Small-Occupation Density Functional Correlation Energy Correction to Wave Function Approximations.

In this work, we introduce a novel hybrid approach, termed WFT-soDFT, designed to seamlessly incorporate DFT correlation into wave function ansatzes. This is achieved through a partitioning of the orbital space, distinguishing between large and small natural occupation numbers associated with wave function theory (WFT) and DFT correlation, respectively. The method uses a novel criterion for partitioning the orbital space and mapping the electron density in natural orbitals with a small occupation with the correlation energy of fast electrons within the homogeneous electron gas. Central to our approach is the introduction of a separation parameter ν, the choice of the WFT approach, and the correlation functional. Here, we combine the RASCI wave function with hole and particle truncation with a local density correlation functional to only account for small-occupation correlation energy. We investigate the performance of the method in the study of small but challenging chemical systems, for which WFT-soDFT demonstrates notable improvements over pristine wave function calculations. These findings collectively highlight the potential of the WFT-soDFT approach as a computationally affordable strategy to improve the accuracy of WFT electronic structure calculations.

Spin-Orbit Couplings of Open-Shell Systems with Restricted Active Space Configuration Interaction.

In this work we perform electronic structure calculations to unravel the origin of spin-orbit couplings (SOCs) in open-shell molecules. For that, we select systems displaying di or polyradical character, e.g., trimethylene, and analyze the changes in the magnitude of SOC constants along molecular distortions of ethylene and in the presence of intermolecular interactions between open and closed-shell moieties in the O2-C2H4 system. Calculations were performed by using nonrelativistic wave functions obtained with the restricted active space configuration interaction (RASCI) method, in conjunction with a recent implementation for the calculation of SOC based on the spin-orbit mean field approximation. Our results demonstrate the suitability of RASCI in the calculation of SOCs of open-shell systems, while providing a deep understanding of the relationship between couplings and the nature of the electronic states. Moreover, we introduce a new definition of the SOC constant for the study of molecular aggregates.

Simple evaluation of dynamic disorder effects on exciton transport.

Exciton transport in molecular materials is usually well described by Fermi's golden rule within the Condon approximation. However, when collective or molecular vibrations are thermally accessible, dynamic disorder effects have a sizable impact on the predicted exciton transfer rates and need to be considered for quantitative evaluation. In this work, we derive an analytic expression for the distribution of the electronic couplings that gives direct access to averaged quantities without the need to perform explicit calculations for a distribution of structural conformations. The distribution of exciton couplings and transfer rates obtained by this simple model in the study of singlet exciton transfer in the crystal naphthalene are in very good agreement with the data generated from molecular dynamics.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods. Methods highlighted in Q-Chem 5 include a suite of tools for modeling core-level spectroscopy, methods for describing metastable resonances, methods for computing vibronic spectra, the nuclear-electronic orbital method, and several different energy decomposition analysis techniques. High-performance capabilities including multithreaded parallelism and support for calculations on graphics processing units are described. Q-Chem boasts a community of well over 100 active academic developers, and the continuing evolution of the software is supported by an "open teamware" model and an increasingly modular design.

Short-range DFT energy correction to multiconfigurational wave functions for open-shell systems.

Electronic structure methods emerging from the combination of multiconfigurational wave functions and density functional theory (DFT) aim to take advantage of the strengths of the two nearly antagonistic theories. One of the common strategies employed to merge wave function theory (WFT) with DFT relies on the range separation of the Coulomb operator in which DFT functionals take care of the short-distance part, while long-range inter-electronic interactions are evaluated by using the chosen wave function method (WFT-srDFT). In this work, we uncover the limitations of WFT-srDFT in the characterization of open-shell systems. We show that spin polarization effects have a major impact on the (short-range) DFT exchange energy and are of vital importance in order to provide a balanced description between closed and open-shell configurations. We introduce different strategies to account for spin polarization in the short range based on the definition of a spin polarized electron density and with the use of short-range exact exchange. We test the performance of these approaches in the dissociation of the hydrogen molecule, the calculation of energy gaps in spin-triplet atoms and molecular diradicals, and the characterization of low-lying states of the gallium dimer. Our results indicate that the use of short-range DFT correlation in combination with a (full-range) multiconfigurational wave function might be an excellent approach for the study of open-shell molecules and largely improves the performance of WFT and WFT-srDFT.

Calculation of spin-orbit couplings using RASCI spinless one-particle density matrices: Theory and applications.

