Accurate Potential Energy Surfaces and Beyond: Chemical Reactivity, Binding, Long-Range Interactions, and SpectroscopyView this Special Issue
Research Article | Open Access
Anyang Li, Sen Lin, Daiqian Xie, "
Ab Initio Potential Energy Surfaces for Both the Ground () and Excited () Electronic States of HSiBr and the Absorption and Emission Spectra of HSiBr/DSiBr
Ab Initio potential energy surfaces for the ground () and excited () electronic states of HSiBr were obtained by using the single and double excitation coupled-cluster theory with a noniterative perturbation treatment of triple excitations and the multireference configuration interaction with Davidson correction, respectively, employing an augmented correlation-consistent polarized valence quadruple zeta basis set. The calculated vibrational energy levels of HSiBr and DSiBr of the ground and excited electronic states are in excellent agreement with the available experimental band origins. In addition, the absorption and emission spectra of HSiBr and DSiBr were calculated using an efficient single Lanczos propagation method and are in good agreement with the available experimental observations.
Silylenes and its halogenated analogs are important reactive intermediates in the chemical vapor deposition of silicon thin films  and plasma etching process . The identification and quantification of such intermediates could help make these processes more efficient, so that they have attracted much attention in experimental and theoretical studies [3–17]. However, because these radicals are typically short-lived and highly reactive, it is difficult to monitor them. Due to the lack of comprehensive spectroscopic signatures for these species, the detailed mechanism of such semiconductor growth processes is still not fully understood.
In this work, we focus on the monobromosilylene (HSiBr) system, which was first detected by Herzberg and Verma in 1964 . Both absorption and emission spectra of HSiBr in the 410–600 nm were obtained by flash photolysis of SiH3Br. The vibrational fundamentals and geometries for both the ground and excited states were confirmed after vibrational and rotational analyses of the spectra. Although no spin splittings were observed, the occurrence of subbands with and led them to assume that the electronic transition was triplet-singlet. Subsequently in 1965, these electronic transitions were confirmed to be by Hougen and Watson via an “axis-switching” mechanism . The spectra of the system of jet-cooled HSiBr and its deuterated analog were obtained about 15 years ago by Harjanto et al.  using pulsed electric discharge techniques, and the structures for the ground and excited states were determined from the rotational analyses of the band. Later in 2001, 26/51 ground state vibrational levels of HSiBr/DSiBr were observed by Hostutler et al.  from the single vibronic level dispersed fluorescence spectra of jet-cooled HSiBr/DSiBr by laser excitation of selected bands.
Unlike HSiF and HSiCl, only a few theoretical studies have been reported for monobromosilylene (HSiBr) [6, 13]. In 1979, Gilchrist et al.  determined the geometrical structures and bending potentials for the excited state of HSiBr by fitting the Herzberg and Verma’s data  and also obtained the H–Si stretching frequency ( cm−1), which is agreement with the later experimental value of 1787 cm−1 . In order to ascertain the validity of their refined force constants, Hostutler et al.  calculated the independent ground and excited state structures at B3LYP level with 6-311G(3df,3pd) basis set in 2001. To our best knowledge, however, no potential energy surface (PES) has been reported for either the ground or excited electronic state of HSiBr. The lack of reliable PESs will hinder our understanding of the spectroscopy of this important molecule, particularly for highly excited vibrational levels which can be probed by emission spectroscopy.
In the present work, we extend our previous studies on the HGeCl , HGeBr , and HSiCl  systems by reporting accurate ab initio PESs for both the ground () and excited () electronic states of HSiBr using the coupled cluster singles and doubles with perturbative triples method [CCSD(T)] and the internally contracted multireference configuration interaction method with the Davidson correction for higher excitations (MRCI + Q), respectively, employing an augmented correlation-consistent polarized valence quadruple zeta (AVQZ) basis set. The vibrational energy levels on both the two electronic states as well as the absorption and emission spectra were calculated and compared with the available experimental data. The reasonable good agreement between our results and experimental data demonstrates that the PESs are very accurate. This paper is organized as follows. In Section 2, we describe the details of the ab initio calculations and the analytical representation of the PESs and transition dipole moments, as well as the quantum mechanical method to calculate the vibrational energy levers. Section 3 discusses the main features of the PESs, vibrational states, and electronic spectra, respectively. A brief conclusion is summarized in Section 4.
