Embedded density functional theory for covalently bonded and strongly interacting subsystems

Integrated Multiscale Multilevel Approach to Open Shell Molecular Systems

We present a novel multiscale approach to study the electronic structure of open shell molecular systems embedded in an external environment. The method is based on the coupling of multilevel Hartree-Fock (MLHF) and Density Functional Theory (MLDFT), suitably extended to the unrestricted formalism, to Molecular Mechanics (MM) force fields (FF). Within the ML region, the system is divided into active and inactive parts, thus describing the most relevant interactions (electrostatic, polarization, and Pauli repulsion) at the quantum level. The surrounding MM part, which is formulated in terms of nonpolarizable or polarizable FFs, permits a physically consistent treatment of long-range electrostatics and polarization effects. The approach is extended to the calculation of hyperfine coupling constants and applied to selected nitroxyl radicals in an aqueous solution.

Characterization of excited states in time-dependent density functional theory using localized molecular orbitals

Localized molecular orbitals are often used for the analysis of chemical bonds, but they can also serve to efficiently and comprehensibly compute linear response properties. While conventional canonical molecular orbitals provide an adequate basis for the treatment of excited states, a chemically meaningful identification of the different excited-state processes is difficult within such a delocalized orbital basis. In this work, starting from an initial set of supermolecular canonical molecular orbitals, we provide a simple one-step top-down embedding procedure for generating a set of orbitals, which are localized in terms of the supermolecule but delocalized over each subsystem composing the supermolecule. Using an orbital partitioning scheme based on such sets of localized orbitals, we further present a procedure for the construction of local excitations and charge-transfer states within the linear response framework of time-dependent density functional theory (TDDFT). This procedure provides direct access to approximate diabatic excitation energies and, under the Tamm-Dancoff approximation, also their corresponding electronic couplings-quantities that are of primary importance in modeling energy transfer processes in complex biological systems. Our approach is compared with a recently developed diabatization procedure based on subsystem TDDFT using projection operators, which leads to a similar set of working equations. Although both of these methods differ in the general localization strategies adopted and the type of basis functions (Slaters vs Gaussians) employed, an overall decent agreement is obtained.

Structure optimization with stochastic density functional theory

Linear-scaling techniques for Kohn-Sham density functional theory are essential to describe the ground state properties of extended systems. Still, these techniques often rely on the localization of the density matrix or accurate embedding approaches, limiting their applicability. In contrast, stochastic density functional theory (sDFT) achieves linear- and sub-linear scaling by statistically sampling the ground state density without relying on embedding or imposing localization. In return, ground state observables, such as the forces on the nuclei, fluctuate in sDFT, making optimizing the nuclear structure a highly non-trivial problem. In this work, we combine the most recent noise-reduction schemes for sDFT with stochastic optimization algorithms to perform structure optimization within sDFT. We compare the performance of the stochastic gradient descent approach and its variations (stochastic gradient descent with momentum) with stochastic optimization techniques that rely on the Hessian, such as the stochastic Broyden-Fletcher-Goldfarb-Shanno algorithm. We further provide a detailed assessment of the computational efficiency and its dependence on the optimization parameters of each method for determining the ground state structure of bulk silicon with varying supercell dimensions.

Initial Maximum Overlap Method Embedded with Extremely Localized Molecular Orbitals for Core-Ionized States of Large Systems

Despite great advances in X-ray absorption spectroscopy for the investigation of small molecule electronic structure, the application to biosystems of experimental techniques developed within this research field remains a challenge. To partially circumvent the problem, users resort to theoretical methods to interpret or predict the X-ray absorption spectra of large molecules. To accomplish this task, only low-cost computational strategies can be exploited. For this reason, some of them are single Slater determinant wavefunction approaches coupled with multiscale embedding techniques designed to treat large systems of biological interest. Therefore, in this work, we propose to apply the recently developed IMOM/ELMO embedding method to the determination of core-ionized states. The IMOM/ELMO technique resulted from the combination of the single Slater determinant Δself-consistent-field-initial maximum overlap approach (ΔSCF-IMOM) with the QM/ELMO (quantum mechanics/extremely localized molecular orbital) embedding strategy, a method where only the chemically relevant region of the examined system is treated at fully quantum chemical level, while the rest is described through transferred and frozen extremely localized molecular orbitals (ELMOs). The IMOM/ELMO technique was initially validated by computing core-ionization energies for small molecules, and it was afterwards exploited to study larger biosystems. The obtained results are in line with those reported in previous studies that applied alternative ΔSCF approaches. This makes us envisage a possible future application of the proposed method to the interpretation of X-ray absorption spectra of large molecules.

