Development of Relativistic Configuration Interaction Method using Reduced Frozen-core Approximation

(1)相对论冻结核近似（RFCA）-经过大量的数值实验，我们现在已经找到了确定类核基组的最佳方法;首先，我们使用大量的基函数进行Dirac-Fock-Rooth aan计算。然后我们用较少的基函数来拟合价轨道。我们已经尝试了核心哈密顿矩阵的各种谱表示。然而，所获得的数值是不够准确的再现其确切的值和进一步的工作仍有待完成。(2)相对论组态相互作用（CI）程序-我们在制定有效的算法处理四分量波函数和大量的分子积分时遇到了许多困难。我们现在有一个小的CI程序，但是，应该进一步改进。(3)全电子分子计算：根据他们的兴趣和RFCA的参考文献，我们对GdF、GdF_2和ThO进行了相对论和非相对论SCF计算，估计了这些分子中的相对论效应。(4)分子积分的计算方法--给出了Laguerre Gaussian-type函数（GTF）上分子积分的递推公式，球面GTF上分子积分的紧致表达式，以及Talmi系数的简单推导方法。(5)利用相对论模型势方法计算了汞二聚体的势能曲线，并进行了分子动力学模拟，再现了液-固相变过程。我们已经开始了一个生成相对论基组的项目，在这个项目中，GTF的轨道指数被优化而没有变分坍缩。

(1) Relativistic frozen-core approximation (RFCA)-After considerable amount of numerical experiments we have now found the best method for determining the corelike basis sets ; First we perform a Dirac-Fock-Rooth aan calculation using a large number of basis functions. Then we fit the valence orbital using smaller number of basis functions. We have tried various kinds of spectral representations for the core Hamiltonian matrix. However, the obtained numerical values are not accurate enough to reproduce their exact values and further works remain to be done.(2) Relativistic con figuration-in teraction (CI) program-We had many difficulties when formulating efficient algorithm for treatment of 4-component wave functions and of huge number of molecular integrals. We have now a small CI program which should, however, be improved further.(3) All-electron molecular calculations-By their in terests and for the references for the RFCA, we performed relativistic and non relativistic SCF calculations on GdF, GdF_2, and ThO and estimated the relativistic effects in these molecules.(4) Methods for calculation of molecular integrals-We found reccurence formulas for the molecular integrals over Laguerre Gaussian-type functions (GTF), compact expressions for the integrals over the spherical GTFs, and a simple method of derivation for the Talmi coefficients.(5) Ohers-Using relativistic model potential method we calculated potential curves for mercury dimer and performed molecular dynamic simulations which reproduced the liquid-solid phase transition. We have started a project of generating relativistic basis sets, in which the orbital exponents of GTFs are optimized without variational collapse.