2. Computational Details
2.1. Potential Energy Surfaces and Transition Dipole Moment Surface
Ab Initio calculations were carried out to determine the potential energy surfaces (PESs) for both the and states of HSiBr by using the MOLPRO  suite of quantum chemistry programs. The corresponding transition dipole moment surfaces were also calculated in this work.
The two PESs were constructed independently. For the closed-shell ground () electronic state, the single-reference RCCSD(T) method  was employed with Dunning’s AVQZ basis set , which generates a total of 223 cGTOs, and the core electrons were frozen in all the ab initio calculations. A nonuniform and truncated direct product grid in the internal coordinates () was selected for the calculations of PES, where and are the H–Si and Si–Br internuclear distances, respectively, and is the enclosed bond angle ∠HSiBr. For the two radial coordinates, we have chosen 17 points covering the H–Si radial coordinate from 2.2 to 6.5 and 15 points in the Si–Br radial coordinate from 3.2 to 5.4 . In the angle coordinate, 12 points ranging from 55° to 180° were used. This gives a total of 3060 geometry-unique points.
In the case of the open-shell excited electronic state () of HSiBr, which can not be adequately treated by single electronic configuration, the MRCI + Q [24–26] calculations were carried out using the Dunning’s AVQZ basis set. After primary test calculations, the state-averaged complete active space self-consistent field (SA-CASSCF) [27, 28] for equally weighted 11 and 21 states were employed with a large active space (18 active electrons in 12 active orbitals) to further consider the core-valence correlation effect [15, 18–20]. The remnant sixteen core orbitals were kept doubly occupied but fully optimized. Based on the CASSCF natural orbitals, the subsequent MRCI + Q calculations were carried out for the full valence active space (12 electrons in 9 orbitals), where core-valence and core-core correlations were also included by single and double excitations from three 2p orbitals of Si in each configuration state function. The total number of contracted configurations is about . A relatively extensive range is also chosen for the ab initio points. In particular, sixteen points from 2.2 to 5.5 for and fourteen points from 3.25 to 5.15 for were selected. In the angle direction, twelve points were used ranging from 55 to 180°. A total of 2688 geometry-unique points were generated.
In addition, we have also calculated the non-zero () transition dipole moment, which is perpendicular to the molecular plane, using the MRCI + Q method with the AVTZ basis set.
Finally, the potential energies and the transition dipole moment at any arbitrary point were obtained using the three-dimensional cubic spline interpolation. The corresponding FORTRAN codes are available upon request.
2.2. Vibrational Energy Levels
The vibrational energy levels were obtained by solving the vibrational Hamiltonian with the total angular momentum in Radau coordinates (), where and are the atomic mass of H and Br, respectively. The transformation between the Radau coordinates () and the internal coordinates (, , ) is well documented . The vibrational wave functions were represented in a direct product discrete variable representation (DVR)  grid, and the vibrational energy levels were calculated using the Lanczos algorithm , which generates the eigenvalues of the Hamiltonian by a three-term recursion. Extensive convergence tests were carried out to ascertain the accuracy of the results against the number of recursion steps and grid size. When eigenfunctions were required, the Lanczos recursion was repeated to assemble the wave functions of interest.
For the ground electronic state, was represented by 50 potential optimized DVR (PODVR) [32, 33] grid points derived from the one-dimensional Hamiltonian, in which the two other coordinates were fixed at their equilibrium values. The other radial coordinate was represented by 30 PODVR grid points from the corresponding one-dimensional Hamiltonian. For the angular variable, 80 Gauss-Legendre  grid points were used. The converged vibrational energy levels below 7500 cm−1 were generated by performing about 7000 Lanczos recursion steps with a cutoff of 4.0 eV for the potential energy.
