密度泛函计算3d/4d过渡金属原子轨道能与其同核双原子分子键能相关性的研究

The present available density functional theory (DFT) approximations often show larger errors for transition metal species than for typical main-group compounds. It is usually assumed that these larger errors arise from high multireference character in transition metal compounds. However, according to a DFT study, which was carried out by the applicant of this project, on bond energy calculations of V2 molecule, it was found that the errors in estimated bond energies of vanadium dimer V2 can primarily be related to the calculated energy gap between the 4s and 3dz2 atomic orbitals of the vanadium atom. This interesting correlation can be attributed to involving of linear combination of those two atomic orbitals for formation of the two σ bonding molecular orbitals in V2. According to the molecular orbital theory, we can infer that the magnitude of predicted energy gap between the 4s and 3dz2 atomic orbitals of the vanadium atom would directly affect the predicted bond energy of V2. This unexpected correlation reminds us that accurate predictions of bond energies should start with realistic descriptions of the atomic orbital energies of the atoms involved in the bond. In the basis of this study on DFT calculations of bond energy of V2, a more systematic investigation on bond energy calculations of 3d and 4d transition metal homonuclear diatomic molecules will be performed in this project. We plan to choose various present available functionals to calculate corresponding atomic orbital energies and molecular bond energies, analysis and discuss in detail about correlations between those two quantities, and then reveal the general rules of linear combination of 3d/4d transition metal atomic orbitals. We aim to provide a new clue for explorations of reasons about why DFT cannot perform so well for transition metal systems, and to establish a foundation for construction of new database relating to atomic orbital energy and development of new density functionals intending to improve the accuracy for transition metal species.

现有的密度泛函理论（DFT）近似对过渡金属体系的计算精度远远落后于对典型主族元素体系的计算。目前普遍认为过渡金属体系显著的多参考态特征是导致这一现象的主要原因。申请人读博期间在用DFT方法计算V2键能的研究中发现，泛函预测钒的4s与3dz2原子轨道能级差与其预测V2键能的误差之间密切相关，这是因为V2中两个σ成键分子轨道涉及这两个原子轨道的线性组合，故泛函对这两个原子轨道能级相近程度的预测会直接影响其对分子键能值的预测。这启发我们，对分子键能的准确描述需从寻找理想的原子轨道模型开始。本项目拟在此研究基础上对全部3d和4d过渡金属同核双原子分子进行深入系统研究，运用多种泛函方法分别计算原子轨道能和分子键能，讨论分析二者之间的相关性，总结3d/4d金属原子轨道的组合成键规律，为探索现有DFT方法不能精确计算过渡金属体系的原因提供新思路，为构建新的有关原子轨道能的数据库和发展新泛函奠定研究基础。

本项目主要研究了密度泛函理论（DFT）方法计算3d/4d过渡金属同核双原子分子键能的准确性与其预测的金属原子价层s和dz2轨道能级差之间的相关性。基于项目申请人攻读博士学位期间对V2分子键能的DFT理论预测进行研究的结果和思路，本项目对其余3d和4d同核双原子分子的键能和相关原子轨道能进行了系统研究。结果表明，对于d轨道全充满的Cu、Zn、Pd、Ag和Cd，除个别泛函（LSDA，HF，OHLYP，SOGGA11等）外，绝大多数泛函给出的键能的误差较小（MUE < 10 kcal/mol）。特别地，对于Zn和Cd，除LSDA外，其余所有测试的泛函预测的键能与实验值符合的较好（MUE < 2 kcal/mol），因此后续暂未对这四个分子进行进一步的分析讨论。对于d轨道半充满前的原子，测试的45个交换相关（exchange-correlation，xc）泛函中，多数泛函预测的分子键能误差较大。例如，Ti2分子的实验键能为32.3 kcal/mol，而其计算键能的误差MSE值高达 -52~81 kcal/mol。对于d轨道半充满（Cr，Mn，Tc和Mo）和半充满后的原子，预测精度较好的泛函数目有所增加。在所测试的泛函中，对3d金属同核双原子分子键能计算MUE最小的五个泛函依次为：B3LYP，HSE，τ-HCTHhyb，TPSSh和PBE。进一步地，我们统计分析各泛函计算的金属原子的价层s和dz2原子轨道能发现，对于d轨道半充满的Cr，Mn，Tc和Mo，所有测试的泛函给出的dz2和其余四个d原子轨道能级相同。通过绘制相关泛函（MUE最大和最小的五个泛函）给出的分子轨道能级图证实泛函计算键能的误差MSE与其计算的原子价层s和dz2轨道的能级差有很好的相关性。这些计算结果再次证明对分子键能的准确描述需从寻找理想的原子轨道模型开始，并为构建新的有关原子轨道能的数据库和发展新的xc泛函提供了有价值的参考。