Time propagation of electronic wavefunctions using nonorthogonal determinant expansions.

The use of truncated configuration interaction in real-time time-dependent simulations of electron dynamics provides a balance of computational cost and accuracy, while avoiding some of the failures associated with real-time time-dependent density functional theory. However, low-order truncated configuration interaction also has limitations, such as overestimation of polarizability in configuration interaction singles, even when perturbative doubles are included. Increasing the size of the determinant expansion may not be computationally feasible, and so, in this work, we investigate the use of nonorthogonality in the determinant expansion to establish the extent to which higher-order substitutions can be recovered, providing an improved description of electron dynamics. Model systems are investigated to quantify the extent to which different methods accurately reproduce the (hyper)polarizability, including the high-harmonic generation spectrum of H2, water, and butadiene.

Protonation state control of electric field induced molecular switching mechanisms.

Scanning tunneling microscopy tip-induced deprotonation has been demonstrated experimentally and can be used as an additional control mechanism in electric-field induced molecular switching. The goal of the current work is to establish whether (de)protonation can be used to inhibit or enhance the electric field controlled thermal and photoisomerization processes. Dihydroxyazobenzene is used as a model system, where protonation/deprotonation of the free hydroxyl moiety changes the azo bond order, and so modifies the rate of electric field induced isomerization. Through the combined action of deprotonation and applied field, it was found that the cis-to-trans thermal isomerization barrier could be completely removed, changing the isomerization half-life from the order of several months. In addition, due to the presence of multiple isomerization mechanisms, electric fields could modify the isomerization kinetics by increasing the number of energetically viable isomerization pathways, rather than reducing the activation barrier of the lowest energy pathway. Excited state calculations indicated that the protonation state and electric field could be used together to control the presence of electronic degeneracies along the rotation pathway between S0/S1, and along all three pathways between S1/S2. This work provides insight into the mechanisms that enable the use of protonation state, light, and electric fields in concert to control molecular switches.

Reactivity of Group 5 and 6 Single-Site Photocatalysts for Partial Oxidation of Methane: Comparison of Chromium, Niobium, and Tungsten-Doped Mesoporous Amorphous Silica.

Single-site transition-metal-doped photocatalysts can potentially be used for partial oxidation of methane (POM) at remote sites where natural gas is extracted and methane is often flared or released to the atmosphere. While there have been several investigations into the performance of vanadium, there has been no general survey of the performance of other metals. This work aims and examines Cr, Nb, and W metal oxide materials embedded in amorphous SiO2 to determine the viability of each metal in catalyzing the POM. Photoexcited states are examined to determine the nature of the photoactivated species, and then the subsequent POM reaction mechanisms are elucidated. Using the calculated energies of reaction intermediates and transition states, the rate of methanol formation is evaluated through the use of a microkinetic model. The findings indicate that all three metals are potentially more suitable for catalyzing POM than vanadium but that niobium shows the most favorable energy profile.

Role of Exact Exchange in Difference Projected Double-Hybrid Density Functional Theory for Treatment of Local, Charge Transfer, and Rydberg Excitations.

Difference approaches to the study of excited states have undergone a renaissance in recent years, with the development of a plethora of algorithms for locating self-consistent field approximations to excited states. Density functional theory is likely to offer the best balance of cost and accuracy for difference approaches, and yet there has been little investigation of how the parametrization of density functional approximations affects performance. In this work, we aim to explore the role of the global Hartree-Fock exchange parameter in tuning accuracy of different excitation types within the framework of the recently introduced difference projected double-hybrid density functional theory approach and contrast the performance with conventional time-dependent double-hybrid density functional theory. Difference projected double-hybrid density functional theory was demonstrated to give vertical excitation energies with average error and standard deviation with respect to multireference perturbation theory comparable to more expensive linear-response coupled cluster approaches ( J. Chem. Phys.2020, 153, 074103). However, despite benchmarking of local excitations, there has been no investigation of the methods performance for charge transfer or Rydberg excitations. In this work we report a new benchmark of charge transfer, Rydberg, and local excited state vertical excitation energies and examine how the exact Hartree-Fock exchange affects the benchmark performance to provide a deeper understanding of how projection and nonlocal correlation balance differing sources of error in the ground and excited states.

