Configuration interaction based on constrained density functional theory: a multireference method

Using Adiabatic Energy Splitting To Compute Dexter Energy Transfer Couplings

Dexter energy transfer and transport (DET) are of broad interest in energy science, and DET rates depend on electronic couplings between donor and acceptor species. DET couplings are challenging to compute since they originate from both one- and two-particle interactions, and the strength of this interaction drops approximately exponentially with donor-acceptor distances. Using adiabatic energy splitting to compute DET couplings has advantages because adiabatic states can be calculated directly using conventional quantum chemical methods. We describe a minimum energy splitting method to compute the DET coupling by altering molecular geometries to drive the systems into a T1/T2 energy quasi-degenerate-activated DA complex. We explore the accuracy of various quantum chemical approaches to calculate the Dexter couplings.

Approximate Functionals for Multistate Density Functional Theory

Recently Lu and Gao [J. Phys. Chem. Lett. 2022, 13 (33), 7762-7769] published a new, rigorous density functional theory for excited states and proved that the projection of the kinetic and electron-repulsion operators into the subspace of the lowest electronic states are a universal functional of the matrix density D(r). This is the first attempt to find an approximation to the multistate universal functional F [ D ( r ) ] . It is shown that F (i) does not explicitly depend on the number of electronic states and (ii) is an analytic matrix functional. The Thomas-Fermi-Dirac-von Weizsäcker model and the correlation energy of the homogeneous electron gas are turned into matrix functionals guided by two principles: that each matrix functional should transform properly under basis set transformations and that the ground state functional should be recovered for a single electronic state. Lieb-Oxford-like bounds on the average kinetic and electron-repulsion energies in the subspace are given. When evaluated on the numerically exact matrix density of LiF, this simple approximation reproduces the matrix elements of the electron-repulsion operator in the basis of the exact eigenstates accurately for all bond lengths. In particular the off-diagonal elements of the effective Hamiltonian that come from the interactions of different electronic states can be calculated with the same or better accuracy than the diagonal elements. Unsurprisingly, the largest error comes from the kinetic energy functional. More exact conditions that constrain the functional form of F are needed to go beyond the local density approximation.

A fast and smooth one-electron approach for investigating charge transfer states and D1-D0 crossings for systems with odd numbers of electrons

We propose an efficient version of ensemble Hartree-Fock/density functional theory to calculate a set of two charge-transfer states for systems with odd-numbers of electrons. The approach does require definitions of donor/acceptor fragments; however, the approach is not very sensitive to such definitions-even in the limit of very strong electronic coupling. The key ansatz is that, by mandating that the vector space spanned by the active orbitals projects equally onto the donor and acceptor fragments, such a constraint eliminates all intra-molecular local excitations and makes it far easier to generate potential energy surfaces that are smooth over a wide region of configuration space. The method is fast, working with only two electron configurations, and should be useful for ab initio non-adiabatic dynamics in the near future.

Probing Nonadiabaticity of Proton-Coupled Electron Transfer in Ribonucleotide Reductase

The enzyme ribonucleotide reductase, which is essential for DNA synthesis, initiates the conversion of ribonucleotides to deoxyribonucleotides via radical transfer over a 32 Å pathway composed of proton-coupled electron transfer (PCET) reactions. Previously, the first three PCET reactions in the α subunit were investigated with hybrid quantum mechanical/molecular mechanical (QM/MM) free energy simulations. Herein, the fourth PCET reaction in this subunit between C439 and guanosine diphosphate (GDP) is simulated and found to be slightly exoergic with a relatively high free energy barrier. To further elucidate the mechanisms of all four PCET reactions, we analyzed the vibronic and electron-proton nonadiabaticities. This analysis suggests that interfacial PCET between Y356 and Y731 is vibronically and electronically nonadiabatic, whereas PCET between Y731 and Y730 and between C439 and GDP is fully adiabatic and PCET between Y730 and C439 is in the intermediate regime. These insights provide guidance for selecting suitable rate constant expressions for these PCET reactions.

Hybrid Density Functional Valence Bond Method with Multistate Treatment

Recently, a hybrid density functional valence bond (VB) method, λ-DFVB(U), has been proposed and shown to give accuracy that is comparable to that of CASPT2 in calculations of atomization energies, atomic excitation energies, and reaction barriers, while its computational cost is approximately the same as the valence bond self-consistent-field (VBSCF) method. However, the interaction between electronic states is not included in λ-DFVB(U) since the last step of λ-DFVB(U) is not a diagonalization of the Hamiltonian matrix on the electronic state basis. Therefore, λ-DFVB(U) gives the wrong topology of the potential energy surfaces (PESs) near the conical intersection region. In the present paper, we propose a novel hybrid density functional VB method with multistate treatment, named λ-DFVB(MS), in which an effective Hamiltonian matrix is constructed on the basis of the diabatic states obtained by the valence-bond-based compression approach for the diabatization scheme, and the interaction between electronic states can be included through the diagonalization of the effective Hamiltonian matrix. Test calculations show that λ-DFVB(MS) gives the correct topology of the PESs near the conical intersection region. We also show that the VBSCF wave function with selected VB structures can be applied as a reference in λ-DFVB(MS).