Molecular Interactions From the Density Functional Theory for Chemical Reactivity: The Interaction Energy Between Two-Reagents

Reactivity descriptors indicate where a reagent is most reactive and how it is most likely to react. However, a reaction will only occur when the reagent encounters a suitable reaction partner. Determining whether a pair of reagents is well-matched requires developing reactivity rules that depend on both reagents. This can be achieved using the expression for the minimum-interaction-energy obtained from the density functional reactivity theory. Different terms in this expression will be dominant in different circumstances; depending on which terms control the reactivity, different reactivity indicators will be preferred.

Environment Effects on X-Ray Absorption Spectra With Quantum Embedded Real-Time Time-Dependent Density Functional Theory Approaches

In this work we implement the real-time time-dependent block-orthogonalized Manby-Miller embedding (rt-BOMME) approach alongside our previously developed real-time frozen density embedding time-dependent density functional theory (rt-TDDFT-in-DFT FDE) code, and investigate these methods' performance in reproducing X-ray absorption spectra (XAS) obtained with standard rt-TDDFT simulations, for model systems comprised of solvated fluoride and chloride ions ([X@( H 2 O ) 8 - , X = F, Cl). We observe that for ground-state quantities such as core orbital energies, the BOMME approach shows significantly better agreement with supermolecular results than FDE for the strongly interacting fluoride system, while for chloride the two embedding approaches show more similar results. For the excited states, we see that while FDE (constrained not to have the environment densities relaxed in the ground state) is in good agreement with the reference calculations for the region around the K and L1 edges, and is capable of reproducing the splitting of the 1s1 (n + 1)p1 final states (n + 1 being the lowest virtual p orbital of the halides), it by and large fails to properly reproduce the 1s1 (n + 2)p1 states and misses the electronic states arising from excitation to orbitals with important contributions from the solvent. The BOMME results, on the other hand, provide a faithful qualitative representation of the spectra in all energy regions considered, though its intrinsic approximation of employing a lower-accuracy exchange-correlation functional for the environment induces non-negligible shifts in peak positions for the excitations from the halide to the environment. Our results thus confirm that QM/QM embedding approaches are viable alternatives to standard real-time simulations of X-ray absorption spectra of species in complex or confined environments.

Plasmon Couplings from Subsystem Time-Dependent Density Functional Theory

Many applications in plasmonics are related to the coupling between metallic nanoparticles (MNPs) or between an emitter and a MNP. The theoretical analysis of such a coupling is thus of fundamental importance to analyze the plasmonic behavior and to design new systems. While classical methods neglect quantum and spill-out effects, time-dependent density functional theory (TD-DFT) considers all of them and with Kohn-Sham orbitals delocalized over the whole system. Thus, within TD-DFT, no definite separation of the subsystems (the single MNP or the emitter) and their couplings is directly available. This important feature is obtained here using the subsystem formulation of TD-DFT, which has been originally developed in the context of weakly interacting organic molecules. In subsystem TD-DFT, interacting MNPs are treated independently, thus allowing us to compute the plasmon couplings directly from the subsystem TD-DFT transition densities. We show that subsystem TD-DFT, as well as a simplified version of it in which kinetic contributions are neglected, can reproduce the reference TD-DFT calculations for gap distances greater than about 6 Å or even smaller in the case of hybrid plasmonic systems (i.e., molecules interacting with MNPs). We also show that the subsystem TD-DFT can be also used as a tool to analyze the impact of charge-transfer effects.

