Multireference Brillouin−Wigner Coupled Cluster Singles and Doubles Study of the Singlet−Triplet Separation in Alkylcarbenes

Potential energy surface studies via a single root multireference coupled cluster theory

We have employed complete active space based single root multireference coupled cluster method (the resulting method is referred to by the acronym sr-MRCC) to compute the potential energy surfaces (PESs) of some well studied "protypical model" systems for which a highly accurate and reliable database is available for comparison. As that of state-specific theory, the sr-MRCC approach focuses and correlates one state while using a multiconfigurational reference and thus it naturally avoids intruder states. The present method is structurally different from the well known state specific multireference coupled cluster (SS-MRCC) method introduced by Mahapatra et al. [Mol. Phys. 94, 157 (1998)]. As that of the SS-MRCC theory, the present method is also based on the Jeziorski-Monkhorst ansatz where a different exponential cluster operator exp(T(mu)) acts on its corresponding model function phi(mu). The final cluster finding equations contain coupling between the cluster operators for all the mu, which are mainly responsible to prove the extensivity of both the cluster amplitudes and the energy. The present sr-MRCC theory is size-extensive and size-consistent when localized orbitals are used. The systems considered here exhibit varying degrees of degeneracy at different regions of PES. The treatment of these systems via traditional effective Hamiltonian based methods suffers from divergence problems in the iterative solution of the CC equations (the issue termed as "intruder state"). The sr-MRCC results lie closer to the ones obtained by the SS-MRCC method for these systems. To judge the efficacy of the present method, we have compared our results with other previously published theoretical estimations, which clearly indicate that the present method is reliable in studying the dissociation PES of states plagued by electronic degeneracy as well as notorious intruder effects. The highly satisfactory performance of the sr-MRCC method, vis-a-vis the other sophisticated methods, in describing the lowest and the first excited singlet states of BeH(2) at points of high degeneracy is noticeable.

Relativistic effects in atomic and molecular properties

We present an overview of basic principles and methods of the relativistic quantum chemistry. Practical aspects of different methods will be discussed stressing their capability of providing accurate predictions of molecular properties, particularly in species containing a heavy metal element. We will present a series of examples showing the importance of relativistic effects in a variety of molecular properties including electron affinities, ionization potentials, reaction and dissociation energies, electric, spectroscopic and other properties. It is possible to recognize a link between these properties and behaviour of materials in some cases. Particular attention is paid to relativistic calculations of the nuclear quadrupole moments for which accurate theoretical electric field gradient is combined with data from the microwave spectra. Important aspect of the present paper is understanding of trends in electronically related atoms throughout the Mendeleev Periodic Table rather than focusing on highly accurate numbers. We will show that relativistic effects represent an unavoidable instrument for explaining some unexpected properties of heavy metal containing compounds. We will also discuss an interplay between the many-electron correlation and relativistic effects.

Analytic gradient for the multireference Brillouin-Wigner coupled cluster method and for the state-universal multireference coupled cluster method

We present the analytic gradient theory and its pilot implementation for the multireference Brillouin-Wigner coupled cluster (BWCC) method and for the state-universal multireference coupled cluster method. The analytic gradient has been derived for three cases: (i) BWCC method without a size-extensivity correction, (ii) BWCC method with the iterative size-extensivity correction, and (iii) for the rigorously size-extensive state-universal method. The pilot implementation is based on full-configuration interaction expansions and is presently limited to single and double excitation levels; however, the resulting equations are general. For BWCC methods, they also do not contain terms explicitly mixing amplitudes of different reference configurations and can thus be implemented in an efficient way. The analytic gradients have been verified with respect to numerically computed ones on the example of CH2 molecule, and geometry optimizations of CH2 and SiH2 have been carried out.