Addressing electronic and dynamical evolution of molecules and molecular clusters: DFTB simulations of energy relaxation in polycyclic aromatic hydrocarbons

We present a review of the capabilities of the density functional based Tight Binding (DFTB) scheme to address the electronic relaxation and dynamical evolution of molecules and molecular clusters following energy deposition via either collision or photoabsorption. The basics and extensions of DFTB for addressing these systems and in particular their electronic states and their dynamical evolution are reviewed. Applications to PAH molecules and clusters, carbonaceous systems of major interest in astrochemical/astrophysical context, are reported. A variety of processes are examined and discussed such as collisional hydrogenation, fast collisional processes and induced electronic and charge dynamics, collision-induced fragmentation, photo-induced fragmentation, relaxation in high electronic states, electronic-to-vibrational energy conversion and statistical versus non-statistical fragmentation. This review illustrates how simulations may help to unravel different relaxation mechanisms depending on various factors such as the system size, specific electronic structure or excitation conditions, in close connection with experiments.

Tryptophan to Tryptophan Hole Hopping in an Azurin Construct

Electron transfer (ET) between neutral and cationic tryptophan residues in the azurin construct [ReI(H126)(CO)3(dmp)](W124)(W122)CuI (dmp = 4,7-Me2-1,10-phenanthroline) was investigated by Born-Oppenheimer quantum-mechanics/molecular mechanics/molecular dynamics (QM/MM/MD) simulations. We focused on W124•+ ← W122 ET, which is the middle step of the photochemical hole-hopping process *ReII(CO)3(dmp•-) ← W124 ← W122 ← CuI, where sequential hopping amounts to nearly 10,000-fold acceleration over single-step tunneling (ACS Cent. Sci. 2019, 5, 192-200). In accordance with experiments, UKS-DFT QM/MM/MD simulations identified forward and reverse steps of W124•+ ↔ W122 ET equilibrium, as well as back ET ReI(CO)3(dmp•-) → W124•+ that restores *ReII(CO)3(dmp•-). Strong electronic coupling between the two indoles (≥40 meV in the crossing region) makes the productive W124•+ ← W122 ET adiabatic. Energies of the two redox states are driven to degeneracy by fluctuations of the electrostatic potential at the two indoles, mainly caused by water solvation, with contributions from the protein dynamics in the W122 vicinity. ET probability depends on the orientation of Re(CO)3(dmp) relative to W124 and its rotation diminishes the hopping yield. Comparison with hole hopping in natural systems reveals structural and dynamics factors that are important for designing efficient hole-hopping processes.

Nonorthogonal Active Space Decomposition of Wave Functions with Multiple Correlation Mechanisms

The nonorthogonal active space decomposition (NO-ASD) methodology is proposed for describing systems containing multiple correlation mechanisms. NO-ASD partitions the wave function by a correlation mechanism, such that the interactions between different correlation mechanisms are treated with an effective Hamiltonian approach, while interactions between correlated orbitals in the same correlation mechanism are treated explicitly. As a result, the determinant expansion scales polynomially with the number of correlation mechanisms rather than exponentially, which significantly reduces the factorial scaling associated with the size of the correlated orbital space. Despite the nonorthogonal framework of NO-ASD, the approach can take advantage of computational efficient matrix element evaluation when performing nonorthogonal coupling of orthogonal determinant expansions. In this work, we introduce and examine the NO-ASD approach in comparison to complete active space methods to establish how the NO-ASD approach reduces the problem dimensionality and the extent to which it affects the amount of correlation energy recovered. Calculations are performed on ozone, nickel-acetylene, and isomers of μ-oxo dicopper ammonia.

Analytical gradients and derivative couplings for the TDDFT-1D method

We derive and implement analytic gradients and derivative couplings for time-dependent density functional theory plus one double (TDDFT-1D) which is a semiempirical configuration interaction method whereby the Hamiltonian is diagonalized in a basis of all singly excited configurations and one doubly excited configuration as constructed from a set of reference Kohn-Sham orbitals. We validate the implementation by comparing against finite difference values. Furthermore, we show that our implementation can locate both optimized geometries and minimum-energy crossing points along conical seams of S₁/S₀ surfaces for a set of test cases.

Subsystem density-functional theory: A reliable tool for spin-density based properties

Subsystem density-functional theory compiles a set of features that allow for efficiently calculating properties of very large open-shell radical systems such as organic radical crystals, proteins, or deoxyribonucleic acid stacks. It is computationally less costly than correlated ab initio wave function approaches and can pragmatically avoid the overdelocalization problem of Kohn-Sham density-functional theory without employing hard constraints on the electron-density. Additionally, subsystem density-functional theory calculations commonly start from isolated fragment electron densities, pragmatically preserving a priori specified subsystem spin-patterns throughout the calculation. Methods based on subsystem density-functional theory have seen a rapid development over the past years and have become important tools for describing open-shell properties. In this Perspective, we address open questions and possible developments toward challenging future applications in connection with subsystem density-functional theory for spin-dependent properties.