Initial Maximum Overlap Method for Large Systems by the Quantum Mechanics/Extremely Localized Molecular Orbital Embedding Technique

Quantum chemistry offers a large variety of methods to treat excited states. Many of them are based on a multireference wave function ansatz and are therefore characterized by an intrinsic complexity and high computational costs. To overcome these drawbacks and also some limitations of simpler single-reference approaches (e.g., configuration interaction singles and time-dependent density functional theory), the single-determinant Δself-consistent field-initial maximum overlap method (ΔSCF-IMOM) has been proposed. This strategy substitutes the aufbau principle with a criterion that occupies molecular orbitals at successive SCF iterations on the basis of their maximum overlap with a proper set of guess orbitals for the target excited state. In this way, it prevents the SCF process to collapse to the ground state wave function and provides excited state single Slater determinant solutions to the SCF equations. Here, we propose to extend the applicability of the IMOM to the treatment of localized excited states of large systems. To accomplish this task, we coupled it with the QM/ELMO (quantum mechanics/extremely localized molecular orbitals) strategy, a quantum mechanical embedding method in which the most chemically relevant part of the system is treated with traditional quantum chemical approaches, while the rest is described by extremely localized molecular orbitals transferred from recently constructed libraries or proper model molecules. After presenting the theoretical foundations of the new IMOM/ELMO technique, in this paper, we will show and discuss the results of preliminary test calculations carried out on both model systems (i.e., decanoic acid, decene, decapentaene, and solvated acrolein) and a system of biological interest (flavin mononucleotide in the flavodoxin protein). We observed that, for localized excited states, the new IMOM/ELMO method provides reliable results, and it reproduces the outcomes of fully IMOM calculations within the chemical accuracy threshold (i.e., 0.043 eV) by including only a limited number of atoms in the QM region. Furthermore, the first application of our embedding technique to a larger biological system gave completely plausible results in line with those obtained through more traditional quantum mechanical methods, thus opening the possibility of using the new approach in future investigations of photobiology problems.

Stochastic density functional theory: Real- and energy-space fragmentation for noise reduction

Stochastic density functional theory (sDFT) is becoming a valuable tool for studying ground-state properties of extended materials. The computational complexity of describing the Kohn-Sham orbitals is replaced by introducing a set of random (stochastic) orbitals leading to linear and often sub-linear scaling of certain ground-state observables at the account of introducing a statistical error. Schemes to reduce the noise are essential, for example, for determining the structure using the forces obtained from sDFT. Recently, we have introduced two embedding schemes to mitigate the statistical fluctuations in the electron density and resultant forces on the nuclei. Both techniques were based on fragmenting the system either in real space or slicing the occupied space into energy windows, allowing for a significant reduction in the statistical fluctuations. For chemical accuracy, further reduction of the noise is required, which could be achieved by increasing the number of stochastic orbitals. However, the convergence is relatively slow as the statistical error scales as 1/N_χ according to the central limit theorem, where N_χ is the number of random orbitals. In this paper, we combined the embedding schemes mentioned above and introduced a new approach that builds on overlapped fragments and energy windows. The new approach significantly lowers the noise for ground-state properties, such as the electron density, total energy, and forces on the nuclei, as demonstrated for a G-center in bulk silicon.

Environmental Effects with Frozen-Density Embedding in Real-Time Time-Dependent Density Functional Theory Using Localized Basis Functions

Frozen-density embedding (FDE) represents a versatile embedding scheme to describe the environmental effect on electron dynamics in molecular systems. The extension of the general theory of FDE to the real-time time-dependent Kohn-Sham method has previously been presented and implemented in plane waves and periodic boundary conditions [Pavanello, M.; J. Chem. Phys. 2015, 142, 154116]. In the current paper, we extend our recent formulation of the real-time time-dependent Kohn-Sham method based on localized basis set functions and developed within the Psi4NumPy framework to the FDE scheme. The latter has been implemented in its "uncoupled" flavor (in which the time evolution is only carried out for the active subsystem, while the environment subsystems remain at their ground state), using and adapting the FDE implementation already available in the PyEmbed module of the scripting framework PyADF. The implementation was facilitated by the fact that both Psi4NumPy and PyADF, being native Python API, provided an ideal framework of development using the Python advantages in terms of code readability and reusability. We employed this new implementation to investigate the stability of the time-propagation procedure, which is based on an efficient predictor/corrector second-order midpoint Magnus propagator employing an exact diagonalization, in combination with the FDE scheme. We demonstrate that the inclusion of the FDE potential does not introduce any numerical instability in time propagation of the density matrix of the active subsystem, and in the limit of the weak external field, the numerical results for low-lying transition energies are consistent with those obtained using the reference FDE calculations based on the linear-response TDDFT. The method is found to give stable numerical results also in the presence of a strong external field inducing nonlinear effects. Preliminary results are reported for high harmonic generation (HHG) of a water molecule embedded in a small water cluster. The effect of the embedding potential is evident in the HHG spectrum reducing the number of the well-resolved high harmonics at high energy with respect to the free water. This is consistent with a shift toward lower ionization energy passing from an isolated water molecule to a small water cluster. The computational burden for the propagation step increases approximately linearly with the size of the surrounding frozen environment. Furthermore, we have also shown that the updating frequency of the embedding potential may be significantly reduced, much less than one per time step, without jeopardizing the accuracy of the transition energies.

