers from poor phase-space overlap and slow numerical convergence, while the present trajectory equality closely matches the exact free energy difference over a broad range of coupling strengths.

cond-mat.stat-mech↗

arXiv2025

An improved guess for the variational calculation of charge-transfer excitations in large systems

Charge-transfer excited states are highly relevant for applications in molecular electronics. However, the accurate calculation of these states in large systems is challenging since wave function methods are prohibitively expensive, time-dependent density functional theory with typical functionals is not precise, and the complicated topology of the electronic hypersurface makes the variational convergence to the targeted excited states a difficult task. We address the latter aspect by providing suitable initial guesses which we obtain by two separate constrained algorithms. Combined with subsequent squared-gradient minimization schemes, we demonstrate that OO-DFT calculations can reliably converge to the charge-transfer states of interest even for large molecular systems. We test this approach on two chemically very different supramolecular structures and also analyze the performance of two recently proposed methods for the tuning of the range-separation parameter in time-dependent DFT with range-separated hybrid functionals. Our results demonstrate that with the methods presented here, reliable convergence of charge-transfer excited states can be achieved with variational excited-state DFT methods, while time-dependent DFT calculations with an adequate tuning procedure for the range-separation parameter can provide a computationally efficient initial estimate of the corresponding energies.

physics.chem-ph↗

arXiv2025

Thermodynamic potentials from a probabilistic view on the system-environment interaction energy

In open systems with strong coupling, the interaction energy between the system and the environment is significant, so thermodynamic quantities cannot be reliably obtained by traditional statistical mechanics methods. The Hamiltonian of mean force $\mathcal{H}^{*}_β$ offers an in principle accurate theoretical basis by explicitly accounting for the interaction energy. However, calculating the Hamiltonian of mean force is challenging both theoretically and computationally. We demonstrate that when the condition $\text{Var}_{\mathcal{E}_0} (e^{-β{V}_{\mathcal{SE}}}) = 0$ is met, the dependence of thermodynamic variables can be shifted from $\{P_β(x_{\mathcal{S}}), \mathcal{H}^{*}_β(x_{\mathcal{S}})\}$ to $\{P_β(x_{\mathcal{S}}), P(V_{\mathcal{SE}})\}$. This change simplifies thermodynamic measurements. As a central result, we derive a general equality that holds for arbitrary coupling strengths and from which an inequality follows - aligned with Jensen's inequality applied to the Gibbs-Bogoliubov-Feynman bound. This equality, analogous in importance to the Jarzynski equality, offers deeper insight into free energy differences in strongly coupled systems. Finally, by combining our result with said Jarzynski equality, we derive additional relations that further clarify thermodynamic behavior in strongly coupled open systems.

cond-mat.stat-mech↗

arXiv2025

A probabilistic approach to system-environment coupling

We introduce a unified statistical framework for quantifying system-environment coupling by treating the interaction energy $V_\mathcal{SE}$ as a stochastic variable. Using a reference-particle decomposition, we derive exact, closed-form expressions for the mean and variance of $V_\mathcal{SE}$ in terms of the single-particle density and up to four-body correlation functions. When $V_\mathcal{SE}$ is approximately Gaussian, these two moments suffice to compute the free energy shift of the strongly coupled system. To validate our framework, we ran explicit Monte Carlo simulations of the full system-environment configurations across a range of system sizes, generating reference distributions of the interaction energy $V_\mathcal{SE}$. We then applied our derived analytical formulas to predict these distributions and found excellent agreement in both the weak- and strong-coupling regimes.

physics.chem-ph↗

arXiv2024

Spin parameter optimization for spin-polarized extended tight-binding methods

We present an optimization strategy for atom-specific spin-polarization constants within the spin-polarized GFN2-xTB framework, aiming to enhance the accuracy of molecular simulations. We compare a sequential and global optimization of spin parameters for hydrogen, carbon, nitrogen, oxygen, and fluorine. Sensitivity analysis using Sobol indices guides the identification of the most influential parameters for a given reference dataset, allowing for a nuanced understanding of their impact on diverse molecular properties. In the case of the W4-11 dataset, substantial error reduction was achieved, demonstrating the potential of the optimization. Transferability of the optimized spin-polarization constants over different properties, however, is limited, as we demonstrate by applying the optimized parameters on a set of singlet-triplet gaps in carbenes. Further studies on ionization potentials and electron affinities highlight some inherent limitations of current extended tight-binding methods that can not be resolved by simple parameter optimization. We conclude that the significantly improved accuracy strongly encourages the present re-optimization of the spin-polarization constants, whereas the limited transferability motivates a property-specific optimization strategy.

physics.chem-ph↗

arXiv2024

Benchmarking DFT-based excited-state methods for intermolecular charge-transfer excitations

