High-Spin Blatter's Triradicals.

Robust organic triradicals with high-spin quartet ground states provide promising applications in molecular magnets, spintronics, etc. In this context, a triradical based on Blatter's radical has been synthesized recently, having two low-lying non-degenerate doublet states with a quartet ground state. The traditional broken-symmetry (BS)-DFT computed doublet-quartet energy gaps are reported to be somewhat overestimated in comparison to the experimentally observed values. In this work, we have employed different ab initio methods on this prototypical system to obtain more accurate doublet-quartet energy gaps for this triradical. The spin-constraint broken-symmetry (CBS)-DFT method has been used to reduce the overestimation of energy gaps from BS-DFT. To address the issues of spin-contamination and the multireference nature of low-spin states affecting the DFT methods, we have computed the energy gaps using appropriately state-averaged CASSCF and NEVPT2 computations. Using a series of active spaces, our calculations are shown to provide quite accurate values in concordance with the experimentally observed results. Furthermore, we have proposed and modeled another two triradicals based on Blatter's radical, which are of interest for experimental synthesis and characterization. Our computations show that all these triradicals also have a quartet ground state with a similar energy difference between the excited doublet states.

Toward an efficient implementation of internally contracted coupled-cluster methods.

A new implementation of the internally contracted multireference coupled-cluster with singles and doubles (icMRCCSD) method is presented. The new code employs an efficient tensor contraction kernel and can also avoid full four-external integral transformations, which significantly extends the scope of the applicability of icMRCCSD. The new implementation is currently restricted to the simple case of two active electrons in two orbitals and also supports the computation of spin-adapted doublet and triplet coupled-cluster wavefunctions. This contribution describes the basic approach for the automated derivation of working equations and benchmarks the current code against efficient implementations of standard methods, such as single-reference coupled-cluster singles and doubles (CCSD) and internally contracted multireference configuration interaction (icMRCI). Run times for linearized variants of icMRCCSD are only twice as long as comparable CCSD runs and similar to those of the icMRCI implementation, while non-linear terms of more complete variants of icMRCCSD lead to an order of magnitude longer computation times. Nevertheless, the new code allows for computations at larger scales than it was possible previously, with less demands on memory and disk-space resources. This is exemplified by numerical structure optimizations and harmonic force field determinations of NC2H5 isomers and the singlet and triplet states of m-benzyne. In addition, the exchange coupling of a dinuclear copper complex is determined. This work also defines a new commutator approximation for icMRCCSD, which includes all terms that are also present in the single-reference CCSD method, thus yielding a consistent pair of single-reference and multireference coupled-cluster methods.

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.

Potential Energy Curves of Molecular Nitrogen for Singly and Doubly Ionized States with Core and Valence Holes.

Theoretical description of potential energy curves (PECs) of molecular ions is essential for interpretation and prediction of coupled electron-nuclear dynamics following ionization of parent molecule. However, an accurate representation of these PECs for core or inner valence ionized state is nontrivial, especially at stretched geometries for double- or triple-bonded systems. In this work, we report PECs of singly and doubly ionized states of molecular nitrogen using state-of-the-art quantum chemical methods. The valence, inner valence, and core ionized states have been computed. A double-loop optimization scheme that separates the treatment of the core and the valence orbitals during the orbital optimization step of the multiconfiguration self-consistent field method has been implemented. This technique allows the energy to be converged to any desired ionized state with any number of core or inner-shell holes. The present work also compares the PECs obtained using both delocalized and localized sets of orbitals for the core hole states. The PECs of a number of singly and doubly ionized valence states have also been computed and compared with previous studies. The computed PECs reported here are expected to be of importance for future studies to understand the interplay between photoionization and Auger spectra during the breakup of molecular nitrogen when interacting with intense free electron lasers.

Beyond Born-Oppenheimer constructed diabatic potential energy surfaces for F + H2 reaction.