Localized Molecular Orbital-Based Embedding Scheme for Correlated Methods

Embedding strategies currently provide the best compromise between accuracy and computational cost in modeling chemical properties and processes of large and complex systems. In this framework, different methods have been proposed all over the years, from the very popular QM/MM approaches to the more recent and very promising density matrix and density functional embedding techniques. Here, we present a further development of the quantum mechanics/extremely localized molecular orbital technique (QM/ELMO) method, a recently proposed multiscale embedding strategy in which the chemically active region of the investigated system is treated at a fully quantum mechanical level, while the rest is described by frozen extremely localized molecular orbitals previously transferred from proper libraries or tailor-made model molecules. In particular, in this work we discuss and assess in detail the extension of the QM/ELMO approach to density functional theory and post-Hartree-Fock techniques by evaluating its performances when it is used to describe chemical reactions, bond dissociations, and intermolecular interactions. The preliminary test calculations have shown that, in the investigated cases, the new embedding strategy enables the results of the corresponding fully quantum mechanical computations to be reproduced within chemical accuracy in almost all the cases but with a significantly reduced computational cost, especially when correlated post-Hartree-Fock strategies are used to describe the quantum mechanical subsystem. In light of the obtained results, we already envisage the future application of the new correlated QM/ELMO techniques to the investigation of more challenging problems, such as the modeling of enzyme catalysis, the study of excited states of biomolecules, and the refinement of macromolecular X-ray crystal structures.

Stochastic embedding DFT: Theory and application to p-nitroaniline in water

Over this past decade, we combined the idea of stochastic resolution of identity with a variety of electronic structure methods. In our stochastic Kohn-Sham density functional theory (DFT) method, the density is an average over multiple stochastic samples, with stochastic errors that decrease as the inverse square root of the number of sampling orbitals. Here, we develop a stochastic embedding density functional theory method (se-DFT) that selectively reduces the stochastic error (specifically on the forces) for a selected subsystem(s). The motivation, similar to that of other quantum embedding methods, is that for many systems of practical interest, the properties are often determined by only a small subsystem. In stochastic embedding DFT, two sets of orbitals are used: a deterministic one associated with the embedded subspace and the rest, which is described by a stochastic set. The method agrees exactly with deterministic calculations in the limit of a large number of stochastic samples. We apply se-DFT to study a p-nitroaniline molecule in water, where the statistical errors in the forces on the system (the p-nitroaniline molecule) are reduced by an order of magnitude compared with nonembedding stochastic DFT.

Energy window stochastic density functional theory

Linear scaling density functional theory is important for understanding electronic structure properties of nanometer scale systems. Recently developed stochastic density functional theory can achieve linear or even sublinear scaling for various electronic properties without relying on the sparsity of the density matrix. The basic idea relies on projecting stochastic orbitals onto the occupied space by expanding the Fermi-Dirac operator and repeating this for N_χ stochastic orbitals. Often, a large number of stochastic orbitals are required to reduce the statistical fluctuations (which scale as N_χ ^-1/2) below a tolerable threshold. In this work, we introduce a new stochastic density functional theory that can efficiently reduce the statistical fluctuations for certain observable and can also be integrated with an embedded fragmentation scheme. The approach is based on dividing the occupied space into energy windows and projecting the stochastic orbitals with a single expansion onto all windows simultaneously. This allows for a significant reduction of the noise as illustrated for bulk silicon with a large supercell. We also provide theoretical analysis to rationalize why the noise can be reduced only for a certain class of ground state properties, such as the forces and electron density.

