The article information
 Weixiu Pang, Yunbin Sun, Jianjun Zhao, Yi Lu
 庞伟秀, 孙运斌, 赵建军, 鲁毅
 Ab initio Study of Anharmonic Force Field and Spectroscopic Constants for Germanium Dichloride
 用从头算方法研究GeCl_{2}分子的非谐振力场和光谱常数
 Chinese Journal of Chemical Physics, 2016, 29(6): 657662
 化学物理学报, 2016, 29(6): 657662
 http://dx.doi.org/10.1063/16740068/29/cjcp1604076

Article history
 Received on: April 14, 2016
 Accepted on: June 23, 2016
Transient molecules containing silicon and germanium have attracted considerable attention recently because of their roles as important intermediates in the technologically important production of semiconductors. In order to optimize the manufacturing processes, it is crucial to establish sensitive methods for detecting and characterizing such intermediates in theory and experiment. High resolution infrared and microwave spectroscopy are the most important sources of information for molecular force fields. Given the anharmonic potential, the molecular vibrational and rotational energy levels are easily obtained using variational or perturbation theories. The most useful analytical methods for studying semiconductor growth processes are likely to be spectroscopic in nature. Since its first observation in the late 1960s, the electronic absorption spectrum [1, 2] of germanium dichloride has attracted several experimental [36] and theoretical [69] attention.
The potential function under the influence of which the nuclei are moving is the same for isotopic molecules, since these isotopologues have the same electronic structure. But because of the difference in the masses the vibrational frequencies are different. A study of isotope shifts in spectra of germanium dichloride may be helpful in ascertaining which molecule (or radical) is responsible for a given spectrum and it may also aid in the spectrum. In addition, an accurate measurement of the isotope effect can be used to obtain a precise value for the ratio of the masses of the two kinds of isotopic atoms concerned. Under favorable conditions, the accuracy of the ratio of the masses so obtained is comparable with the accuracy of massspectrographic values. Apart from that, the study of the isotope effect in electronic band spectra has led to the discovery of new isotopes and an unambiguous confirmation of the quantum mechanical formula for the energy levels of the oscillator.
Employing the given force field, one can determine all spectroscopic constants of molecule, such as harmonic constants, anharmonic constants, rotational constants, centrifugal distortion constants, rotationvibration interaction constants, etc. [10]. Recently, with the development of the method of analytic second derivatives of molecular energy, it has become possible to calculate the rovibrational spectra, harmonic or anharmonic force field of small or middle molecules by ab initio method [1115]. It has been shown that spectroscopic constants from accurate, purely ab initio anharmonic force field are reliable [1216].
As far as we know, there have been very few reports about the anharmonic force field and the isotopic effects of GeCl_{2}. In 1995, Masaki et al. observed the millimeterwave spectrum of GeC1_{2} and its isotopic species in the ground and vibrationally excited states,
In this work, we determined the equilibrium structure, and calculated the ab initio anharmonic force field at several levels of theories. Accuracy was checked by comparing the ab initio spectroscopic constants with their corresponding experimental values. We also discussed the isotopic effects on anharmonic force field and spectroscopic constants for four isotopologues.