Perturbative Expansion of Nonorthogonal Product Approach for Charge Transfer States

Modeling of the excited states of multichromophoric systems is crucial for the understanding of photosynthesis functioning. The excitonic Hamiltonian method is widely used for such calculations. Excited states of the combined system are constructed from the wave functions of individual chromophores while their interactions are described by excitonic couplings. In the current study, we enhance a previously proposed nonorthogonal product approach to incorporate dynamic correlation effects accounted for by the multireference perturbation theory. We discuss the problems of constructing the excitonic Hamiltonian including charge transfer states for the molecular systems where the overlap contribution to the excitonic couplings is non-negligible. The benchmark calculations were performed for a model system. It was shown that the overlap component of the excitonic coupling is of great importance. The enhanced method provides an accurate description of the excited state energies and other properties.

Implementation and Validation of Constrained Density Functional Theory Forces in the CP2K Package

Constrained density functional theory (CDFT) is a powerful tool for the prediction of electron transfer parameters in condensed phase simulations at a reasonable computational cost. In this work we present an extension to CDFT in the popular mixed Gaussian/plane wave electronic structure package CP2K, implementing the additional force terms arising from a constraint based on Hirshfeld charge partitioning. This improves upon the existing Becke partitioning scheme, which is prone to give unphysical atomic charges. We verify this implementation for a variety of systems: electron transfer in (H₂O)₂⁺ in a vacuum, electron tunnelling between oxygen vacancy centers in solid MgO, and electron self-exchange in aqueous Ru²⁺–Ru³⁺. We find good agreement with previous plane-wave CDFT results for the same systems, but at a significantly lower computational cost, and we discuss the general reliability of condensed phase CDFT calculations.

Variational Density Functional Calculations of Excited States: Conical Intersection and Avoided Crossing in Ethylene Bond Twisting

Theoretical studies of photochemical processes require a description of the energy surfaces of excited electronic states, especially near degeneracies, where transitions between states are most likely. Systems relevant to photochemical applications are typically too large for high-level multireference methods, and while time-dependent density functional theory (TDDFT) is efficient, it can fail to provide the required accuracy. A variational, time-independent density functional approach is applied to the twisting of the double bond and pyramidal distortion in ethylene, the quintessential model for photochemical studies. By allowing for symmetry breaking, the calculated energy surfaces exhibit the correct topology around the twisted-pyramidalized conical intersection even when using a semilocal functional approximation, and by including explicit self-interaction correction, the torsional energy curves are in close agreement with published multireference results. The findings of the present work point to the possibility of using a single determinant time-independent density functional approach to simulate nonadiabatic dynamics, even for large systems where multireference methods are impractical and TDDFT is often not accurate enough.

Relativistic nonorthogonal configuration interaction: application to L2,3-edge X-ray spectroscopy

In this article, we develop a relativistic exact-two-component nonorthogonal configuration interaction (X2C-NOCI) for computing L-edge X-ray spectra. This article to our knowledge is the first time NOCI has been used for relativistic wave functions. A set of molecular complexes, including SF₆, SiCl₄ and [FeCl₆]^3-, are used to demonstrate the accuracy and computational scaling of the X2C-NOCI method. Our results suggest that X2C-NOCI is able to satisfactorily capture the main features of the L_2,3-edge X-ray absorption spectra. Excitations from the core require a large amount of orbital relaxation to yield reasonable energies and X2C-NOCI allows us to treat orbital optimization explicitly. However, the cost of computing the nonorthogonal coupling is higher than in conventional CI. Here, we propose an improved integral screening using overlap-scaled density combined with a continuous measure of the generalized Slater-Condon rules that allows us to estimate if an element is zero before attempting a two-electron integral contraction.

Importance of dynamical electron correlation in diabatic couplings of electron-exchange processes

We demonstrate the importance of the dynamical electron correlation effect in diabatic couplings of electron-exchange processes in molecular aggregates. To perform a multireference perturbation theory with large active space of molecular aggregates, an efficient low-rank approximation is applied to the complete active space self-consistent field reference functions. It is known that kinetic rates of electron-exchange processes, such as singlet fission, triplet-triplet annihilation, and triplet exciton transfer, are not sufficiently explained by the direct term of the diabatic couplings but efficiently mediated by the low-lying charge transfer states if the two molecules are in close proximity. It is presented in this paper, however, that regardless of the distance of the molecules, the direct term is considerably underestimated by up to three orders of magnitude without the dynamical electron correlation, i.e., the diabatic states expressed in the active space are not adequate to quantitatively reproduce the electron-exchange processes.

