Abinitio evaluation of the fine structure and radiative lifetime of the 3A2(n→π*) state of formaldehyde
Abinitio evaluation of the fine structure and radiative lifetime of the 3A2(n→π*) state of formaldehyde
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甲醛3A2(n→π*)态精细结构和辐射寿命的从头计算
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发表时间：
1976
期刊：
影响因子：
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通讯作者：
E. Davidson
中科院分区：
文献类型：
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作者：
S. Langhoff;E. Davidson
利用完整的breit -泡利哈密顿量计算了CH2O a2 （n→π*）态中自旋轨道对零场分裂（ZFS）的贡献。所有的计算都是在平面基态几何上进行的，使用双zeta加偏振基，收缩高斯瓣函数加上漫射s和p函数。用典型的3a轨道构造了构型相互作用波函数，用自旋轨道哈密顿量描述了3a态和所有与之耦合的态。由这些波函数得到的激振能和振子强度与其他理论计算和实验结果吻合较好。在自旋轨道相互作用的二阶微扰理论处理中考虑的12个态中，a1基态和附近的3a （π→π*）态是最重要的。观察到里德伯态具有非常小的自旋轨道矩阵元素，因此对ZFS的影响很小。自旋轨道对ZFS参数D和E的贡献分别为- 0.224和0.009 cm−1，加上先前论文[S]中得到的自旋-自旋贡献。R. Langhoff， S. T. Elbert， E. R. Davidson, Int。J.量子化学，7,999(1973)]给出了D=0.314 cm−1和E=0.04 cm−1的总价值。这些结果均大于Birss E= 0.141 cm−1和E=0.02 cm−1的最佳实验结果。董仁勇，董仁勇，拉姆齐，化学。理论物理。[图18,11(1973)]从3a 2←1a跃迁的0+←0波段的旋转分析。还进行了广泛的计算，以评估二阶摄动理论处理的收敛程度。考虑了a1、b1和b2对称的最低100个单重态和三重态的贡献，其中每个态都由100项CI波函数描述。这个计算给出了自旋轨道对D的贡献为- 0.221 cm - 1，与之前的结果基本相同，从而证明了二阶处理确实是收敛的。三态的三个亚能级的辐射寿命是用相同的表示方式来确定的。在高温极限下，测定了辐射寿命在0.02 ~ 0.06秒之间，略长于0.01秒的实验估计值，并确定了a1基态和3a态的相互摄动以及3a （π→π*）态对3a态的摄动是决定寿命的最重要因素。这些结果保证了发射的光主要沿碳氧键偏振光，与实验结果一致。对数值结果的定量有效性进行了严格的检查，以评估理论确定的寿命的可靠性。
The spin–orbit contribution to the zero‐field splitting (ZFS) in the CH2O 3 A 2(n→π*) state is evaluated using the full Breit–Pauli Hamiltonian. All calculations are carried out at the planar ground state geometry using a double‐zeta plus polarization basis of contracted Gaussian‐lobe functions augmented with diffuse s and p functions. Configuration–interaction wavefunctions, constructed using the 3 A 2 canonical orbitals, are used to describe the 3 A 2 state and all states coupling to it via the spin–orbit Hamiltonian. The excitation energies and oscillator strengths obtained from these wavefunctions are in good agreement with other theoretical calculations and with experiment. Of the 12 states considered in the second‐order perturbation theorytreatment of the spin–orbit interaction, the 1 A 1 ground and the nearby 3 A 1(π→π*) states were the most important. Rydberg states were observed to have very small spin–orbit matrix elements and consequently to have little effect on the ZFS. The spin–orbit contributions to the ZFS parameters D and E were −0.224 and 0.009 cm−1, respectively, which when added to the spin–spin contribution obtained in an earlier paper [S. R. Langhoff, S. T. Elbert, E. R. Davidson, Int. J. Quantum Chem. 7, 999 (1973)] give total values of D=0.314 cm−1 and E=0.04 cm−1. These results are larger than the best experimental results of D=0.141 cm−1 and E=0.02 cm−1, determined by Birss e t a l. [F. W. Birss, R. Y. Dong, and D. A. Ramsay, Chem. Phys. Lett. 18, 11 (1973)] from a rotational analysis of the 0+←0 bands of the 3 A 2←1 A 1 transition. An extensive calculation was also undertaken to assess the degree of convergence in the second‐order perturbation theorytreatment. The contribution of the lowest 100 singlet and triplet states of A 1, B 1, and B 2 symmetry were considered where each state was described by a 100‐term CI wavefunction. This calculation gives a spin–orbit contribution to D of −0.221 cm−1 essentially identical to the previous result providing evidence that the second‐order treatment has indeed converged. The radiative lifetimes of the three sublevels of the triplet state were determined using the same representations for the manifold of electronic states. In the high temperature limit, the radiative lifetime was determined to be between 0.02 and 0.06 sec, somewhat longer than the estimated experimental value of 0.01 sec. The mutual perturbation of the 1 A 1 ground and 3 A 2 states and the perturbation of the 3 A 2 state by the 1 A 1(π→π*) state were determined to be most important in determining the lifetime. These results ensure that the emitted light is polarized primarily along the carbon–oxygen bond in agreement with experiment. A critical examination of the quantitative validity of the numerical results is presented to assess the reliability of the theoretically determined lifetimes.