Femtosecond Dynamics of the tert-Butyl Radical, t-C4H9

The excited-state dynamics of the tert-butyl radical, t-C4H9, was investigated by femtosecond time-resolved photoionization and photoelectron spectroscopy. The experiments were supported by ab initio calculations. tert-Butyl radicals, generated by flash pyrolysis of azo-tert-butane, were excited into the A 2A1 (3s) state between 347 and 307 nm and the 3p band at 274 and 268 nm and ionized by 810-nm radiation, in a [1 + 2'] or [1 + 3'] process. Electronic structure calculations confirm that the two states are of s and p Rydberg characters, respectively. The carbon framework becomes planar and thus ion-like in both states. The photoelectron spectra are broad and seem to be mediated by accidental intermediate resonances in the probe step. All time-resolved photoelectron spectra can be described by a single decay time. For the A 2A1 state, lifetimes between 180 and 69 fs were measured. Surprisingly, a much longer lifetime of around 2 ps was found for the 3p state. To understand the decay dynamics, the potential energy was computed as a function of several important nuclear coordinates. A [1,2] H-atom shift to the isobutyl radical seems not to be important for the excited-state dynamics. Qualitative considerations indicate curve crossings between the ground state, the 3s state, and a valence state along the asymmetric C-C stretch coordinate that correlates to the dimethylcarbene + methyl product channel. The implications of the present study for earlier work on the nanosecond time scale are discussed.

The Singlet−Triplet Gap in Trimethylenmethane and the Ring-Opening of Methylenecyclopropane: A Multireference Brillouin−Wigner Coupled Cluster Study

We performed an ab initio study of the singlet-triplet gap in trimethylenmethane (TMM) and of the ring-opening of methylenecyclopropane by the multireference BWCC method. Since the singlet states of TMM and intermediates between TMM and methylenecyclopropane have a strong multiconfigurational character, it is necessary to use a multireference method. The cc-pVDZ and cc-pVTZ basis sets were used. We compared our results with experiments, where available, and with previous calculations performed by MCSCF and spin-flip coupled-cluster-type methods.

Multireference Brillouin-Wigner coupled clusters method with noniterative perturbative connected triples

We developed and implemented the state-specific Brillouin-Wigner coupled cluster method with singles, doubles, and noniterative perturbative triples, called MR BWCCSD(T), for a general number of closed- and open-shell reference configurations. To assess the accuracy of the method, we performed calculations of the three lowest electronic states of the oxygen molecule and of the automerization barrier of cyclobutadiene. For the oxygen molecule, the results were in a good agreement in comparison with those of the iterative MR BWCCSDTalpha method. For cyclobutadiene, the effect of connected triples was found to be minor, which is in agreement with the previous study by and Balková and Bartlett [J. Chem. Phys. 101, 8972 (1994)].

A molecular orbital analysis of Cu(I)-catalysed cyclopropanation using diazoalkanes with CH3 and CF3 substituents

The mechanism of cyclopropanation catalysed by Cu(I) complexes has been investigated by calculation using a series of diazoalkanes containing inductive electron donating (methyl) and withdrawing (CF3) substituents and a range of metal fragments (Cu+, [(DAB)Cu]+, ClCu and (triflate)Cu). Copper-diazoalkane complexes exist as an equilibrium of C- and N-bonded isomers. Catalysis occurs through lowering of the activation energy for rate determining C-N bond cleavage of the C-bonded isomer; this is most marked for (triflate)Cu. Direct reaction of the copper-carbene complex occurs to yield stable cupracyclobutanes in all but one case. Associative substitution of the cupracyclobutane by diazoalkane completes the catalytic cycle.

Towards the multireference Brillouin–Wigner coupled-clusters method with iterative connected triples: MR BWCCSDT-α approximation

We developed and implemented an approximation of the state-specific Brillouin-Wigner coupled-cluster method with singles, doubles, and triples, called MRBWCCSDT-alpha, for a general number of closed- and open-shell reference configurations. The accuracy of the method is assessed on the calculation of the oxygen molecule in the X3sigma(g-), a1delta(g), and b1sigma(g+) states and the results of this multireference treatment are compared with previous MRBWCCSD results and with those obtained by the doubly ionized similarity transformed equation-of-motion CCSD and multireference configuration interaction methods and with experimental spectroscopic data. Explicit tests of the size-extensivity of the MRBWCCSDT-alpha method with iterative size-extensivity correction are also performed.