Theoretical Modeling of Electrochemical Proton-Coupled Electron Transfer

Proton-coupled electron transfer (PCET) plays an essential role in a wide range of electrocatalytic processes. A vast array of theoretical and computational methods have been developed to study electrochemical PCET. These methods can be used to calculate redox potentials and pK_a values for molecular electrocatalysts, proton-coupled redox potentials and bond dissociation free energies for PCET at metal and semiconductor interfaces, and reorganization energies associated with electrochemical PCET. Periodic density functional theory can also be used to compute PCET activation energies and perform molecular dynamics simulations of electrochemical interfaces. Various approaches for maintaining a constant electrode potential in electronic structure calculations and modeling complex interactions in the electric double layer (EDL) have been developed. Theoretical formulations for both homogeneous and heterogeneous electrochemical PCET spanning the adiabatic, nonadiabatic, and solvent-controlled regimes have been developed and provide analytical expressions for the rate constants and current densities as functions of applied potential. The quantum mechanical treatment of the proton and inclusion of excited vibronic states have been shown to be critical for describing experimental data, such as Tafel slopes and potential-dependent kinetic isotope effects. The calculated rate constants can be used as input to microkinetic models and voltammogram simulations to elucidate complex electrocatalytic processes.

Extended Mulliken-Hush Method with Applications to the Theoretical Study of Electron Transfer

A novel adiabatic-to-diabatic (ATD) transformation strategy, namely, the extended Mulliken-Hush (XMH) method, is proposed to evaluate diabatic properties including electronic couplings, potential energy surfaces, and their crossings. The XMH method is developed by adopting our recently proposed ATD transformation formula of a general vectorial physical observable, in which a useful ATD transformation is further determined by using an auxiliary dipole between localized frontier orbitals as a simple approximation of the diabatic transition dipole. The XMH method is simple and practical that provides a flexible way to construct diabatic states. To some extent, it can be regarded as an extension of the generalized Mulliken-Hush (GMH) method since the latter takes a stronger approximation, in which the diabatic transition dipole is assumed to be vanishing. Test calculations on the HeH₂⁺ system show that the electronic couplings predicted by the XMH method are closer to the ones calculated by the valence bond block-diagonalization approach than the GMH ones since the XMH method takes into account both the magnitude and direction of the diabatic transition dipole, which is consistent with the properties of this molecule. In the study of electron transfer in the two kinds of donor-bridge-acceptor systems, the XMH method maintains the simplicity of the GMH method and gives reasonable results even when the latter fails, wherein the diabatic transition dipole is nearly perpendicular to the difference of the initial and final adiabatic dipoles. More importantly, the XMH method can be easily combined with high-level electronic structure methods, in which the properties of the ground and excited states may be more accurately calculated, and hence, one may expect that further development of the XMH method would result in a general computational model for studying electron transfer reactions.

Interaction Energy Analysis of Monovalent Inorganic Anions in Bulk Water Versus Air/Water Interface

Soft anions exhibit surface activity at the air/water interface that can be probed using surface-sensitive vibrational spectroscopy, but the structural implications of this surface activity remain a matter of debate. Here, we examine the nature of anion-water interactions at the air/water interface using a combination of molecular dynamics simulations and quantum-mechanical energy decomposition analysis based on symmetry-adapted perturbation theory. Results are presented for a set of monovalent anions, including Cl-, Br-, I-, CN-, OCN-, SCN-, NO2-, NO3-, and ClOn- (n=1,2,3,4), several of which are archetypal examples of surface-active species. In all cases, we find that average anion-water interaction energies are systematically larger in bulk water although the difference (with respect to the same quantity computed in the interfacial environment) is well within the magnitude of the instantaneous fluctuations. Specifically for the surface-active species Br-(aq), I-(aq), ClO4-(aq), and SCN-(aq), and also for ClO-(aq), the charge-transfer (CT) energy is found to be larger at the interface than it is in bulk water, by an amount that is greater than the standard deviation of the fluctuations. The Cl-(aq) ion has a slightly larger CT energy at the interface, but NO3-(aq) does not; these two species are borderline cases where consensus is lacking regarding their surface activity. However, CT stabilization amounts to <20% of the total induction energy for each of the ions considered here, and CT-free polarization energies are systematically larger in bulk water in all cases. As such, the role of these effects in the surface activity of soft anions remains unclear. This analysis complements our recent work suggesting that the short-range solvation structure around these ions is scarcely different at the air/water interface from what it is in bulk water. Together, these observations suggest that changes in first-shell hydration structure around soft anions cannot explain observed surface activities.

Dynamic-then-Static Approach for Core Excitations of Open-Shell Molecules

Delta self-consistent-field methods are widely used in studies of electronically excited states. However, the nonaufbau determinants are generally spin-contaminated. Here, we describe a general approach for spin-coupling interactions of open-shell molecules, making use of multistate density functional theory (MSDFT). In particular, the effective exchange integrals that determine spin coupling are obtained by enforcing the multiplet degeneracy of the S+1 state in the M_S = S manifold. Consequently, they are consistent with the energy of the high-spin state that is adequately treated by Kohn-Sham density functional theory (DFT) and, thereby, free of double counting of correlation. The method was applied to core excitations of open-shell molecules and compared with those by spin-adapted time-dependent DFT. An excellent agreement with experiment was found employing the BLYP functional and aug-cc-pCVQZ basis set. Overall, MSDFT provides an effective combination of the strengths of DFT and wave function theory to achieve efficiency and accuracy.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