First principles based beyond Born-Oppenheimer theory has been implemented on the F + H2 system for constructing multistate global diabatic Potential Energy Surfaces (PESs) through the incorporation of Nonadiabatic Coupling Terms (NACTs) explicitly. The spin-orbit (SO) coupling effect on the collision process of the F + H2 reaction has been included as a perturbation to the non-relativistic electronic Hamiltonian. Adiabatic PESs and NACTs for the lowest three electronic states (12A', 22A', and 12A″) are determined in hyperspherical coordinates as functions of hyperangles for a grid of fixed values of the hyperradius. Jahn-Teller (JT) type conical intersections between the two A' states translate along C2v and linear geometries in F + H2. In addition, A' and A″ states undergo Renner-Teller (RT) interaction at collinear configurations of this system. Both JT and RT couplings are validated by integrating NACTs along properly chosen contours. Subsequently, we have solved adiabatic-to-diabatic transformation (ADT) equations to evaluate the ADT angles for constructing the diabatic potential matrix of F + H2, including the SO coupling terms. The newly calculated diabatic PESs are found to be smooth, single-valued, continuous, and symmetric and can be invoked for performing accurate scattering calculations on the F + H2 system.

Aluminum containing molecular bowls and pyridinophanes: use of pyridine modules to access different molecular topologies.

Molecular topologies varying from simple complexes to pyridinophanes (neutral and cationic) and to bicyclic pyridinophane containing organoaluminum (Al-Me) species were synthesized by varying the relative stoichiometry of bis(trimethylsilyl)-N,N'-2,6-diaminopyridine (bap) and the reactive partner (AlMe3). The ultimate goal of these reactions was to systematically design cyclic structures containing group 13 elements. To highlight the reaction potential of these shapes, the bowl-shaped pyridinophane was reacted with the Lewis acid, B(C6F5)3, to generate a stable cationic derivative. An unprecedented bicyclic pyridinophane, [2,6-(Me3SiN)2C5H3N]3Al2, was obtained from the reaction of bap with AlH3·NMe2Et. The formation of [2,6-(Me3SiN)2C5H3N]3Al2 is in contrast to the known reaction between BH3·SMe2 and bap that afforded the syn-tetraazadibora[3.3](2,6)pyridinophane. Quantum chemical calculations have been performed to rationalize the preference for the formation of B-pyridinophane and Al-bicyclic pyridinophane and can be attributed to the nature of B-N and Al-N bonds.

Electronically Unsaturated Three-Coordinate Aluminum Hydride and Organoaluminum Cations.

New three-coordinate and electronically unsaturated aluminum hydride [LAlH]+ [HB(C6 F5 )3 ]- (LH=[{(2,6-iPr2 C6 H3 N)P(Ph2 )}2 N]H) and aluminum methyl [LAlMe]+ [MeB(C6 F5 )3 ]- cations have been prepared. The quantitative estimation of Lewis acidity by Gutmann-Beckett method revealed [LAlH]+ [HB(C6 F5 )3 ]- to be better Lewis acid than B(C6 F5 )3 and AlCl3 making these compounds ideal catalysts for Lewis acid-mediated reactions. To highlight that the work is of fundamental importance, catalytic hydroboration of aliphatic and aromatic aldehydes and ketones have been demonstrated. Important steps of the catalytic cycle have been probed by using multinuclear NMR measurements, including successful characterization of the proposed aluminum benzyloxide cationic intermediate, [LAl-O-CH2 Ph]+ [HB(C6 F5 )3 ]- . The proposed catalytic cycle has been found to be consistent with experimental observations and computational studies clearly indicating the migration of hydride from cationic aluminum center to the carbonyl carbon is the rate-limiting step of the catalytic cycle.

Two Different Pathways in the Reduction of [(S=)PCl(µ-NtBu)]2 with Na.

Reduction of the cyclodiphosphazane [(S=)ClP(µ-NtBu)]2 (1) with sodium metal in refluxing toluene proceeds via two different pathways. One is a Wurtz-type pathway involving elimination of NaCl from 1 followed by head-to-tail cyclization to give the hexameric macrocycle [(µ-S)P(µ-NtBu)2 P(=S)]6 (2). The other pathway involves reduction of the P=S bonds of 1 to generate colorless singlet biradicaloid dianion trans-[S-P(Cl)(µ-NtBu)]2 (2-) , which is observed in the polymeric structures of three-dimensional [{(S-)ClP(µ-NtBu)2 PCl(S)}Na(Na⋅THF2 )]n (3) and two dimensional [{(S-)ClP(µ-NtBu)2 PCl(S)} (Na⋅THF)2 ]n (4).