Projection-Based Wavefunction-in-DFT Embedding

Complex chemical systems present challenges to electronic structure theory stemming from large system sizes, subtle interactions, coupled dynamical time scales, and electronically nonadiabatic effects. New methods are needed to perform reliable, rigorous, and affordable electronic structure calculations for simulating the properties and dynamics of such systems. This Account reviews projection-based quantum embedding for electronic structure, which provides a formally exact method for density functional theory (DFT) embedding. The method also provides a rigorous and accurate approach for describing a small part of a chemical system at the level of a correlated wavefunction (WF) method while the remainder of the system is described at the level of DFT. A key advantage of projection-based embedding is that it can be formulated in terms of an extremely simple level-shift projection operator, which eliminates the need for any optimized effective potential calculation or kinetic energy functional approximation while simultaneously ensuring that no extra programming is needed to perform WF-in-DFT embedding with an arbitrary WF method. The current work presents the theoretical underpinnings of projection-based embedding, describes use of the method for combining wavefunction and density functional theories, and discusses technical refinements that have improved the applicability and robustness of the method. Applications of projection-based WF-in-DFT embedding are also reviewed, with particular focus on recent work on transition-metal catalysis, enzyme reactivity, and battery electrolyte decomposition. In particular, we review the application of projection-based embedding for the prediction of electrochemical potentials and reaction pathways in a Co-centered hydrogen evolution catalyst. Projection-based WF-in-DFT calculations are shown to provide quantitative accuracy while greatly reducing the computational cost compared with a reference coupled cluster calculation on the full system. Additionally, projection-based WF-in-DFT embedding is used to study the mechanism of citrate synthase; it is shown that projection-based WF-in-DFT largely eliminates the sensitivity of the potential energy landscape to the employed DFT exchange-correlation functional. Finally, we demonstrate the use of projection-based WF-in-DFT to study electron transfer reactions associated with battery electrolyte decomposition. Projection-based WF-in-DFT embedding is used to calculate the oxidation potentials of neat ethylene carbonate (EC), neat dimethyl carbonate (DMC), and 1:1 mixtures of EC and DMC in order to overcome qualitative inaccuracies in the electron densities and ionization energies obtained from conventional DFT methods. By further embedding the WF-in-DFT description in a molecular mechanics point-charge environment, this work enables an explicit description of the solvent and ensemble averaging of the solvent configurations. Looking forward, we anticipate continued refinement of the projection-based embedding methodology as well as its increasingly widespread application in diverse areas of chemistry, biology, and materials science.

Computational Approach to Molecular Catalysis by 3d Transition Metals: Challenges and Opportunities

Computational chemistry provides a versatile toolbox for studying mechanistic details of catalytic reactions and holds promise to deliver practical strategies to enable the rational in silico catalyst design. The versatile reactivity and nontrivial electronic structure effects, common for systems based on 3d transition metals, introduce additional complexity that may represent a particular challenge to the standard computational strategies. In this review, we discuss the challenges and capabilities of modern electronic structure methods for studying the reaction mechanisms promoted by 3d transition metal molecular catalysts. Particular focus will be placed on the ways of addressing the multiconfigurational problem in electronic structure calculations and the role of expert bias in the practical utilization of the available methods. The development of density functionals designed to address transition metals is also discussed. Special emphasis is placed on the methods that account for solvation effects and the multicomponent nature of practical catalytic systems. This is followed by an overview of recent computational studies addressing the mechanistic complexity of catalytic processes by molecular catalysts based on 3d metals. Cases that involve noninnocent ligands, multicomponent reaction systems, metal-ligand and metal-metal cooperativity, as well as modeling complex catalytic systems such as metal-organic frameworks are presented. Conventionally, computational studies on catalytic mechanisms are heavily dependent on the chemical intuition and expert input of the researcher. Recent developments in advanced automated methods for reaction path analysis hold promise for eliminating such human-bias from computational catalysis studies. A brief overview of these approaches is presented in the final section of the review. The paper is closed with general concluding remarks.