Intermolecular charge-transfer is a highly important process in biology and energy-conversion applications where generated charges need to be transported over several moieties. However, its theoretical description is challenging since the high accuracy required to describe these excited states must be accessible for calculations on large molecular systems. In this benchmark study, we identify reliable low-scaling computational methods for this task. Our reference results were obtained from highly accurate wavefunction calculations that restrict the size of the benchmark systems. However, the density-functional theory based methods that we identify as accurate can be applied to much larger systems. Since targeting charge-transfer states requires the unambiguous classification of an excited state, we first analyze several charge-transfer descriptors for their reliability concerning intermolecular charge-transfer and single out DCT as an optimal choice for our purposes. In general, best results are obtained for orbital-optimized methods - and among those, IMOM proved to be the most numerically stable variant - but optimally-tuned range-separated hybrid functionals combined with rather small basis sets proved to yield surprisingly good results. This makes these fast calculations attractive for high-throughput screening applications.

physics.chem-ph↗

arXiv2023

Automated, Consistent, and Even-handed Selection of Active Orbital Spaces for Quantum Embedding

A widely used strategy to reduce the computational cost in quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts and an environment that is treated at a lower computational level. The system partitioning is mostly based on localized molecular orbitals. When reaction paths or energy differences are to be calculated, it is crucial to keep the orbital space consistent for all structures. Inconsistencies in the orbital space can lead to unpredictable errors in the potential energy surface. While successful strategies to ensure this consistency have been established for organic and even metal-organic systems, these methods often fail for metal clusters or nanoparticles with a high density of near-degenerate and delocalized molecular orbitals. However, such systems are highly relevant for catalysis. Accurate yet feasible quantum-mechanical ab initio calculations are therefore highly desired. In this work, we present an approach based on the SPADE algorithm that allows us to ensure an automated and consistent partitioning even for systems with delocalized and near-degenerate molecular orbitals and demonstrate the validity of this method for the binding energies of small molecules on transition-metal clusters.

physics.chem-ph↗

arXiv2023

High-throughput ab initio reaction mechanism exploration in the cloud with automated multi-reference validation

Quantum chemical calculations on atomistic systems have evolved into a standard approach to study molecular matter. These calculations often involve a significant amount of manual input and expertise although most of this effort could be automated, which would alleviate the need for expertise in software and hardware accessibility. Here, we present the AutoRXN workflow, an automated workflow for exploratory high-throughput lectronic structure calculations of molecular systems, in which (i) density functional theory methods are exploited to deliver minimum and transition-state structures and corresponding energies and properties, (ii) coupled cluster calculations are then launched for optimized structures to provide more accurate energy and property estimates, and (iii) multi-reference diagnostics are evaluated to back check the coupled cluster results and subject hem to automated multi-configurational calculations for potential multi-configurational cases. All calculations are carried out in a cloud environment and support massive computational campaigns. Key features of all omponents of the AutoRXN workflow are autonomy, stability, and minimum operator interference. We highlight the AutoRXN workflow at the example of an autonomous reaction mechanism exploration of the mode of action of a homogeneous catalyst for the asymmetric reduction of ketones.

physics.chem-ph↗

arXiv2022

A statistical perspective on microsolvation

The lack of a procedure to determine equilibrium thermodynamic properties of a small system interacting with a bath is frequently seen as a weakness of conventional statistical mechanics. A typical example for such a small system is a solute surrounded by an explicit solvation shell. One way to approach this problem is to enclose the small system of interest in a large bath of explicit solvent molecules, considerably larger than the system itself. The explicit inclusion of the solvent degrees of freedom is obviously limited by the available computational resources. A potential remedy to this problem is a microsolvation approach where only a few explicit solvent molecules are considered and surrounded by an implicit solvent bath. Still, the sampling of the solvent degrees of freedom is challenging with conventional grand canonical Monte Carlo methods, since no single chemical potential for the solvent molecules can be defined in the realm of small-system thermodynamics. In this work, a statistical thermodynamic model based on the grand canonical ensemble is proposed that avoids the conventional system size limitations and accurately characterizes the properties of the system of interest subject to the thermodynamic constraints of the bath. We extend an existing microsolvation approach to a generalized multi-bath "micro-statistical" model and show that the previously derived approaches result as a limit of our model. The framework described here is universal and we validate our method numerically for a Lennard-Jones model fluid.

physics.chem-ph↗

arXiv2021

NewtonNet: A Newtonian message passing network for deep learning of interatomic potentials and forces

We report a new deep learning message passing network that takes inspiration from Newton's equations of motion to learn interatomic potentials and forces. With the advantage of directional information from trainable latent force vectors, and physics-infused operators that are inspired by the Newtonian physics, the entire model remains rotationally equivariant, and many-body interactions are inferred by more interpretable physical features. We test NewtonNet on the prediction of several reactive and non-reactive high quality ab initio data sets including single small molecule dynamics, a large set of chemically diverse molecules, and methane and hydrogen combustion reactions, achieving state-of-the-art test performance on energies and forces with far greater data and computational efficiency than other deep learning models.

