Comprehending the quadruple bonding conundrum in C2 from excited state potential energy curves

Eliminating all bonds from the ground state gives rise to ionic bonding in high-spin states of heterodiatomics

Understanding chemical bonding in second-row diatomics has been central to elucidating the basics of bonding itself. Bond strength and the number of bonds are the two factors that decide the reactivity of molecules. While bond strengths have been theoretically computed accurately and experimentally determined, the number of bonds is a more contentious issue, especially for complicated multi-reference systems like C2. We have developed an experimentally verifiable approach to determine bond numbers from excited spin state potential energy surfaces. On applying this to a series of second-row heterodiatomics, we obtain the surprising phenomenon of an inverted charge transfer ionic state after all the ground state bonds are broken via higher spin states. These ionic states are ubiquitous in all heterodiatomics and unexpected in non-metallic systems.

Machine Learning Diffusion Monte Carlo Forces

Diffusion Monte Carlo (DMC) is one of the most accurate techniques available for calculating the electronic properties of molecules and materials, yet it often remains a challenge to economically compute forces using this technique. As a result, ab initio molecular dynamics simulations and geometry optimizations that employ Diffusion Monte Carlo forces are often out of reach. One potential approach for accelerating the computation of "DMC forces" is to machine learn these forces from DMC energy calculations. In this work, we employ Behler-Parrinello Neural Networks to learn DMC forces from DMC energy calculations for geometry optimization and molecular dynamics simulations of small molecules. We illustrate the unique challenges that stem from learning forces without explicit force data and from noisy energy data by making rigorous comparisons of potential energy surface, dynamics, and optimization predictions among ab initio density functional theory (DFT) simulations and machine-learning models trained on DFT energies with forces, DFT energies without forces, and DMC energies without forces. We show for three small molecules─C₂, H₂O, and CH₃Cl─that machine-learned DMC dynamics can reproduce average bond lengths and angles within a few percent of known experimental results at one hundredth of the typical cost. Our work describes a much-needed means of performing dynamics simulations on high-accuracy, DMC PESs and for generating DMC-quality molecular geometries given current algorithmic constraints.

The Hitchhiker's Guide to the Wave Function∥

The electronic wave function of molecules is 3N-dimensional and inseparable in the coordinates of the N electrons. Whereas molecular orbitals are often invoked to visualize the electronic structure, they are nonunique, with the same 3N-dimensional wave function being represented by an infinite number of 3-D, one-electron functions (orbitals). Furthermore, multireference wave functions cannot be described by an antisymmetrized product of a single set of occupied orbitals. What is required is a way to visualize the full dimensionality of the wave function, including the effects of correlation, as a 3N-dimensional being would be able to do. In the past 5 years, we have been developing a way to analyze and visualize highly dimensional wave functions by focusing on the structure of the repeating unit demanded by fermionic behavior. This 3N-dimensional repeating unit, the wave function "tile", can be projected onto the three dimensions of each electron, in turn, to reveal the complete electronic structure. It is found that the tile reproduces canonical chemical motifs such as core-electrons, single bonds and lone pairs. Multiple bonds emerge as the "banana" bonds favored by Pauling. As a function of the reaction coordinate, electron motions are visualized that correspond to the curly arrow notation of organic chemists. Excited states can also be inspected. Analyzing a wave function in terms of fermionic tiling allows for insight not facilitated by the inspection of orbitals or configuration interaction vectors: The wave function tiles of resonance structures reveal that electron correlation in benzene pushes opposing spin electrons to occupy alternate Kekulé structures, and in C₂, the emerging structure supports the notion of a triply bonded structure with a weak, fourth bonding contribution.

Comparing Isoelectronic, Quadruple-Bonded Metalloporphyrin and Metallocorrole Dimers: Scalar-Relativistic DFT Calculations Predict a >1 eV Range for Ionization Potential and Electron Affinity

A scalar-relativistic DFT study of isoelectronic, quadruple-bonded Group 6 metalloporphyrins (M = Mo, W) and Group 7 metallocorroles (M = Tc, Re) has uncovered dramatic differences in ionization potential (IP) and electron affinity (EA) among the compounds. Thus, both the IPs and EAs of the corrole derivatives are 1 eV or more higher than those of the porphyrin derivatives. These differences largely reflect the much lower orbital energies of the δ- and δ*-orbitals of the corrole dimers relative to those of the porphyrin dimers, which in turn reflect the higher (+III as opposed to +II) oxidation states of the metals in the former compounds. Significant differences have also been determined between Mo and W porphyrin dimers and between Tc and Re corrole dimers. These differences are thought to largely reflect greater relativistic destabilization of the 5d orbitals of W and Re relative to the 4d orbitals of Mo and Tc. The calculated differences in IP and EA should translate to major differences in electrochemical redox potentials-a prediction that in our opinion is well worth confirming.

Routes involving no free C2 in a DFT-computed mechanistic model for the reported room-temperature chemical synthesis of C2

Recent lively debates about the nature of the quadruple bonding in the diatomic species C2 have been heightened by recent suggestions of molecules in which carbon may be similarly bonded to other elements. The desirability of having methods for generating such species at ambient temperatures and in solution in order to study their properties may have been realized by a recent report of the first chemical synthesis of free C2 itself under mild conditions. The method involved unimolecular fragmentation of an alkynyl zwitterion 2 as generated from the precursor 1, resulting in production and then trapping of free C2 at ambient temperatures rather than the high temperature gas phase methods normally employed for C2 generation. Here, alternative mechanisms are proposed for this reaction based on DFT calculations involving bimolecular 1,1- or 1,2-iodobenzene displacement reactions from 2 directly by galvinoxyl radical, or hydride transfer from 9,10-dihydroanthracene to 2. These mechanisms result in the same trapped products as observed experimentally, but unlike that involving unimolecular generation of free C2, exhibit calculated free energy barriers commensurate with the reaction times observed at room temperatures. The relative energies of the transition states for 1,1 vs. 1,2 substitution provide a rationalisation for the observed isotopic substitution patterns. The same mechanism also provides an energetically facile path to polymeric synthesis of carbon rich species by extending the carbon chain attached to the iodonium group, eventually resulting in formation of amorphous carbon and discrete molecules such as C60.