An extended multireference study of the electronic states of para-benzyne

Variations on the Bergman Cyclization Theme: Electrocyclizations of Ionic Penta-, Hepta-, and Octadiynes

The Bergman cyclization of (Z)-hexa-3-ene-1,5-diyne to form the aromatic diradical p-benzyne has garnered attention as a potential antitumor agent due to its relatively low cyclization barrier and the stability of the resulting diradical. Here, we present a theoretical investigation of several ionic extensions of the fundamental Bergman cyclization: electrocyclizations of the penta-1,4-diyne anion, hepta-1,6-diyne cation, and octa-1,7-diyne dication, leveraging the spin-flip formulation of the equation-of-motion coupled cluster theory with single and double substitutions (EOM-SF-CCSD). Though the penta-1,4-diyne anion exhibits a large cyclization barrier of +66 kcal mol-1, cyclization of both the hepta-1,6-diyne cation and octa-1,7-diyne dication along a previously unreported triplet pathway requires relatively low energy. We also identified the presence of significant aromaticity in the triplet diradical products of these two cationic cyclizations.

Signatures of diradicals in x-ray absorption spectroscopy

Theoretical simulations are critical to analyze and interpret the x-ray absorption spectrum of transient open-shell species. In this work, we propose a model of the many-body core-excited states of symmetric diradicals. We apply this model to analyze the carbon K-edge transitions of o-, m-, and p-benzyne, three organic diradicals with diverse and unusual electronic structures. The predictions of our model are compared with high-level multireference computations of the K-edge spectrum of the benzynes obtained with the driven similarity renormalization group truncated to third order. Our model shows the importance of a many-body treatment of the core-excited states of the benzynes and provides a theoretical framework to understand which properties of the ground state of these diradicals can be extracted from their x-ray spectrum.

Photochemistry of 3,6-Didehydropyridazine Biradical─An Untraceable Para Benzyne Analogue

We report matrix isolation infrared spectroscopic studies to characterize 3,6-didehydropyridazine 6, a heterocyclic analogue of para benzyne, combined with computations. In this regard, we have utilized 3,6-diiodopyridazine 11 as a photolytic precursor. The experiments toward the generation of the biradical are carried out in argon and nitrogen matrices at 4 K. Instead of the elusive biradical, we have observed a ring-opening product maleonitrile (Z)-7 upon irradiation at 254 nm. In contrast, prolonged irradiation at 254 nm leads only to Z-E isomerization, forming fumaronitrile (E)-7. The mechanistic aspects of ring-opening, product selectivity, and Z-E photoisomerization steps have been investigated in detail using high-level ab initio computations. These studies have found that 3,6-didehydropyridazine 6 is an untraceable intermediate, and the ring-opening step leading to maleonitrile is barrierless. In addition, we have proposed the involvement of the S₁ (π-π*) state via conical intersection in the Z-E photoisomerization of maleonitrile.

Mixed-Reference Spin-Flip Time-Dependent Density Functional Theory (MRSF-TDDFT) as a Simple yet Accurate Method for Diradicals and Diradicaloids

Due to their multiconfigurational nature featuring strong electron correlation, accurate description of diradicals and diradicaloids is a challenge for quantum chemical methods. The recently developed mixed-reference spin-flip (MRSF)-TDDFT method is capable of describing the multiconfigurational electronic states of these systems while avoiding the spin-contamination pitfalls of SF-TDDFT. Here, we apply MRSF-TDDFT to study the adiabatic singlet-triplet (ST) gaps in a series of well-known diradicals and diradicaloids. On average, MRSF displays a very high prediction accuracy of the adiabatic ST gaps with the mean absolute error (MAE) amounting to 0.14 eV. In addition, MRSF is capable of accurately describing the effect of the Jahn-Teller distortion occurring in the trimethylenemethane diradical, the violation of the Hund rule in a series of the didehydrotoluene diradicals, and the potential energy surfaces of the didehydrobenzene (benzyne) diradicals. A convenient criterion for distinguishing diradicals and diradicaloids is suggested on the basis of the easily obtainable quantities. In all of these cases, which are difficult for the conventional methods of density functional theory (DFT), MRSF shows results consistent with the experiment and the high-level ab initio computations. Hence, the present study documents the reliability and accuracy of MRSF and lays out the guidelines for its application to strongly correlated molecular systems.