Electrostatics, Charge Transfer, and the Nature of the Halide-Water Hydrogen Bond

Binary halide-water complexes X^-(H₂O) are examined by means of symmetry-adapted perturbation theory, using charge-constrained promolecular reference densities to extract a meaningful charge-transfer component from the induction energy. As is known, the X^-(H₂O) potential energy surface (for X = F, Cl, Br, or I) is characterized by symmetric left and right hydrogen bonds separated by a C_2v-symmetric saddle point, with a tunneling barrier height that is <2 kcal/mol except in the case of F^-(H₂O). Our analysis demonstrates that the charge-transfer energy is correspondingly small (<2 kcal/mol except for X = F), considerably smaller than the electrostatic interaction energy. Nevertheless, charge transfer plays a crucial role determining the conformational preferences of X^-(H₂O) and provides a driving force for the formation of quasi-linear X··· H-O hydrogen bonds. Charge-transfer energies correlate well with measured O-H vibrational redshifts for the halide-water complexes and also for OH^-(H₂O) and NO₂^-(H₂O), providing some indication of a general mechanism.

A Valence-Bond-Based Multiconfigurational Density Functional Theory: The λ-DFVB Method Revisited

A recently developed valence-bond-based multireference density functional theory, named λ-DFVB, is revisited in this paper. λ-DFVB remedies the double-counting error of electron correlation by decomposing the electron-electron interactions into the wave function term and density functional term with a variable parameter λ. The λ value is defined as a function of the free valence index in our previous scheme, denoted as λ-DFVB(K) in this paper. Here we revisit the λ-DFVB method and present a new scheme based on natural orbital occupation numbers (NOONs) for parameter λ, named λ-DFVB(IS), to simplify the process of λ-DFVB calculation. In λ-DFVB(IS), the parameter λ is defined as a function of NOONs, which are straightforwardly determined from the many-electron wave function of the molecule. Furthermore, λ-DFVB(IS) does not involve further self-consistent field calculation after performing the valence bond self-consistent field (VBSCF) calculation, and thus, the computational effort in λ-DFVB(IS) is approximately the same as the VBSCF method, greatly reduced from λ-DFVB(K). The performance of λ-DFVB(IS) was investigated on a broader range of molecular properties, including equilibrium bond lengths and dissociation energies, atomization energies, atomic excitation energies, and chemical reaction barriers. The computational results show that λ-DFVB(IS) is more robust without losing accuracy and comparable in accuracy to high-level multireference wave function methods, such as CASPT2.

Theoretical Description of the Primary Proton-Coupled Electron Transfer Reaction in the Cytochrome bc1 Complex

The cytochrome bc₁ complex is a transmembrane enzymatic protein complex that plays a central role in cellular energy production and is present in both photosynthetic and respiratory chain organelles. Its reaction mechanism is initiated by the binding of a quinol molecule to an active site, followed by a series of charge transfer reactions between the quinol and protein subunits. Previous work hypothesized that the primary reaction was a concerted proton-coupled electron transfer (PCET) reaction because of the apparent absence of intermediate states associated with single proton or electron transfer reactions. In the present study, the kinetics of the primary bc₁ complex PCET reaction is investigated with a vibronically nonadiabatic PCET theory in conjunction with all-atom molecular dynamics simulations and electronic structure calculations. The computed rate constants and relatively high kinetic isotope effects are consistent with experimental measurements on related biomimetic systems. The analysis implicates a concerted PCET mechanism with significant hydrogen tunneling and nonadiabatic effects in the bc₁ complex. Moreover, the employed theoretical framework is shown to serve as a general strategy for describing PCET reactions in bioenergetic systems.

Structural modulation of the photophysical and electronic properties of pyrene-based 3D metal–organic frameworks derived from s-block metals

Materials in which charge delocalization and migration can be tuned are critical for electronic applications.

Block-Localized Excitation for Excimer Complex and Diabatic Coupling

We describe a block-localized excitation (BLE) method to carry out constrained optimization of block-localized orbitals for constructing valence bond-like, diabatic excited configurations using multistate density functional theory (MSDFT). The method is an extension of the previous block-localized wave function method through a fragment-based ΔSCF approach to optimize excited determinants within a molecular complex. In BLE, both the number of electrons and the electronic spin of different fragments in a whole system can be constrained, whereas electrostatic, exchange, and polarization interactions among different blocks can be fully taken into account of. To avoid optimization collapse to unwanted states, a ΔSCF projection scheme and a maximum overlap of wave function approach have been presented. The method is illustrated by the excimer complex of two naphthalene molecules. With a minimum of eight spin-adapted configurational state functions, it was found that the inversion of L_a^- and L_b^- states near the optimal structure of the excimer complex is correctly produced, which is in quantitative agreement with DMRG-CASPT2 calculations and experiments. Trends in the computed transfer integrals associated with excited-state energy transfer both in the singlet and triplet states are discussed. The results suggest that MSDFT may be used as an efficient approach to treat intermolecular interactions in excited states with a minimal active space (MAS) for interpretation of the results and for dynamic simulations, although the selection of a small active space is often system dependent.