Oriented External Electric Field Tuning of Unsubstituted Azoheteroarene Thermal Isomerization Half-Lives.

Azoheteroarenes are relatively new photoswitchable compounds, where one of the phenyl rings of an azobenzene molecule is replaced by a heteroaromatic five-membered ring. Recent findings on methylated azoheteroarenes show that these photoswitches have potential in various optically addressable applications. The thermal stability of molecular switches is one of the primary factors considered in the design process. For molecular memory or energy storage devices, long thermal relaxation times are required. However, inducing a short thermal isomerization lifetime is required to release stored energy or as an alternative to photoswitching to avoid overlapping absorption spectra that reduce switching fidelity. In this study, we investigate how oriented external electric fields can be used to tune the thermal isomerization properties of three unsubstituted heteroaryl azo compounds-azoimidazole, azopyrazole, and azopyrrole. We show that favorable electric field orientations can increase the thermal half-life of studied molecules by as much as 60 times or reduce it from tens of days to seconds, compared to their half-life values in the field-free environment. A deeper understanding of the relationship between structure and kinetic properties provides insight as to how molecular switches can be designed for their electric field response in switching applications.

Orbital optimization in nonorthogonal multiconfigurational self-consistent field applied to the study of conical intersections and avoided crossings.

Nonorthogonal approaches to electronic structure methods have recently received renewed attention, with the hope that new forms of nonorthogonal wavefunction Ansätze may circumvent the computational bottleneck of orthogonal-based methods. The basis in which nonorthogonal configuration interaction is performed defines the compactness of the wavefunction description and hence the efficiency of the method. Within a molecular orbital approach, nonorthogonal configuration interaction is defined by a "different orbitals for different configurations" picture, with different methods being defined by their choice of determinant basis functions. However, identification of a suitable determinant basis is complicated, in practice, by (i) exponential scaling of the determinant space from which a suitable basis must be extracted, (ii) possible linear dependencies in the determinant basis, and (iii) inconsistent behavior in the determinant basis, such as disappearing or coalescing solutions, as a result of external perturbations, such as geometry change. An approach that avoids the aforementioned issues is to allow for basis determinant optimization starting from an arbitrarily constructed initial determinant set. In this work, we derive the equations required for performing such an optimization, extending previous work by accounting for changes in the orthogonality level (defined as the dimension of the orbital overlap kernel between two determinants) as a result of orbital perturbations. The performance of the resulting wavefunction for studying avoided crossings and conical intersections where strong correlation plays an important role is examined.

Effect of Oriented External Electric Fields on the Photo and Thermal Isomerization of Azobenzene.

Azobenzene is a prototype molecule with potential applications in molecular switches, solar thermal batteries, sensors, photoresponsive membranes, molecular electronics, data storage, and nonlinear optics. Photo and thermal isomerization pathways exhibit different charge-transfer character and dipole moments, implying that the use of electric fields can be used to modulate the reactivity of azobenzene. This article examines the differential effect of orientated electric fields on the rotation and inversion thermal and photoisomerization pathways of azobenzene to explore the feasibility of using electric fields in the design of azobenzene-based molecular devices. Our findings demonstrate that the application of orientated electric fields modifies the accessibility of the S0/S1 seam of electronic degeneracy, as well as changes the energetically favored relaxation pathway in the branching space to yield different photoproducts. In addition, we observed strong-field dipole-inversion effects that cause a topographical change in the response of the potential energy surface to the applied field and can result in geometric minima that do not exist under field-free conditions. On the S0 surface, transition barriers can be modified on the order of ±10 kcal mol-1, enabling control of thermal isomerization rates.

Difference projection-after-variation double-hybrid density functional theory applied to the calculation of vertical excitation energies.

The use of projection-after-variation double-hybrid density functional theory is proposed and examined as a difference method for the calculation of excited states. The strengths and weaknesses of the proposed method are discussed with particular reference to connections with linear response coupled-cluster theory. Vertical excitation energies are computed for the 28 molecule benchmark of Schreiber and co-workers in order to compare how the model performs with linear response coupled-cluster theories and multireference perturbation theory. The findings of this study show that the proposed method can achieve standard deviations in the error of computed vertical excitation energies compared to complete active space second-order perturbation theory of similar size to linear response coupled-cluster theories.

