The ground state and first singlet excited state of ethylene, so-called N and V states, respectively, are studied by means of modern valence bond methods. It is found that extremely compact wave functions, made of three VB structures for the N state and four structures for the V state, provide an N → V transition energy of 8.01 eV, in good agreement with experiment (7.88 eV for the N → V transition energy estimated from experiments). Further improvement to 7.96/7.93 eV is achieved at the variational and diffusion Monte Carlo (MC) levels, respectively, VMC/DMC, using a Jastrow factor coupled with the same compact VB wave function. Furthermore, the measure of the spatial extension of the V state wave function, 19.14 a02, is in the range of accepted values obtained by large-scale state-of-the-art molecular orbital-based methods. The σ response to the fluctuations of the π electrons in the V state, known to be a crucial feature of the V state, is taken into account using the breathing orbital valence bond method, which allows the VB structures to have different sets of orbitals. Further valence bond calculations in a larger space of configurations, involving explicit participation of the σ response, with 9 VB structures for the N state and 14 for the V state, confirm the results of the minimal structure set, yielding an N → V transition energy of 7.97 eV and a spatial extension of 19.16 a02 for the V state. Both types of valence bond calculations show that the V state of ethylene is not fully ionic as usually assumed, but involving also a symmetry-adapted combination of VB structures each with asymmetric covalent π bonds. The latter VB structures have cumulated weights of 18–26 % and stabilize the V state by about 0.9 eV. It is further shown that these latter VB structures, rather than the commonly considered zwitterionic ones, are the ones responsible for the spatial extension of the V state, known to be ca. 50 % larger than the V state.
Valence bond Quantum Monte Carlo V state of ethylene Breathing orbitals
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W. W. is supported by the Natural Science Foundation of China (Nos. 21120102035, 21273176, 21290193). SS thanks the Israel Science Foundation (ISF grant 1183/13). B. B. thanks the IDRIS computational center for an allocation of computer time.
1.The State Key Laboratory of Physical Chemistry of Solid Surfaces, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, College of Chemistry and Chemical EngineeringXiamen UniversityXiamenChina
2.Laboratoire de Chimie Théorique, CNRS, UMR 7616UPMC Université Paris 06Paris Cedex 05France
3.Institute of Chemistry and The Lise Meitner-Minerva Center for Computational Quantum ChemistryHebrew University of JerusalemJerusalemIsrael
4.Laboratoire de Chimie Physique, CNRS UMR8000, Bat. 349Université de Paris-SudOrsay CédexFrance