physics.chem-ph↗

arXiv2020

Semiclassical Dispersion Corrections efficiently improve Multi-Configurational Theory with Short-Range Density-Functional Dynamic Correlation

Multi-configurational wave functions are known to describe electronic structure across a Born-Oppenheimer surface qualitatively correct. However, for quantitative reaction energies, dynamical correlation originating from the many configurations involving excitations out of the restricted orbital space, the active space, must be considered. Standard procedures involve approximations that eventually limit the ultimate accuracy achievable (most prominently, multi-reference perturbation theory). At the same time, the computational cost increase dramatically due to the necessity to obtain higher-order reduced density matrices. It is this disproportion that leads us here to propose a MC-srDFT-D hybrid approach of semiclassical dispersion (D) corrections to cover long-range dynamical correlation in a multi-configurational (MC) wave function theory which includes short-range (sr) dynamical correlation by density functional theory (DFT) without double counting. We demonstrate that the reliability of this approach is very good (at negligible cost), especially when considering that standard second-order multi-reference perturbation theory usually overestimates dispersion interactions.

physics.chem-ph↗

arXiv2019

The Poisson-Boltzmann model for implicit solvation of electrolyte solutions: Quantum chemical implementation and assessment via Sechenov coefficients

We present the theory and implementation of a Poisson-Boltzmann implicit solvation model for electrolyte solutions. This model can be combined with arbitrary electronic structure methods that provide an accurate charge density of the solute. A hierarchy of approximations for this model includes a linear approximation for weak electrostatic potentials, finite size of the mobile electrolyte ions and a Stern-layer correction. Recasting the Poisson-Boltzmann equations into Euler-Lagrange equations then significantly simplifies the derivation of the free energy of solvation for these approximate models. The parameters of the model are then either fit directly to experimental observables, e.g. the finite ion size, or optimized for agreement with experimental results. Experimental data for this optimization is available in the form of Sechenov coefficients that describe the linear dependence of the salting-out effect of solutes with respect to the electrolyte concentration. In the final part we rationalize the qualitative disagreement of the finite ion size modification to the Poisson-Boltzmann model with experimental observations by taking into account the electrolyte concentration dependence of the Stern layer. A route towards a revised model that captures the experimental observations while including the finite ion size effects is then outlined. This implementation paves the way for the study of electrochemical and electrocatalytic processes of molecules and cluster models with accurate electronic structure methods.

physics.comp-ph↗

arXiv2019

autoCAS: a program for fully automated multi-configurational calculations

We present our implementation autoCAS for fully automated multi-configurational calculations, which we also make available free of charge on our webpages. The graphical user interface of autoCAS connects a general electronic structure program with a density matrix renormalization group program to carry out our recently introduced automated active space selection protocol for multi-configurational calculations [J. Chem. Theory Comput., 2016, 12, 1760]. Next to this active space selection, autoCAS carries out several steps of multi-configurational calculations so that only a minimal input is required to start them, comparable to that of a standard Kohn-Sham density functional theory calculation, so that black-box multi-configurational calculations become feasible. Furthermore, we introduce a new extension to the selection algorithm that facilitates automated selections for molecules with large valence orbital spaces consisting of several hundred orbitals.

physics.chem-ph↗

arXiv2019

Optimization of highly excited matrix product states with an application to vibrational spectroscopy

Configuration-interaction-type calculations on electronic and vibrational structure are often the method of choice for the reliable approximation of many-particle wave functions and energies. The exponential scaling, however, limits their application range. An efficient approximation to the full configuration interaction solution can be obtained with the density matrix renormalization group (DMRG) algorithm without a restriction to a predefined excitation level. In a standard DMRG implementation, however, excited states are calculated with a ground-state optimization in the space orthogonal to all lower lying wave function solutions. A trivial parallelization is therefore not possible and the calculation of highly excited states becomes prohibitively expensive, especially in regions with a high density of states. Here, we introduce two variants of the density matrix renormalization group algorithm that allow us to target directly specific energy regions and therefore highly excited states. The first one, based on shift-and-invert techniques, is particularly efficient for low-lying states, but is not stable in regions with a high density of states. The second one, based on the folded auxiliary operator, is less efficient, but more accurate in targeting high-energy states. We apply the algorithm to the solution of the nuclear Schroedinger equation, but emphasize that it can be applied to the diagonalization of general Hamiltonians as well, such as the electronic Coulomb Hamiltonian to address X-ray spectra. In combination with several root-homing algorithms and a stochastic sampling of the determinant space, excited states of interest can be adequately tracked and analyzed during the optimization. We demonstrate that we can accurately calculate prominent spectral features of large molecules such as the sarcosyn-glycine dipeptide.

physics.comp-ph↗