The Influence of ß-Ammonium Substitution on the Reaction Kinetics of Aminooxy Condensations with Aldehydes and Ketones.

The click-chemistry capture of volatile aldehydes and ketones by ammonium aminooxy compounds has proven to be an efficient means of analyzing the carbonyl subset in complex mixtures, such as exhaled breath or environmental air. In this work, we examine the carbonyl condensation reaction kinetics of three aminooxy compounds with varying ß-ammonium ion substitution using Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR-MS). We determined the activation energies for the reactions of the aminooxy compounds ATM, ADMH and AMAH with a panel of ketones and aldehydes that included acrolein and crotonaldehyde. The measurements indicate that the activation energies for the oximation reactions are quite low, less than 75 kJ mol-1 . ADMH is observed to react the fastest with the carbonyls studied. We postulate this result may be attributed to the ADMH ammonium proton effecting a Brønsted-Lowry acid-catalyzed elimination of water during the rate-determining step of oxime ether formation. A theoretical study of oxime ether formation is presented to explain the enhanced reactivity of ADMH relative to the tetraalkylammonium analog ATM.

On the linear geometry of lanthanide hydroxide (Ln-OH, Ln = La-Lu).

Lanthanide hydroxides are key species in a variety of catalytic processes and in the preparation of corresponding oxides. This work explores the fundamental structure and bonding of the simplest lanthanide hydroxide, LnOH (Ln = La-Lu), using density functional theory calculations. Interestingly, the calculations predict that all structures of this series will be linear. Furthermore, these results indicate a valence electron configuration of σ2π4 for all LnOH compounds, suggesting that the lanthanide-hydroxide bond is best characterized as a covalent triple bond.

Global elucidation of broken symmetry solutions to the independent particle model through a Lie algebraic approach.

Broken symmetry solutions-solutions to the independent particle model that do not obey all symmetries required by the Hamiltonian-have attracted significant interest for capturing multireference properties with mean-field scaling. However, identification and optimization of broken-symmetry solutions is difficult owing to the non-linear nature of the self-consistent field (SCF) equations, particularly for solutions belonging to low-symmetry subgroups and where multiple broken symmetry solutions are sought. Linearization of SCF solution space results in the Lie algebra, which this work utilizes as a framework for elucidation of the set of solutions that exist at the desired symmetry. To demonstrate that searches constructed in the Lie algebra yield the set of broken symmetry solutions, a grid-based search of real-restricted, real-unrestricted, complex-restricted, paired-unrestricted, and real-general solutions of the C 2 v (nearly D 4h ) H4 molecule is performed.

Explaining the MoVO4- photoelectron spectrum: Rationalization of geometric and electronic structure.

Attempts to reconcile simulated photoelectron spectra of MoVO4- clusters are complicated by the presence of very low energy barriers in the potential energy surfaces (PESs) of the lowest energy spin states and isomers. Transition state structures associated with the inversion of terminal oxygen ligands are found to lie below, or close to, the zero point energy of associated modes, which themselves are found to be of low frequency and thus likely to be significantly populated in the experimental characterization. Our simulations make use of Boltzmann averaging over low-energy coordinates and full mapping of the PES to obtain simulations in good agreement with experimental spectra. Furthermore, molecular orbital analysis of accessible final spin states reveals the existence of low energy two-electron transitions in which the final state is obtained from a finite excitation of an electron along with the main photodetachment event. Two-electron transitions are then used to justify the large difference in intensity between different bands present in the photoelectron spectrum. Owing to the general presence of terminal ligands in metal oxide clusters, this study identifies and proposes a solution to issues that are generally encountered when attempting to simulate transition metal cluster photoelectron spectroscopy.

Natural ionization orbitals for interpreting electron detachment processes.

A compact orbital representation of ionization processes is described utilizing the difference of calculated one-particle density matrices. Natural orbital analysis involving this difference density matrix simplifies interpretation of electronic detachment processes and allows differentiation between one-electron transitions and shake-up/shake-off transitions, in which one-electron processes are accompanied by excitation of a second electron into the virtual orbital space.

Modeling the Photoelectron Spectra of MoNbO2(-) Accounting for Spin Contamination in Density Functional Theory.