Communication: Density functional theory embedding with the orthogonality constrained basis set expansion procedure

Density functional theory (DFT) embedding approaches have generated considerable interest in the field of computational chemistry because they enable calculations on larger systems by treating subsystems at different levels of theory. To circumvent the calculation of the non-additive kinetic potential, various projector methods have been developed to ensure the orthogonality of molecular orbitals between subsystems. Herein the orthogonality constrained basis set expansion (OCBSE) procedure is implemented to enforce this subsystem orbital orthogonality without requiring a level shifting parameter. This scheme is a simple alternative to existing parameter-free projector-based schemes, such as the Huzinaga equation. The main advantage of the OCBSE procedure is that excellent convergence behavior is attained for DFT-in-DFT embedding without freezing any of the subsystem densities. For the three chemical systems studied, the level of accuracy is comparable to or higher than that obtained with the Huzinaga scheme with frozen subsystem densities. Allowing both the high-level and low-level DFT densities to respond to each other during DFT-in-DFT embedding calculations provides more flexibility and renders this approach more generally applicable to chemical systems. It could also be useful for future extensions to embedding approaches combining wavefunction theories and DFT.

Directly patching high-level exchange-correlation potential based on fully determined optimized effective potentials

The key element in Kohn-Sham (KS) density functional theory is the exchange-correlation (XC) potential. We recently proposed the exchange-correlation potential patching (XCPP) method with the aim of directly constructing high-level XC potential in a large system by patching the locally computed, high-level XC potentials throughout the system. In this work, we investigate the patching of the exact exchange (EXX) and the random phase approximation (RPA) correlation potentials. A major challenge of XCPP is that a cluster's XC potential, obtained by solving the optimized effective potential equation, is only determined up to an unknown constant. Without fully determining the clusters' XC potentials, the patched system's XC potential is "uneven" in the real space and may cause non-physical results. Here, we developed a simple method to determine this unknown constant. The performance of XCPP-RPA is investigated on three one-dimensional systems: H₂₀, H₁₀Li₈, and the stretching of the H₁₉-H bond. We investigated two definitions of EXX: (i) the definition based on the adiabatic connection and fluctuation dissipation theorem (ACFDT) and (ii) the Hartree-Fock (HF) definition. With ACFDT-type EXX, effective error cancellations were observed between the patched EXX and the patched RPA correlation potentials. Such error cancellations were absent for the HF-type EXX, which was attributed to the fact that for systems with fractional occupation numbers, the integral of the HF-type EXX hole is not -1. The KS spectra and band gaps from XCPP agree reasonably well with the benchmarks as we make the clusters large.

Correcting density-driven errors in projection-based embedding

Projection-based embedding provides a simple and numerically robust framework for multiscale wavefunction-in-density-functional-theory (WF-in-DFT) calculations. The approach works well when the approximate DFT is sufficiently accurate to describe the energetics of the low-level subsystem and the coupling between subsystems. It is also necessary that the low-level DFT produces a qualitatively reasonable description of the total density, and in this work, we study model systems where delocalization error prevents this from being the case. We find substantial errors in embedding calculations on open-shell doublet systems in which self-interaction errors cause spurious delocalization of the singly occupied orbital. We propose a solution to this error by evaluating the DFT energy using a more accurate self-consistent density, such as that of Hartree-Fock (HF) theory. These so-called WF-in-(HF-DFT) calculations show excellent convergence towards full-system wavefunction calculations.

Point charge embedding for ONIOM excited states calculations

Hybrid quantum mechanical methods can assist in the interpretation and prediction of the electronic spectra of large molecular structures. In this work, we study the performance of the ONIOM (Our own N-layered Integrated molecular Orbital molecular Mechanics) hybrid method for the calculation of transition energies and oscillator strengths by embedding the core region in a field of fixed point charges. These charges introduce polarization effects from the substituent groups to the core region. We test various charge definitions, with particular attention to the issue of overpolarization near the boundary between layers. To minimize this issue, we fit the charges on the electrostatic potential of the entire structure in the presence of the link atoms used to cap dangling bonds. We propose two constrained fitting strategies: one that produces an average set of charges common to both model system calculations, EE(L1), and one that produces two separate sets of embedding charges, EE(L2). The results from our tests show that indeed electronic embedding with constrained-fitted charges tends to improve the performance of ONIOM compared to non-embedded calculations. However, the EE(L2) charges work best for transition energies, and the EE(L1) charges work best for oscillator strengths. This may be an indication that fixed point charges do not have enough flexibility to adapt to each system, and other effects (e.g., polarization of the embedding field) may be necessary.