Reactivity of a dihydroboron species: synthesis of a hydroborenium complex and an expedient entry into stable thioxo- and selenoxo-boranes.

The reaction of a recently synthesized dihydroboron species complexed with bis(phosphinimino)amide, LBH2 (), (L = [N(Ph2PN(2,4,6-Me3C6H2))2](-)) with 3 equivalents of BH2Cl·SMe2 or one equivalent of BCl3 affords the first stable monohydridoborenium ion, [LBH](+)[HBCl3](-) () that is stable without a weakly coordinating bulky anion. Compound can also be prepared directly by refluxing LH with 3 equivalents of BH2Cl·SMe2. Interestingly, reaction of LBH2 () with elemental sulfur and selenium involves oxidative addition of S and Se into B-H bonds and subsequent release of H2S (or H2Se) from the intermediate LB(SH)2 (or LB(SeH)2) species forming stable compounds with terminal boron-chalcogen double bonds LB[double bond, length as m-dash]S () and LB[double bond, length as m-dash]Se (). The electronic structures of compounds , and were elucidated by high resolution mass spectrometry, multi-nuclear NMR and single crystal X-ray diffraction studies. Ab initio calculations on are in excellent agreement with its experimental structure and clearly support the existence of the boron-sulfur double bond.

Communication: multireference equation of motion coupled cluster: a transform and diagonalize approach to electronic structure.

The novel multireference equation-of-motion coupled-cluster (MREOM-CC) approaches provide versatile and accurate access to a large number of electronic states. The methods proceed by a sequence of many-body similarity transformations and a subsequent diagonalization of the transformed Hamiltonian over a compact subspace. The transformed Hamiltonian is a connected entity and preserves spin- and spatial symmetry properties of the original Hamiltonian, but is no longer Hermitean. The final diagonalization spaces are defined in terms of a complete active space (CAS) and limited excitations (1h, 1p, 2h, …) out of the CAS. The methods are invariant to rotations of orbitals within their respective subspaces (inactive, active, external). Applications to first row transition metal atoms (Cr, Mn, and Fe) are presented yielding results for up to 524 electronic states (for Cr) with an rms error compared to experiment of about 0.05 eV. The accuracy of the MREOM family of methods is closely related to its favorable extensivity properties as illustrated by calculations on the O2-O2 dimer. The computational costs of the transformation steps in MREOM are comparable to those of closed-shell Coupled Cluster Singles and Doubles (CCSD) approach.

Charge symmetric dissociation of doubly ionized N2 and CO molecules.

We report a comparative study of the features in dissociative double ionization by high energy electron impact of N2 and CO molecules. The ratio of cross-section of charge symmetric dissociative ionization to non-dissociative ionization (CSD-to-ND ratio) and the kinetic energy release (KER) spectra of dissociation are experimentally measured and carefully corrected for various ion transmission losses and detector inefficiencies. Given that the double ionization cross sections of these iso-electronic diatomics are very similar, the large difference in the CSD-to-ND ratios must be attributable to the differences in the evolution dynamics of the dications. To understand these differences, potential energy curves (PECs) of dications have been computed using multi-reference configuration interaction method. The Franck-Condon factors and tunneling life times of vibrational levels of dications have also been computed. While the KER spectrum of N2 (++) can be readily explained by considering dissociation via repulsive states and tunneling of meta-stable states, indirect dissociation processes such as predissociation and autoionization have to be taken into account to understand the major features of the KER spectrum of CO(++). Direct and indirect processes identified on the basis of the PECs and experimental KER spectra also provide insights into the differences in the CSD-to-ND ratios.

A new internally contracted multi-reference configuration interaction method.