This work presents the formalism and implementation for calculations of spin-orbit couplings (SOCs) using the Breit-Pauli Hamiltonian and non-relativistic wave functions described by the restricted active space configuration interaction (RASCI) method with general excitation operators of spin-conserving spin-flipping, ionizing, and electron-attaching types. The implementation is based on the application of the Wigner-Eckart theorem within the spin space, which enables the calculation of the entire SOC matrix based on the explicit calculation of just one transition between the two spin multiplets. Numeric results for a diverse set of atoms and molecules highlight the importance of a balanced treatment of correlation and adequate basis sets and illustrate the overall robust performance of RASCI SOCs. The new implementation is a useful addition to the methodological toolkit for studying spin-forbidden processes and molecular magnetism.

Singlet fission in spiroconjugated dimers.

Spiroconjugation results in a unique arrangement of conjugated fragments providing a novel way to chemically connect chromophoric units and control their electronic interaction, which is a key factor for the viability of the singlet fission photophysical reaction. In this study, we computationally explore the possibility of intramolecular singlet fission in spiroconjugated dimers by characterizing the nature of the low-lying excited electronic states, evaluating the magnitude of interstate couplings, describing possible singlet fission mechanisms, and investigating the potential role of low and high frequency vibrational modes in the exciton fission process. The spiro linkage of organic chromophores with the proper excited singlet and triplet energies favors the presence of low-lying charge resonance states, which play a major role in the formation of the triplet pair state. Overall, our results suggest that spiroconjugated dimers are potentially good candidates to efficiently generate independent triplet states through singlet fission.

Conformational analysis of enantiomerization coupled to internal rotation in triptycyl-n-helicenes.

We present a computational study of a reduced potential energy surface (PES) to describe enantiomerization and internal rotation in three triptycyl-n-helicene molecules, centering the discussion on the issue of a proper reaction coordinate choice. To reflect the full symmetry of both strongly coupled enantiomerization and rotation processes, two non-fixed combinations of dihedral angles must be used, implying serious computational problems that required the development of a complex general algorithm. The characteristic points on each PES are analyzed, the intrinsic reaction coordinates are calculated, and finally they are projected on the reduced PES. Unlike what was previously found for triptycyl-3-helicene, the surfaces for triptycyl-4-helicene and triptycyl-5-helicene contain valley-ridge-inflection (VRI) points. The reaction paths on the reduced surfaces are analyzed to understand the dynamical behaviour of these molecules and to evaluate the possibility of a molecule of this family exhibiting a Brownian ratchet behaviour.

Charge Delocalization, Oxidation States, and Silver Mobility in the Mixed Silver-Copper Oxide AgCuO2 ¤.

The electronic structure of AgCuO2, and more specifically the possible charge delocalization and its implications for the transport properties, has been the object of debate. Here the problem is faced by means of first-principles density functional theory calculations of the electron and phonon band structures as well as molecular dynamics simulations for different temperatures. It is found that both Cu and Ag exhibit noninteger oxidation states, in agreement with previous spectroscopic studies. The robust CuO2 chains impose a relatively short contact distance to the silver atoms, which are forced to partially use their d z2 orbitals to build a band. This band is partially emptied through overlap with a band of the CuO2 chain, which should be empty if copper were in a Cu3+ oxidation state. In that way, although structural correlations could roughly be consistent with an Ag+Cu3+O2 formulation, the appropriate oxidation states for the silver and copper atoms become Ag(1+δ)+ and Cu(3-δ)+, and as a consequence, the stoichiometric material should be metallic. The study of the electronic structure suggests that Ag atoms form relatively stable chains that can easily slide despite the linear coordination with oxygen atoms of the CuO2 chains. Phonon dispersion calculations and molecular dynamics simulations confirm the stability of the structure although pointing out that sliding of the silver chains is an easy motion that does not lead to substantial modifications of the electronic structure around the Fermi level and, thus, should not alter the good conductivity of the system. However, this sliding of the silver atoms from the equilibrium position explains the observed large thermal factors.

Triangular graphene nanofragments: open-shell character and doping.

In this work we study the intricacies of the electronic structure properties of triangular graphene nanofragments (TGNFs) in their ground and low-lying excited states by means of ab initio quantum chemistry calculations. We focus our attention on the radical and diradical characters of phenalenyl and triangulene, the smallest members of the TGNF family, and we describe the nature of their low-lying excited states. Moreover, we rationalize the modulation of the electronic and magnetic properties by means of selective boron or nitrogen substitution of carbon sites and by hydrogen saturation. The obtained results aim to guide future design of graphene-based materials with well-defined properties.

Photophysics of Molecular Aggregates from Excited State Diabatization.

