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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. [ABSTRACT FROM AUTHOR]

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 C2 v 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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 F2, H2O, CO, and N2 are carried out to gauge its accuracy. The convergence strategy is discussed in detail. [ABSTRACT FROM AUTHOR]

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. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

In order to explore spectroscopic properties of a floppy molecule, it is necessary to compute accurate diabatic potential energy surfaces (PESs) around the Franck–Condon region of nuclear configuration space. In such cases, it is desirable to include the non-adiabatic coupling terms (NACTs) through Jahn–Teller (JT) and pseudo Jahn–Teller (PJT) effects as well as other accidental conical intersections (CIs) prevailing among the electronic states of the molecule. In this work, we investigate NACTs among the five lowest doublet electronic states of NO3radical [and 22B2)], in which all those effects (JT, PJT and CIs) have prominent contributions. The study is carried out in terms of normal modes (Qis) of NO3and the CIs (JT and accidental) are located in a plane of nuclear configuration space of two such coordinates (QiandQj). We have calculatedab initioadiabatic PESs and NACTs of those five states of NO3at the MRCI level as functions of pairwiseQis. Further, to explore the nature of a given CI in terms of normal coordinates contributing to NACTs within a particular planeQi-Qj, we have performed CP-MCSCF study computing analytic NACTs and characterised their contributions along variousQks. [ABSTRACT FROM PUBLISHER]

Reduction of the cyclodiphosphazane [(S=)ClP(μ-N tBu)]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-N tBu)2P(=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-N tBu)]22−, which is observed in the polymeric structures of three-dimensional [{(S−)ClP(μ-N tBu)2PCl(S)}Na(Na ⋅THF2)] n ( 3) and two dimensional [{(S−)ClP(μ-N tBu)2PCl(S)} (Na ⋅THF)2] n ( 4). [ABSTRACT FROM AUTHOR]

The k-particle reduced density matrices γk for a singlet state or a spin-orientation averaged ensemble are invariant under the spin rotation group SU(2), i.e. they are independent of spin, even if they are expressed in terms of spin orbitals. The γk contain the same information as their spinfree counterparts Γk expressed in terms of spinfree orbitals. However, the relation between the two quantities is, by no means, elementary. The summation over spin is particularly demanding and surprisingly complicated for the k-particle density cumulants λk and for the formulation of a generalised normal ordering with respect to an arbitrary reference state, including the generalised Wick theorem. Plausible extrapolations from small k turned out to be unjustified and some published expressions for k = 4 need to be revised. A compact general result, valid for all k has not yet been found. [ABSTRACT FROM AUTHOR]

In the present article are analyzed the non‐adiabatic coupling terms (NACT) for two molecular systems, namely H3+ and H3. In contrast to previous occasions in which the NACTs are studied along (closed) circular contours usually surrounding conical intersections (ci), in the present article are studied distribution of the NACTs in (planar) configuration spaces (CS). The motivation for this study has to do with a novel idea being mentioned earlier (Molec. Phys., 116, 2435 [2018]; ArXiv:1801.00103) that NACTs are like a Glue (eventually) associated with the ability of creating molecules and/or protecting them from breaking up. It was found that the distributions of the NACTs due to the two molecules are similar as long as the attention is given to regions close to their equilateral cis, but then they behave significantly different in other regions. In case of H3+, the NACTs are distributed rather uniformly whereas, in case of H3 they become spiky the closer they approach the diatom axis. The main conclusion of this study is that the glue which has its origin in the NACTs is most likely to be effective in case of H3+ that explains the creation and later survival of this molecule. [ABSTRACT FROM AUTHOR]

A sulfur ‐ bridged inorganic macrocycle and a room temperature singlet biradicaloid dianion have been isolated in the Wurtz reduction of a mixture of cis ‐ and trans ‐ dichlorophosph(V)azane. It appears that these products from the same reaction are the outcome of two different reduction pathways. This approach may facilitate the discovery of new types of inorganic macrocycles and new polymeric assemblies similar to those observed in this work. More information can be found in the Full Paper by S. Singh, D. S. Wright et al. on page 12027 ff. [ABSTRACT FROM AUTHOR]

First principles based beyond Born-Oppenheimer theory has been implemented on the F + H 2 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 + H 2 reaction has been included as a perturbation to the non-relativistic electronic Hamiltonian. Adiabatic PESs and NACTs for the lowest three electronic states (1 2 A', 2 2 A', and 1 2 A″) 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 C 2v and linear geometries in F + H 2 . 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 + H 2 , 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 + H 2 system.

New three-coordinate and electronically unsaturated aluminum hydride [LAlH] + [HB(C 6 F 5 ) 3 ] - (LH=[{(2,6-iPr 2 C 6 H 3 N)P(Ph 2 )} 2 N]H) and aluminum methyl [LAlMe] + [MeB(C 6 F 5 ) 3 ] - cations have been prepared. The quantitative estimation of Lewis acidity by Gutmann-Beckett method revealed [LAlH] + [HB(C 6 F 5 ) 3 ] - to be better Lewis acid than B(C 6 F 5 ) 3 and AlCl 3 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-CH 2 Ph] + [HB(C 6 F 5 ) 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., (© 2018 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.)

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)., (© 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)