Atomic Spectral Methods for Ab Initio Molecular Electronic Energy Surfaces: Transitioning From Small-Molecule to Biomolecular-Suitable Approaches

Continuing attention has addressed incorportation of the electronically dynamical attributes of biomolecules in the largely static first-generation molecular-mechanical force fields commonly employed in molecular-dynamics simulations. We describe here a universal quantum-mechanical approach to calculations of the electronic energy surfaces of both small molecules and large aggregates on a common basis which can include such electronic attributes, and which also seems well-suited to adaptation in ab initio molecular-dynamics applications. In contrast to the more familiar orbital-product-based methodologies employed in traditional small-molecule computational quantum chemistry, the present approach is based on an "ex-post-facto" method in which Hamiltonian matrices are evaluated prior to wave function antisymmetrization, implemented here in the support of a Hilbert space of orthonormal products of many-electron atomic spectral eigenstates familiar from the van der Waals theory of long-range interactions. The general theory in its various forms incorporates the early semiempirical atoms- and diatomics-in-molecules approaches of Moffitt, Ellison, Tully, Kuntz, and others in a comprehensive mathematical setting, and generalizes the developments of Eisenschitz, London, Claverie, and others addressing electron permutation symmetry adaptation issues, completing these early attempts to treat van der Waals and chemical forces on a common basis. Exact expressions are obtained for molecular Hamiltonian matrices and for associated energy eigenvalues as sums of separate atomic and interaction-energy terms, similar in this respect to the forms of classical force fields. The latter representation is seen to also provide a long-missing general definition of the energies of individual atoms and of their interactions within molecules and matter free from subjective additional constraints. A computer code suite is described for calculations of the many-electron atomic eigenspectra and the pairwise-atomic Hamiltonian matrices required for practical applications. These matrices can be retained as functions of scalar atomic-pair separations and employed in assembling aggregate Hamiltonian matrices, with Wigner rotation matrices providing analytical representations of their angular degrees of freedom. In this way, ab initio potential energy surfaces are obtained in the complete absence of repeated evaluations and transformations of the one- and two-electron integrals at different molecular geometries required in most ab inito molecular calculations, with large Hamiltonian matrix assembly simplified and explicit diagonalizations avoided employing partitioning and Brillouin-Wigner or Rayleigh-Schrödinger perturbation theory. Illustrative applications of the important components of the formalism, selected aspects of the scaling of the approach, and aspects of "on-the-fly" interfaces with Monte Carlo and molecular-dynamics methods are described in anticipation of subsequent applications to biomolecules and other large aggregates.

A Projector-Embedding Approach for Multiscale Coupled-Cluster Calculations Applied to Citrate Synthase

Projector-based embedding has recently emerged as a robust multiscale method for the calculation of various electronic molecular properties. We present the coupling of projector embedding with quantum mechanics/molecular mechanics modeling and apply it for the first time to an enzyme-catalyzed reaction. Using projector-based embedding, we combine coupled-cluster theory, density-functional theory (DFT), and molecular mechanics to compute energies for the proton abstraction from acetyl-coenzyme A by citrate synthase. By embedding correlated ab initio methods in DFT we eliminate functional sensitivity and obtain high-accuracy profiles in a procedure that is straightforward to apply.

Multi-state extrapolation of UV/Vis absorption spectra with QM/QM hybrid methods

In this work, we present a simple approach to simulate absorption spectra from hybrid QM/QM calculations. The goal is to obtain reliable spectra for compounds that are too large to be treated efficiently at a high level of theory. The present approach is based on the extrapolation of the entire absorption spectrum obtained by individual subcalculations. Our program locates the main spectral features in each subcalculation, e.g., band peaks and shoulders, and fits them to Gaussian functions. Each Gaussian is then extrapolated with a formula similar to that of ONIOM (Our own N-layered Integrated molecular Orbital molecular Mechanics). However, information about individual excitations is not necessary so that difficult state-matching across subcalculations is avoided. This multi-state extrapolation thus requires relatively low implementation effort while affording maximum flexibility in the choice of methods to be combined in the hybrid approach. The test calculations show the efficacy and robustness of this methodology in reproducing the spectrum computed for the entire molecule at a high level of theory.