Excited state diabatization on the cheap using DFT: Photoinduced electron and hole transfer

Excited state electron and hole transfer underpin fundamental steps in processes such as exciton dissociation at photovoltaic heterojunctions, photoinduced charge transfer at electrodes, and electron transfer in photosynthetic reaction centers. Diabatic states corresponding to charge or excitation localized species, such as locally excited and charge transfer states, provide a physically intuitive framework to simulate and understand these processes. However, obtaining accurate diabatic states and their couplings from adiabatic electronic states generally leads to inaccurate results when combined with low-tier electronic structure methods, such as time-dependent density functional theory, and exorbitant computational cost when combined with high-level wavefunction-based methods. Here, we introduce a density functional theory (DFT)-based diabatization scheme that directly constructs the diabatic states using absolutely localized molecular orbitals (ALMOs), which we denote as Δ-ALMO(MSDFT2). We demonstrate that our method, which combines ALMO calculations with the ΔSCF technique to construct electronically excited diabatic states and obtains their couplings with charge-transfer states using our MSDFT2 scheme, gives accurate results for excited state electron and hole transfer in both charged and uncharged systems that underlie DNA repair, charge separation in donor-acceptor dyads, chromophore-to-solvent electron transfer, and singlet fission. This framework for the accurate and efficient construction of excited state diabats and evaluation of their couplings directly from DFT thus offers a route to simulate and elucidate photoinduced electron and hole transfer in large disordered systems, such as those encountered in the condensed phase.

Towards a Holomorphic Density Functional Theory

Self-consistent-field (SCF) approximations formulated using Hartree-Fock (HF) or Kohn-Sham density-functional theory (KS-DFT) have the potential to yield multiple solutions. However, the formal relationship between multiple solutions identified using HF or KS-DFT remains generally unknown. We investigate the connection between multiple SCF solutions for HF or KS-DFT by introducing a parameterized functional that scales between the two representations. Using the hydrogen molecule and a model of electron transfer, we continuously map multiple solutions from the HF potential to a KS-DFT description. We discover that multiple solutions can coalesce and vanish as the functional changes, forming a direct analogy with the disappearance of real HF solutions along a change in molecular structure. To overcome this disappearance of solutions, we develop a complex-analytic extension of DFT-the "holomorphic DFT" approach-that allows every SCF stationary state to be analytically continued across all molecular structures and exchange-correlation functionals.

Dependence upon charge of the vibrational spectra of small Polycyclic Aromatic Hydrocarbon clusters: the example of pyrene

Infrared spectra are computed for neutral and cationic clusters of Polycyclic Aromatic Hydrocarbon clusters, namely( C 16 H 10 ) n = 1 , 4 ( 0 / + ) , using the Density Functional based Tight Binding scheme combined with a Configuration Interaction scheme (DFTB-CI) in the double harmonic approximation. Cross-comparison is carried out with DFT and simple DFTB. Similarly to the monomer cation, the IR spectra of cluster cations are characterized by a depletion of the intensity of the CH stretch modes around 3000 cm-1, with a weak revival for n = 3 and 4. The in-plane CCC modes in the region 1400-2000 cm-1 are enhanced while the CH bending modes in the range 700-1000 cm-1 are significantly weakened with respect to the monomer cation, in particular for n = 2. Finally, soft modes corresponding to diedral fluctuations of the monomers within the central stack of the ion structure, possibly mixed with monomer folding, are also observed in the region 70-120 cm-1.

Mimicking Natural Photosynthesis: Designing Ultrafast Photosensitized Electron Transfer into Multiheme Cytochrome Protein Nanowires

Efficient nanomaterials for artificial photosynthesis require fast and robust unidirectional electron transfer (ET) from photosensitizers through charge-separation and accumulation units to redox-active catalytic sites. We explored the ultrafast time-scale limits of photo-induced charge transfer between a Ru(II)tris(bipyridine) derivative photosensitizer and PpcA, a 3-heme c-type cytochrome serving as a nanoscale biological wire. Four covalent attachment sites (K28C, K29C, K52C, and G53C) were engineered in PpcA enabling site-specific covalent labeling with expected donor-acceptor (DA) distances of 4-8 Å. X-ray scattering results demonstrated that mutations and chemical labeling did not disrupt the structure of the proteins. Time-resolved spectroscopy revealed three orders of magnitude difference in charge transfer rates for the systems with otherwise similar DA distances and the same number of covalent bonds separating donors and acceptors. All-atom molecular dynamics simulations provided additional insight into the structure-function requirements for ultrafast charge transfer and the requirement of van der Waals contact between aromatic atoms of photosensitizers and hemes in order to observe sub-nanosecond ET. This work demonstrates opportunities to utilize multi-heme c-cytochromes as frameworks for designing ultrafast light-driven ET into charge-accumulating biohybrid model systems, and ultimately for mimicking the photosynthetic paradigm of efficiently coupling ultrafast, light-driven electron transfer chemistry to multi-step catalysis within small, experimentally versatile photosynthetic biohybrid assemblies.