The generality of the GUGA MRCI approach in COLUMBUS for treating complex quantum chemistry

The core part of the program system COLUMBUS allows highly efficient calculations using variational multireference (MR) methods in the framework of configuration interaction with single and double excitations (MR-CISD) and averaged quadratic coupled-cluster calculations (MR-AQCC), based on uncontracted sets of configurations and the graphical unitary group approach (GUGA). The availability of analytic MR-CISD and MR-AQCC energy gradients and analytic nonadiabatic couplings for MR-CISD enables exciting applications including, e.g., investigations of π-conjugated biradicaloid compounds, calculations of multitudes of excited states, development of diabatization procedures, and furnishing the electronic structure information for on-the-fly surface nonadiabatic dynamics. With fully variational uncontracted spin-orbit MRCI, COLUMBUS provides a unique possibility of performing high-level calculations on compounds containing heavy atoms up to lanthanides and actinides. Crucial for carrying out all of these calculations effectively is the availability of an efficient parallel code for the CI step. Configuration spaces of several billion in size now can be treated quite routinely on standard parallel computer clusters. Emerging developments in COLUMBUS, including the all configuration mean energy multiconfiguration self-consistent field method and the graphically contracted function method, promise to allow practically unlimited configuration space dimensions. Spin density based on the GUGA approach, analytic spin-orbit energy gradients, possibilities for local electron correlation MR calculations, development of general interfaces for nonadiabatic dynamics, and MRCI linear vibronic coupling models conclude this overview.

An integral-factorized implementation of the driven similarity renormalization group second-order multireference perturbation theory

We report an efficient implementation of a second-order multireference perturbation theory based on the driven similarity renormalization group (DSRG-MRPT2) [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)]. Our implementation employs factorized two-electron integrals to avoid storage of large four-index intermediates. It also exploits the block structure of the reference density matrices to reduce the computational cost to that of second-order Møller-Plesset perturbation theory. Our new DSRG-MRPT2 implementation is benchmarked on ten naphthyne isomers using basis sets up to quintuple-ζ quality. We find that the singlet-triplet splittings (ΔST) of the naphthyne isomers strongly depend on the equilibrium structures. For a consistent set of geometries, the ΔST values predicted by the DSRG-MRPT2 are in good agreements with those computed by the reduced multireference coupled cluster theory with singles, doubles, and perturbative triples.

Towards numerically robust multireference theories: The driven similarity renormalization group truncated to one- and two-body operators

The first nonperturbative version of the multireference driven similarity renormalization group (MR-DSRG) theory [C. Li and F. A. Evangelista, J. Chem. Theory Comput. 11, 2097 (2015)] is introduced. The renormalization group structure of the MR-DSRG equations ensures numerical robustness and avoidance of the intruder-state problem, while the connected nature of the amplitude and energy equations guarantees size consistency and extensivity. We approximate the MR-DSRG equations by keeping only one- and two-body operators and using a linearized recursive commutator approximation of the Baker-Campbell-Hausdorff expansion [T. Yanai and G. K.-L. Chan, J. Chem. Phys. 124, 194106 (2006)]. The resulting linearized MR-DSRG scheme with one- and two-body operators [MR-LDSRG(2)] contains only 39 terms and scales as O(N(2)NP (2)NH (2)) where NH, NP, and N correspond to the number of hole, particle, and total orbitals, respectively. Benchmark MR-LDSRG(2) computations on the hydrogen fluoride and molecular nitrogen binding curves and the singlet-triplet splitting of p-benzyne yield results comparable in accuracy to those from multireference configuration interaction, Mukherjee multireference coupled cluster theory, and internally contracted multireference coupled cluster theory.

Polyradical Character of Triangular Non-Kekulé Structures, Zethrenes, p-Quinodimethane-Linked Bisphenalenyl, and the Clar Goblet in Comparison: An Extended Multireference Study

In this work, two different classes of polyaromatic hydrocarbon (PAH) systems have been investigated in order to characterize the amount of polyradical character and to localize the specific regions of chemical reactivity: (a) the non-Kekulé triangular structures phenalenyl, triangulene and a π-extended triangulene system with high-spin ground state and (b) PAHs based on zethrenes, p-quinodimethane-linked bisphenalenyl, and the Clar goblet containing varying polyradical character in their singlet ground state. The first class of structures already have open-shell character because of their high-spin ground state, which follows from the bonding pattern, whereas for the second class the open-shell character is generated either because of the competition between the closed-shell quinoid Kekulé and the open-shell singlet biradical resonance structures or the topology of the π-electron arrangement of the non-Kekulé form. High-level ab initio calculations based on multireference theory have been carried out to compute singlet–triplet splitting for the above-listed compounds and to provide insight into their chemical reactivity based on the polyradical character by means of unpaired densities. Unrestricted density functional theory and Hartree–Fock calculations have been performed for comparison also in order to obtain better insight into their applicability to these types of complicated radical systems.