Spin contamination in density functional studies has been identified as a cause of discrepancies between theoretical and experimental spectra of metal oxide clusters such as MoNbO2. We perform calculations to simulate the photoelectron spectra of the MoNbO2 anion using broken-symmetry density functional theory incorporating recently developed approximate projection methods. These calculations are able to account for the presence of contaminating spin states at single-reference computational cost. Results using these new tools demonstrate the significant effect of spin-contamination on geometries and force constants and show that the related errors in simulated spectra may be largely overcome by using an approximate projection model.

Second derivatives for approximate spin projection methods.

The use of broken-symmetry electronic structure methods is required in order to obtain correct behavior of electronically strained open-shell systems, such as transition states, biradicals, and transition metals. This approach often has issues with spin contamination, which can lead to significant errors in predicted energies, geometries, and properties. Approximate projection schemes are able to correct for spin contamination and can often yield improved results. To fully make use of these methods and to carry out exploration of the potential energy surface, it is desirable to develop an efficient second energy derivative theory. In this paper, we formulate the analytical second derivatives for the Yamaguchi approximate projection scheme, building on recent work that has yielded an efficient implementation of the analytical first derivatives.

Spin projection with double hybrid density functional theory.

A spin projected double-hybrid density functional theory is presented that accounts for different scaling of opposite and same spin terms in the second order correction. This method is applied to three dissociation reactions which in the unprojected formalism exhibit significant spin contamination with higher spin states. This gives rise to a distorted potential surface and can lead to poor geometries and energies. The projected method presented is shown to improve the description of the potential over unprojected double hybrid density functional theory. Comparison is made with the reference states of the two double hybrid functionals considered here (B2PLYP and mPW2PLYP) in which the projected potential surface is degraded by an imbalance in the description of dynamic and static correlation.

Nonorthogonal Multireference Wave Function Description of Triplet-Triplet Energy Transfer Couplings.

In this study, the use of self-consistent field quasi-diabats is investigated for calculation of triplet energy transfer diabatic coupling elements. It is proposed that self-consistent field quasi-diabats are particularly useful for studying energy transfer (EnT) processes because orbital relaxation in response to changes in electron configuration is implicitly built into the model. The conceptual model that is developed allows for the simultaneous evaluation of direct and charge-transfer mechanisms to establish the importance of the different possible EnT mechanisms. The method's performance is evaluated using two model systems: the ethylene dimer and ethylene with the methaniminium cation. While states that mediate the charge-transfer mechanism were found to be higher in energy than the states involved in the direct mechanism, the coupling elements that control the kinetics were found to be significantly larger in the charge-transfer mechanism. Subsequently, we discuss the advantage of the approach in the context of practical difficulties with the use of established approaches.

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.

Assessing the Calculation of Exchange Coupling Constants and Spin Crossover Gaps Using the Approximate Projection Model To Improve Density Functional Calculations.

This work evaluates the quality of exchange coupling constant and spin crossover gap calculations using density functional theory corrected by the approximate projection model. Results show that improvements using the approximate projection model range from modest to significant. This study demonstrates that, at least for the class of systems examined here, spin projection generally improves the quality of density functional theory calculations of J-coupling constants and spin crossover gaps. Furthermore, it is shown that spin projection can be important for both geometry optimization and energy evaluations. The approximate projection model provides an affordable and practical approach for effectively correcting spin-contamination errors in such calculations.

Global Elucidation of Self-Consistent Field Solution Space Using Basin Hopping.

Reliable global elucidation of (subsets of) self-consistent field solutions is required for continued development and application of computational approaches that utilize these solutions as reference wavefunctions. We report the derivation and implementation of a stochastic approach to perform global elucidation of self-consistent field solutions by exploiting the connection between global optimization and global elucidation problems. We discuss the design of the algorithm through combining basin-hopping search algorithms with a Lie algebraic approach to linearize self-consistent field solution space, while also allowing preservation of desired spin-symmetry properties of the wavefunction. The performance of the algorithm is demonstrated on minimal basis C2v H4 due to its use as a model system for global self-consistent field solution exploration algorithms. Subsequently, we show that the model is capable of successfully identifying low-lying self-consistent solutions of benzene and NO2 with polarized double-zeta and triple-zeta basis sets and examine the properties of these solutions.