Reactivities of singlet oxygen: open-shell or closed-shell?

This work explores the reactivity of singlet oxygen with respect to two typical reactions: cycloaddition to anthracene and excitation energy transfer (EET) to a carotenoid using diabatic states with multistate density functional theory (MSDFT). Noticeably, the degenerate state 1Δg has distinct open-shell (OS) and closed-shell (CS) components, and the closed-shell component showed more reactivity than the open-shell one due to the strong diabatic couplings to the product diabatic states. The diabatic perspective presented in this work could also apply to general singlet fission processes.

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

The ONETEP linear-scaling density functional theory program

We present an overview of the onetep program for linear-scaling density functional theory (DFT) calculations with large basis set (plane-wave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the density matrix and the NGWFs are optimized with localization constraints. By taking advantage of localization, onetep is able to perform calculations including thousands of atoms with computational effort, which scales linearly with the number or atoms. The code has a large and diverse range of capabilities, explored in this paper, including different boundary conditions, various exchange-correlation functionals (with and without exact exchange), finite electronic temperature methods for metallic systems, methods for strongly correlated systems, molecular dynamics, vibrational calculations, time-dependent DFT, electronic transport, core loss spectroscopy, implicit solvation, quantum mechanical (QM)/molecular mechanical and QM-in-QM embedding, density of states calculations, distributed multipole analysis, and methods for partitioning charges and interactions between fragments. Calculations with onetep provide unique insights into large and complex systems that require an accurate atomic-level description, ranging from biomolecular to chemical, to materials, and to physical problems, as we show with a small selection of illustrative examples. onetep has always aimed to be at the cutting edge of method and software developments, and it serves as a platform for developing new methods of electronic structure simulation. We therefore conclude by describing some of the challenges and directions for its future developments and applications.

Density-functional tight-binding: basic concepts and applications to molecules and clusters

The scope of this article is to present an overview of the Density Functional based Tight Binding (DFTB) method and its applications. The paper introduces the basics of DFTB and its standard formulation up to second order. It also addresses methodological developments such as third order expansion, inclusion of non-covalent interactions, schemes to solve the self-interaction error, implementation of long-range short-range separation, treatment of excited states via the time-dependent DFTB scheme, inclusion of DFTB in hybrid high-level/low level schemes (DFT/DFTB or DFTB/MM), fragment decomposition of large systems, large scale potential energy landscape exploration with molecular dynamics in ground or excited states, non-adiabatic dynamics. A number of applications are reviewed, focusing on -(i)- the variety of systems that have been studied such as small molecules, large molecules and biomolecules, bare orfunctionalized clusters, supported or embedded systems, and -(ii)- properties and processes, such as vibrational spectroscopy, collisions, fragmentation, thermodynamics or non-adiabatic dynamics. Finally outlines and perspectives are given.

Unexpectedly Large Couplings Between Orthogonal Units in Anthraquinone Polymers

The unusual electronic properties of directly linked 1,4-polyanthraquinones (14PAQs) are investigated. The dihedral angle between the molecular planes of anthraquinones (AQs) is found to be close to 90°. Contrary to the prevailing notion that the interaction between orthogonal units is negligible due to broken π-electron conjugation, the coupling between neighboring AQ units does not have a minimum at 90° and is much larger than that expected. The unexpectedly large electronic coupling between orthogonal AQ units is explained by the interaction between the lone pairs of the carbonyl oxygen and the π system of the neighboring unit, which allows favorable overlap between frontier molecular orbitals at the orthogonal geometry. It is shown that this effect, which is described computationally for the first time, can be strengthened by adding more quinone units. The effect of thermal fluctuations on the couplings is assessed through ab initio molecular dynamics simulations. The distributions of the couplings reveal that electron transport is resilient to dynamic disorder in all systems considered, whereas the hole couplings are much more sensitive to disorder. Lone pair-π interactions are described, as a previously largely overlooked conjugation mechanism, for incorporation into a new class of disorder-resilient semiconducting redox polymers.

Structures and Energetics of Neutral and Cationic Pyrene Clusters

The low energy structures of neutral and cationic pyrene clusters containing up to seven molecules are searched through a global exploration scheme combining parallel tempering Monte Carlo algorithm and local quenches. The potential energies are computed at the density functional based tight binding level for neutrals and configuration interaction density functional based tight binding for cations in order to treat properly the charge resonance. New simplified versions of these schemes are also presented and used during the global exploration. Neutral clusters are shown to be made of compact assemblies of sub-blocs containing up to three units whereas cations present a charged dimer or trimer core surrounded by neutral units. The structural features of the clusters are analyzed and correlated for the cation with the charge distribution. The stability of clusters is also discussed in terms of cohesive and evaporation energies. Adiabatic and vertical ionization potentials are also discussed.