A detailed understanding of photophysical processes in molecular aggregates requires the precise characterization of electronic excited states resulting from the interaction between chromophoric units. Theoretical descriptions of such systems are usually achieved by means of excitonic models, using effective Hamiltonians built on a basis of diabatic states that enable physical interpretations in terms of local excitations, charge transfer, or multiexcitonic configurations. In this work, we develop an alternative approach based on a diabatization scheme, which allows the decomposition of the adiabatic excited state energies of molecular aggregates into contributions issued from intermolecular couplings, without requiring any a priori definition of diabatic states. The general equations describing the deconvolution of adiabatic energies into different types of contributions are presented for various conformations of symmetrical and nonsymmetrical model dimers and compared to the energy expressions derived from excitonic models. We show that, while perturbative approximations typically employed in the construction of excitonic Hamiltonians assume weak intermolecular interactions, the presented methodology is valid within the entire range of coupling regimes. It should therefore constitute a useful tool to extract accurate ab initio diabatic state energies and interstate couplings for eventual derivation of model excitonic Hamiltonians.

Effects of Temperature on the Shape and Symmetry of Molecules and Solids.

Despite its undeniable problems from a philosophical point of view, the concept of molecular structure, with attributes such as shape and symmetry, directly borrowed from the description of macroscopic objects, is nowadays central to most of the chemical sciences. Descriptions such as "the tetrahedral carbon atom" or "octahedral coordination complexes" are widely used as much in elementary textbooks as in the most up-to-date research articles. The definition of molecular shape is, however, not as simple as it might seem at first sight. Molecules don't behave as macroscopic objects do, and the arrangement of atoms within a molecule changes continuously due to the incessant motion of its constituent particles, nuclei, and electrons. How are molecular shape and symmetry affected by this thermal motion? In this Minireview, we introduce the language of continuous symmetry measures as a new tool to quantitatively describe the effects of temperature on molecular shape and symmetry, enriching in this way the set of molecular descriptors that might be used in the establishment of new empirical structure-property relations, of great interest in concomitant areas such as medicinal chemistry or materials science.

A fullerene-carbene adduct as a crystalline molecular rotor: remarkable behavior of a spherically-shaped rotator.

A new fullerene structure was recently obtained from the reaction of a Lewis basic N-heterocyclic carbene (NHC) and the Lewis acidic C60. The molecular features of the zwitterionic adduct can be described as a molecular rotor with the fullerene cage acting as the rotator that spins about one distinct axis given by its C-C single bond linkage with the imidazolium heterocycle stator. A detailed structural analysis of the compound by means of single-crystal X-ray diffraction (XRD) revealed significant differences in the packing motifs of solvent-free and solvent-containing crystals. Variable temperature single-crystal XRD experiments (80 K ≤ T ≤ 480 K) carried out to investigate the rotational dynamics of the fullerene group in the higher quality solvent-free structure revealed atomic displacement parameters consistent with fast rotation of the highly symmetric fullerene in the solid state, whereas the imidazolium unit remains in a fixed position and therefore represents the stator. DFT and semiempirical calculations were applied to get insight into the profile of the rotational potential of the fullerene unit, particularly considering interactions with the neighboring molecules in the crystal lattice. The results indicate that the crystal environment leads to the presence of one lowest energy minimum that is connected to seven others that are slightly higher in energy through rotational barriers of approximately 1.5-2.5 kcal mol(-1).

Pseudosymmetry analysis of molecular orbitals.

We introduce a pseudosymmetry analysis of molecular orbitals by means of the newly proposed irreducible representation measures. To do that we define first what we consider as molecular pseudosymmetry and the relationships of this concept with those of approximate symmetry and quasisymmetry. We develop a general algorithm to quantify the pseudosymmetry content of a given object within the framework of the finite group algebra. The obtained mathematical expressions are able to decompose molecular orbitals by means of the irreducible representations of any reference symmetry point group. The implementation and usefulness of the pseudosymmetry analysis of molecular orbitals is demonstrated in the study of σ and π orbitals in planar and nonplanar polycyclic aromatic hydrocarbons and the t2 g and eg character of the d-orbitals in the [FeH6](3-) anion in its high spin state along the Bailar twist pathway.

Concurrent symmetries: the interplay between local and global molecular symmetries.

We analyze in this article the degree to which different groups of atoms retain local symmetries when assembled in a molecule. This study is carried out by applying continuous symmetry measures to several families of mixed sandwiches, a variety of piano-stool molecules, and several organic groups. An analysis of the local symmetry of the electron density shows that, sandwiched between two regions of different symmetry that correspond to the ligand sets, its symmetry is cylindrical at the central metal atom.