In the case of the excited electronic state of HSiBr, different parameters were used for calculating the vibrational states. The PODVR grids for and consist of 50 and 30 points, respectively. 80 Gauss-Legendre grid points in the interval [0°, 180°] were used for γ. The converged vibrational energy levels below 6000 cm−1 were generated by performing about 5000 Lanczos recursion steps with a cutoff of 2.5 eV for the potential energy.
2.3. Absorption and Emission Spectra
The absorption and emission spectra can be evaluated as where is the transition dipole moment and and are the vibrational wave functions of the ground and excited electronic states, respectively. The transition amplitude can be calculated directly from the vibrational wave functions, but, in this work, we have used an efficient single Lanczos propagation (SLP) method [35, 36]. This method is particularly efficient for calculating emission from multiple excited state levels, because it requires no explicit construction and storage of the vibrational wave functions, and it has been proved successful in a number of systems .
For the calculation of electronic spectra, the Hamiltonians for both the ground and excited electronic states need to be represented by the same DVR grid. For both absorption and emission spectra, 60 sine-DVR points were employed to cover the R1 range of [2.10, 8.00] and 40 sine-DVR points for the range of [1.7, 2.7] . For γ, an eighty-point Gauss-Legendre DVR grid was used.
3. Results and Discussions
3.1. Ground () State Potential and Vibrational Energy Levels
Figure 1 displays the contour plots of the ground electronic state PES of HSiBr in the internal coordinates (, , ). Figures 1(a), 1(b), and 1(c) show the dependence of the potential on and θ with fixed at its equilibrium value of 2.869 , on and θwith fixed at its equilibrium value of 4.257 , and on the two bond lengths with the bond angle fixed at its equilibrium value of 93.9°, respectively. The equilibrium geometry of HSiBr at the ground electronic state PES was found to be located at , , and ,which is very similar to that of HSiCl , except that the Si–Br bond is longer than the Si–Cl bond. Our results are compared in Table 1 with the previous experimental and theoretical results. It is clear that our equilibrium geometry is in good agreement with the experimental and theoretical values [3, 8, 13].
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The calculated vibrational levels for the ground electronic state () of HSiBr up to 7300 cm−1 are listed in Table 2, together with the available experimental values. The vibrational energy levels are assigned with three vibrational quantum numbers (), representing the H–Si stretching, bending, and Si–Br stretching vibrational modes, respectively. By inspecting the nodal structures of the corresponding wave functions, the assignment of the vibrational levels can be achieved. The plots of nine wave functions of HSiBr are given in Figure 2, in which the nodal structures are clearly visible. The ease of the assignment suggests that the vibration of HSiBr is largely regular with weak intramodal coupling in this spectral region.
From Table 2, it is apparent that the calculated vibrational energy levels reproduce the available experimental data very well. The fundamental frequencies of , , and are in excellent agreement with the experimental values  of 1976.2, 772.0, and 412.4 cm−1, respectively. The good theory-experiment agreement is held all the way to the highest experimentally assigned level (1, 7, 0) near 7200 cm−1.
The vibrational energy levels of DSiBr have also been obtained on the same ab initio ground electronic state PES. The calculated vibrational levels up to 6500 cm−1 are compared with the available experimental data in Table 3. As expected, the substitution by the more massive deuterium not only lowers the energies of the H–Si stretching and bending vibrations, but also decreases the Si–Br stretching vibrational frequency to a small extent. Again, the calculated results are in excellent agreement with experiment. The calculated fundamental vibrational frequencies for the D–Si stretching, Si–Br stretching, and bending modes (1439.8, 405.0, and 562.0 cm−1) are very close to the experimental values  (1439.5, 407.99, and 561.8 cm−1), respectively. As a whole, Tables 2 and 3 show that all the calculated vibrational energy levels for HSiBr/DSiBr are within a reasonable error of the observed values, demonstrating the high accuracy of our ab initio ground electronic state PES.