Combined Density Functional and Algebraic-Diagrammatic Construction Approach for Accurate Excitation Energies and Transition Moments

A composite of time-dependent density functional theory (TDDFT) and the second-order algebraic-diagrammatic construction [ADC(2)] approach is presented for efficient calculation of spectral properties of molecules. Our method can be regarded as a new excited-state double-hybrid (DH) approach or a dressed TDDFT scheme, but it can also be interpreted as an empirically tuned ADC(2) model. Several combinations of exchange-correlation functionals and spin-scaling schemes are explored. Our best-performing method includes the Perdew, Burke, and Ernzerhof exchange and Perdew's 1986 correlation functional and employs the scaled-opposite-spin approximation for the higher-order terms. The computation time of the new method scales as the fourth power of the system size, and an efficient cost-reduction approach is also presented, which further speeds up the calculations. Our benchmark calculations show that the proposed model outperforms not only the existing DH approaches and ADC(2) variants but also the considerably more expensive coupled-cluster methods.

Conical Intersections at the Nanoscale: Molecular Ideas for Materials

The ability to predict and describe nonradiative processes in molecules via the identification and characterization of conical intersections is one of the greatest recent successes of theoretical chemistry. Only recently, however, has this concept been extended to materials science, where nonradiative recombination limits the efficiencies of materials for various optoelectronic applications. In this review, we present recent advances in the theoretical study of conical intersections in semiconductor nanomaterials. After briefly introducing conical intersections, we argue that specific defects in materials can induce conical intersections between the ground and first excited electronic states, thus introducing pathways for nonradiative recombination. We present recent developments in theoretical methods, computational tools, and chemical intuition for the prediction of such defect-induced conical intersections. Through examples in various nanomaterials, we illustrate the significance of conical intersections for nanoscience. We also discuss challenges facing research in this area and opportunities for progress.

Locality of conical intersections in semiconductor nanomaterials

A predictive theory connecting atomic structure to the rate of recombination would enable the rational design of semiconductor nanomaterials for optoelectronic applications. Recently our group has demonstrated that the theoretical study of conical intersections can serve this purpose. Here we review recent work in this area, focusing on the thesis that low-energy conical intersections in nanomaterials share a common feature: locality. We define a conical intersection as local if (a) the intersecting states differ by the excitation of an electron between spatially local orbitals, and (b) the intersection is accessed when the energies of these orbitals are tuned by local distortions of the geometry. After illustrating the locality of the conical intersection responsible for recombination at dangling bond defects in silicon, we demonstrate the locality of low-energy conical intersections in cases where locality may be a surprise. First, we demonstrate the locality of low-energy self-trapped conical intersections in a pristine silicon nanocrystal, which has no defects that one would expect to serve as the center of a local intersection. Second, we demonstrate that the lowest energy intersection in a silicon system with two neighboring dangling bond defects localizes to a single defect site. We discuss the profound implications of locality for predicting the rate of recombination and suggest that the locality of intersections could be exploited in the experimental study of recombination, where spectroscopic studies of molecular models of defects could provide new insights.

λ-Density Functional Valence Bond: A Valence Bond-Based Multiconfigurational Density Functional Theory With a Single Variable Hybrid Parameter

A new valence bond (VB)-based multireference density functional theory (MRDFT) method, named λ-DFVB, is presented in this paper. The method follows the idea of the hybrid multireference density functional method theory proposed by Sharkas et al. (2012). λ-DFVB combines the valence bond self-consistent field (VBSCF) method with Kohn–Sham density functional theory (KS-DFT) by decomposing the electron–electron interactions with a hybrid parameter λ. Different from the Toulouse's scheme, the hybrid parameter λ in λ-DFVB is variable, defined as a function of a multireference character of a molecular system. Furthermore, the E_C correlation energy of a leading determinant is introduced to ensure size consistency at the dissociation limit. Satisfactory results of test calculations, including potential energy surfaces, bond dissociation energies, reaction barriers, and singlet–triplet energy gaps, show the potential capability of λ-DFVB for molecular systems with strong correlation.

Mechanism of Spin-Exchange Internal Conversion: Practical Proxies for Diabatic and Nonadiabatic Couplings

Spin-exchange internal conversion (SEIC) is a general class of reactions having singlet fission and triplet fusion as particular cases. Based on a charge transfer (CT) mediated mechanism and analytical derivation with a model Hamiltonian, we propose proxies for estimating the coupling strength in both diabatic and adiabatic pictures for general SEIC reactions. In the diabatic picture, we demonstrated the existence of a bilinear relationship between the coupling strength and molecular orbital overlap, which provides a practical way to predict diabatic couplings. In the adiabatic picture, we showed that nonadiabatic couplings can be approximated by simple functions of the wave function CT coefficients. These approaches were verified through the investigation of singlet oxygen photosensitization, where both ¹Δ_g and ¹Σ_g oxygen states can be competitively generated by a triplet fusion reaction. The interplay between the CT-mediated mechanism, the spatial factors of the bimolecular complex, and the electronic structure of the oxygen molecule during the reaction explains the curiously small coupling to the ¹Σ_g state along specific incidence directions. The results from both the diabatic and adiabatic pictures provide a comprehensive understanding of the reaction mechanism, which applies to general SEIC problems.