Strongly correlated barriers to rotation from parametric two-electron reduced-density-matrix methods in application to the isomerization of diazene

Universal Generalization of Density Functional Theory for Static Correlation

A major challenge for density functional theory (DFT) is its failure to treat static correlation, yielding errors in predicted charges, band gaps, van der Waals forces, and reaction barriers. Here we combine one- and two-electron reduced density matrix (1- and 2-RDM) theories with DFT to obtain a universal O(N^{3}) generalization of DFT for static correlation. Using the lowest unitary invariant of the cumulant 2-RDM, we generate a 1-RDM functional theory that corrects the convexity of any DFT functional to capture static correlation in its fractional orbital occupations. Importantly, the unitary invariant yields a predictive theory by revealing the dependence of the correction's strength upon the trace of the two-electron repulsion matrix. We apply the theory to the barrier to rotation in ethylene, the relative energies of the benzynes, as well as an 11-molecule, dissociation benchmark. By inheriting the computational efficiency of DFT without sacrificing the treatment of static correlation, the theory opens new possibilities for the prediction and interpretation of significant quantum molecular effects and phenomena.

Theoretical investigation of the isomerization pathways of diazenes: torsion vs. inversion

Diazenes are an important family of organic compounds used widely in synthetic and materials chemistry. These molecules have a planar geometry and exhibit cis-trans isomerization. The simplest of all these molecules - diazene (N2H2) - has been subjected to several experimental and theoretical studies. Two mechanisms have been proposed for the cis-trans isomerization of diazene, which are an in-plane inversion and an out-of-plane torsion. The activation energies for these pathways are similar and the competition between these two mechanisms has been discussed in the literature based on electronic structure theory calculations. Three decades ago, a classical dynamics investigation of diazene isomerization was carried out using a model Hamiltonian and it was indicated that the in-plane inversion is forbidden classically because of a centrifugal barrier and the out-of-plane torsion is the only isomerization pathway. In the present work, we investigated the cis-trans isomerization dynamics of diazene using ab initio classical trajectory simulations at the CASSCF(2,2)/aug-cc-pVDZ level of electronic structure theory. The simulation results confirmed the presence of the aforementioned centrifugal barrier for the inversion and torsion was the only observed pathway. The calculations were repeated for a similar system (difluorodiazene, N2F2) and again the centrifugal barrier prevented the inversion pathway.

Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo

This Perspective contrasts first and second derivative methods in variational Monte Carlo and presents a hybrid optimization approach that combines their advantages.

Development and application of a 2-electron reduced density matrix approach to electron transport via molecular junctions

Can an electronic device be constructed using only a single molecule? Since this question was first asked by Aviram and Ratner in the 1970s [Chem. Phys. Lett. 29, 277 (1974)], the field of molecular electronics has exploded with significant experimental advancements in the understanding of the charge transport properties of single molecule devices. Efforts to explain the results of these experiments and identify promising new candidate molecules for molecular devices have led to the development of numerous new theoretical methods including the current standard theoretical approach for studying single molecule charge transport, i.e., the non-equilibrium Green's function formalism (NEGF). By pairing this formalism with density functional theory (DFT), a wide variety of transport problems in molecular junctions have been successfully treated. For some systems though, the conductance and current-voltage curves predicted by common DFT functionals can be several orders of magnitude above experimental results. In addition, since density functional theory relies on approximations to the exact exchange-correlation functional, the predicted transport properties can show significant variation depending on the functional chosen. As a first step to addressing this issue, the authors have replaced density functional theory in the NEGF formalism with a 2-electron reduced density matrix (2-RDM) method, creating a new approach known as the NEGF-RDM method. 2-RDM methods provide a more accurate description of electron correlation compared to density functional theory, and they have lower computational scaling compared to wavefunction based methods of similar accuracy. Additionally, 2-RDM methods are capable of capturing static electron correlation which is untreatable by existing NEGF-DFT methods. When studying dithiol alkane chains and dithiol benzene in model junctions, the authors found that the NEGF-RDM predicts conductances and currents that are 1-2 orders of magnitude below those of B3LYP and M06 DFT functionals. This suggests that the NEGF-RDM method could be a viable alternative to NEGF-DFT for molecular junction calculations.

Bias-Free Chemically Diverse Test Sets from Machine Learning

Current benchmarking methods in quantum chemistry rely on databases that are built using a chemist's intuition. It is not fully understood how diverse or representative these databases truly are. Multivariate statistical techniques like archetypal analysis and K-means clustering have previously been used to summarize large sets of nanoparticles however molecules are more diverse and not as easily characterized by descriptors. In this work, we compare three sets of descriptors based on the one-, two-, and three-dimensional structure of a molecule. Using data from the NIST Computational Chemistry Comparison and Benchmark Database and machine learning techniques, we demonstrate the functional relationship between these structural descriptors and the electronic energy of molecules. Archetypes and prototypes found with topological or Coulomb matrix descriptors can be used to identify smaller, statistically significant test sets that better capture the diversity of chemical space. We apply this same method to find a diverse subset of organic molecules to demonstrate how the methods can easily be reapplied to individual research projects. Finally, we use our bias-free test sets to assess the performance of density functional theory and quantum Monte Carlo methods.

Energies and structures in biradical chemistry from the parametric two-electron reduced-density matrix method: applications to the benzene and cyclobutadiene biradicals

The treatment of biradical chemistry presents a challenge for electronic structure theory, especially single-reference methods, as it requires the description of varying degrees and kinds of electron correlation.

Accurate prediction of diradical chemistry from a single-reference density-matrix method: Model application to the bicyclobutane to gauche-1,3-butadiene isomerization

Multireference correlation in diradical molecules can be captured by a single-reference 2-electron reduced-density-matrix (2-RDM) calculation with only single and double excitations in the 2-RDM parametrization. The 2-RDM parametrization is determined by N-representability conditions that are non-perturbative in their treatment of the electron correlation. Conventional single-reference wave function methods cannot describe the entanglement within diradical molecules without employing triple- and potentially even higher-order excitations of the mean-field determinant. In the isomerization of bicyclobutane to gauche-1,3-butadiene the parametric 2-RDM (p2-RDM) method predicts that the diradical disrotatory transition state is 58.9 kcal/mol above bicyclobutane. This barrier is in agreement with previous multireference calculations as well as recent Monte Carlo and higher-order coupled cluster calculations. The p2-RDM method predicts the Nth natural-orbital occupation number of the transition state to be 0.635, revealing its diradical character. The optimized geometry from the p2-RDM method differs in important details from the complete-active-space self-consistent-field geometry used in many previous studies including the Monte Carlo calculation.

How much tetraradical character is present in the Si₆Ge₉ cluster?

This study discusses in detail the supposedly tetraradicaloid nature of a spirobis(pentagerma[1.1.1]propellane) derivative recently reported by Ito et al. (J. Am. Chem. Soc., 2013, 135, 6770). The electronic structure properties of the Si6Ge9 cluster are computationally explored by means of the composition of the ground state wavefunction, excitation energies to low-lying singlet, triplet and quintet states, and magnetic couplings between radical centers. Two main conclusions can be extracted from the obtained results regarding the radical character of spriobis(pentagerma[1.1.1]propellane): (i) the ground state of the Si6Ge9 cluster presents a rather small amount of effective unpaired electrons, which might be related to its chemical stability and (ii) there is in fact a perceptible tetraradical character within the small overall radical nature of the molecule. The proposed description do not contradict the conclusions drawn by the introductory work of Ito et al., but it provides a more detailed and precise interpretation of radical character of the molecule.