Ⅱ. COMPUTATIONAL METHODSThe geometry optimizations calculations presented below have been carried out with the Gaussian 03 program [20], and the secondorder M∅llerPlesset perturbation theory [21] (MP2) has been used. At the computed equilibrium geometries, harmonic force fields were evaluated analytically. No orbital has been kept frozen during these calculations. Cubic and semidiagonal quartic normal coordinate force constants have been evaluated using the ACESII [22] program package for the coupled cluster (CC) theory with single and double excitations augmented by a perturbational estimate of the effects of connected triple excitations (CCSD (T)) method [23], while the Gaussian 03 program for the MP2 calculations. Correlation consistent basis set has been used in the geometry optimizations and anharmonic force field, the standard valence ccpVTZ basis has been employed for these isotopomers of germanium dichloride [24]. The electronic configuration describes the distribution of electrons of an atom in atomic orbitals. Considering the ground electronic configuration of Ge and Cl can be written as 1s^{2}2s^{2}2p^{6}3s^{2}3p^{6}3d^{10}4s^{2}4p^{2} and 1s^{2}2s^{2}2p^{6}3s^{2}3p^{5}, respectively, the ccpVTZ basis set is employed. The basis of Ge is the [6s5p3d1f] contraction of a (20s13p9d1f) primitive set [24]. The basis of Cl is the [5s4p2d1f] contraction of a (15s9p2d1f) primitive set [24]. This basis set has also been chosen as it was felt that the basis set enhancement beyond ccpVTZ does not lead to major improvements in the computed anharmonic properties and that polarized triplezeta basis sets should therefore be sufficient in such applications. For each isotopomer the cubic force field has been used to compute spectroscopic parameters using the usual secondorder perturbation theory.
Ⅲ. RESULTS AND DISCUSSIONFor the main isotopic species the theoretical results for the molecular geometries, the spectroscopic constants, and the full quartic force fields are calculated. They are compared with the corresponding experimental or empirical data [6, 9, 17, 25] whenever these are available. While comparison of anharmonic force constants is possibly the most meaningful way to compare different force field representations of the PES of a molecule, it is more usual to compare the anharmonic force fields by their ability to predict standard rovibrational spectroscopic constants [26]. The isotopic composition for chlorine are 75.8% of ^{35}Cl and 24.2% of ^{37}Cl, and the major isotopic species for germanium have a more complex composition with 20.5% of ^{70}Ge, 27.4% of ^{72}Ge, 36.5% of ^{74}Ge, 7.8% of ^{76}Ge [27].
We calculated the ab initio structures and total energy for the optimized geometries of these molecules, at the MP2 and CCSD (T) level of theory using ccpVTZ basis set. The computed equilibrium structures of GeCl_{2} and experimentally derived [17] equilibrium structure are shown in Table Ⅰ. The MP2 results are almost the same values for these isotopomers, due to the fact that the equilibrium internuclear distances are the same in these isotopic molecules but not the effective internuclear distances [10]. So we listed the equilibrium structures of ^{74}GeCl_{2} instead of other isotopomers. The previous computed results are also listed in Table Ⅰ [6, 9, 25]. From Table Ⅰ we can see that the total energy for the optimized geometries of GeCl_{2} calculated by CCSD (T) method is slightly lower than that of MP2 method (about 0.13 Hartree), which means that the optimized structure by CCSD (T) method is more stable.
The refined rotational parameters can be used to determine an improved geometry for germanium dichloride. Table Ⅱ lists the computed rotational constants for ^{70}GeCl_{2}, ^{72}GeCl_{2}, ^{74}GeCl_{2}, and ^{76}GeCl_{2} at MP2 and CCSD (T) methods with ccpVTZ basis set, along with the available experimental data [17]. The theoretical groundstate rotational constants (A_{0}, B_{0}, C_{0}) have been obtained from the associated equilibrium constants (
The calculated vibrationrotation interaction constants
Table Ⅳ presents the calculated harmonic and fundamental vibrational wavenumbers of the major isotopes of GeCl_{2} without any scaling factor. The heavier isotopic molecule has the smaller frequency. For small mass differences the frequencies of the isotopic molecules are close to those of the ordinary molecule. The isotope shifts of
Table Ⅴ presents the anharmonic constants
${{X}}_{11} \approx {X}_{{\rm{33}}} \approx \frac{1}{4}{X}_{{\rm{13}}}$  (1) 
These relations are based on an approximate model, but they provide a useful check on the calculations because it has been observed experimentally that they hold well for some of the XY_{2} type molecule. As the appropriate entries of Table Ⅴ testify, the interrelations presented in the Eq.(1). hold very well for the directly determined ab initio spectroscopic constants. So far, both the harmonic wave numbers and anharmonic constants of these molecules have not been deduced experimentally. In view of the limited experimental data on these constants, ab initio predictions of them are expected to be useful for future experimental work.