We present a new internally contracted multi-reference configuration interaction (MRCI) method which, at the same time, efficiently handles large active orbital spaces, long configuration expansions, and many closed-shell orbitals in the reference function. This is achieved by treating the closed-shell orbitals explicitly, so that all required coupling coefficients and density matrices only depend on active orbital labels. As a result, closed-shell orbitals are handled as efficiently as in a closed-shell single-reference program, and this opens up the possibility to perform high-accuracy MRCI calculations for much larger molecules than before. The enormously complex equations are derived using a new domain-specific computer algebra system and semi-automatically implemented using a newly developed integrated tensor framework. The accuracy and efficiency of the MRCI method is demonstrated with applications to dioxygen-copper complexes with different ligands, some of which involve more than 30 atoms, and to spin-state splittings of ferrocene.

Cumulant decomposition of reduced density matrices, multireference normal ordering, and Wicks theorem: A spin-free approach.

We propose a spin-free approach to the cumulant decomposition of reduced density matrices of singlet and spin-rotation or SU(2) invariant ensemble of nonsinglet states as in [W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 110, 2800 (1999); 116, 4787 (2002)]. We provide a simple recursive procedure to obtain expressions which relate different spin components of spin-orbital reduced density matrices and cumulants of such states to the spin-free counterparts. These results are used to set up a spin-summation procedure to arrive at a definition of spin-free cumulants of any order. Alternatively, an analytic formula for the spin-free form resulting from a spin summation involving product of two spin-orbital cumulants is derived and its utility in spin-free cumulant decomposition of reduced density matrices is demonstrated. This leads to suitable definitions of spin-free analog of multireference normal ordering and the associated Wicks theorem. The results of this formulation are expected to be useful in investigations of spin-free multireference internally contracted coupled-cluster methods where cumulant approximations to the active reduced density matrices are employed.

State specific equation of motion coupled cluster method in general active space.

The state specific equation of motion coupled cluster (SS-EOMCC) method is an internally contracted multireference approach, applicable to both ground and excited states. Attractive features of the method are as follows: (1) the SS-EOMCC wave function is qualitatively correct and rigorously spin adapted, (2) both orbitals and dynamical correlation are optimized for the target state, (3) nondynamical correlation and differential orbital relaxation effects are taken care of by a diagonalization of the transformed Hamiltonian in the multireference configuration-interaction singles space, (4) only one- and two-particle density matrices of a complete-active-space self-consistent-field reference state are needed to define equations for the cluster amplitudes, and (5) the method is invariant with respect to orbital rotations in core, active, and virtual subspaces. Prior applications focused on biradical-like systems, in which only one extra orbital is needed to construct the active space, and similarly, single bond breaking processes. In this paper, the applicability of the method is extended to systems of general active spaces. Studies on F(2), H(2)O, CO, and N(2) are carried out to gauge its accuracy. The convergence strategy is discussed in detail.

Application of double ionization state-specific equation of motion coupled cluster method to organic diradicals.

The state-specific equation of motion coupled cluster method is applied to three systems of diradical character: automerization of cyclobutadiene, singlet-triplet gaps of trimethylmethylene, and Bergman reaction. The aim of the paper is to assess the performance of the method and test numerically the importance of orbital optimization, three-body terms in transformed Hamiltonian, and the choice of cluster equations.

A constrained variational approach for energy derivatives in Fock-space multireference coupled-cluster theory.

In this paper, we present a formulation based on constrained variational approach to enable efficient computation of energy derivatives using Fock-space multireference coupled-cluster theory. Adopting conventional normal ordered exponential with Bloch projection approach, we present a method of deriving equations when general incomplete model spaces are used. Essential simplifications arise when effective Hamiltonian definition becomes explicit as in the case of complete model spaces or some special quasicomplete model spaces. We apply the method to derive explicit generic expressions upto third-order energy derivatives for [0,1], [1,0], and [1,1] Fock-space sectors. Specific diagrammatic expressions for zeroth-order Lagrange multiplier equations for [0,1], [1,0], and [1,1] sectors are presented.