The experimental groundstate values and computed equilibrium quartic centrifugal distortion constants (A reduction [35]) of ^{70}GeCl_{2}, ^{72}GeCl_{2}, ^{74}GeCl_{2}, and ^{76}GeCl_{2} are compared in Table Ⅵ. This permits to check the quality of the harmonic force field. The deviations between the experimental and ab initio are only a few percent, the largest deviation (
The equilibrium sextic centrifugal distortion constants (A reduction [35]) for these isotopmers of GeCl_{2} calculated from the MP2/ccpVTZ cubic force fields are shown in Table Ⅶ. It should be pointed out that the ACESII program used for the CCSD (T) calculations does not permit to calculate sextic centrifugal distortion constants and the comparison is thus restricted to the MP2/ccpVTZ results for these isotopmers. The calculations generally yield the sextic centrifugal distortion constants with the correct sign and with reasonable magnitude. Although no experimental sextic centrifugal distortion constants are found in references, we believe the results of MP2/ccpVTZ are reliable.
The investigation of the vibrational frequencies of molecules isotopic with the one considered gives additional equations for the force constants. While the number of constants in the most general quadratic potential function is usually larger than the number of fundamental frequencies. Thus if only one isotopic species is observed not all the force constants can be evaluated unless simplifying assumptions are made. But with the help of the fundamental frequencies of one or more isotopic molecules a sufficient number of additional equations is in general obtained to determine all constants in the most general (quadratic) potential function. Table Ⅷ lists complete ab initio quartic force fields in normal coordinates for GeCl_{2}. It includes the results of MP2 and CCSD (T) with ccpVTZ basis set. From group theoretical arguments we find that, in its C
In conclusion, we present some results to the isotopic effects on GeCl_{2}. The isotopic effects for germanium dichloride are much weaker. All spectroscopic constants calculated with this approach are in good agreement with the available experimental results, proving the high quality of the underlying anharmonic force field and the viability of the perturbationresonance approach at the same time. The MP2 results are in excellent agreement with the available experimental data for main isotopomers, so that the MP2 predictions for spectroscopic constants yet unknown are expected to be reliable.
Those isotopic molecules are also symmetrical, because the central atom is replaced by an isotope. As an asymmetric top molecule, the effective Hamiltonian in A reduction [35] can be written as
$\begin{align} & {{{\hat{H}}}^{\text{A}}}={{A}_{K}}J_{z}^{2}+{{A}_{J}}{{J}^{2}}+\frac{1}{2}a(J_{+}^{2}+J_{}^{2}){{D}_{K}}J_{z}^{4} \\ & {{D}_{JK}}{{J}^{2}}J_{z}^{2}{{D}_{J}}{{J}^{4}}\text{+}{{H}_{K}}J_{z}^{6}+{{H}_{KJ}}{{J}^{2}}J_{z}^{4}+ \\ & {{H}_{JK}}{{J}^{4}}J_{z}^{2}+{{H}_{J}}{{J}^{6}}+\frac{\text{1}}{2}[{{d}_{K}}J_{z}^{2}{{d}_{J}}{{J}^{2}}+ \\ & {{h}_{K}}J_{z}^{4}+{{h}_{JK}}{{J}^{2}}J_{z}^{2}+{{h}_{J}}{{J}^{4}}, J_{+}^{2}+J_{}^{2}{{]}_{+}} \\ \end{align}$  (2) 
${{A}_{K}}=\frac{A(B+C)}{2}$  (3) 
${{A}_{J}}=\frac{B+C}{2}$  (4) 
$a=\frac{BC}{2}$  (5) 
here
This work was supported by the National Natural Science Foundation of China (No.51562032 and No.61565013) and the Inner Mongolia College Research Project (No.NJZZ13220).
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