The size consistency of the second and third order energies of the multireference perturbation theory(Chen F, Davidson E, Iwata S. Int J Quant Chem, 2002, 86: 256) is investigated theoretically with a su-per-molecular model composed of N-hydrogen molecules separated by a large distance. It is found that the two perturbation series corresponding to two Hamiltonian partitions are not size consistent at the second and third order. However, two size consistent forms are suggested for two Hamiltonian parti-tions at the second order, if some approximations to the denominators of the original second order energies are assumed.
CHEN FeiWu Department of Chemistry, University of Science and Technology Beijing, Beijing 100083, China (email: chenfeiwu@sas.ustb.edu.cn)
利用Harris模型，详细分析了Mazziotti提出的重构方法和Chen提出的一种由低阶约化密度矩阵重构高阶约化密度矩阵的系统方法（Sciencein China B，2006，49：402）的差异．如果忽略Mazziotti方法中的^3△M、^4△M和Chen方法中的^3△M、^4△M计算结果显示两种方法的计算误差相近．更好的近似是只忽略四级项^4△M、^4△M而三级项由相应的四级项通过简缩来计算．采用Mazziotti方法计算出来的有些近似值和精确值连正负号都不同，而用Chen方法计算出来的近似值和精确值不仅正负符号一致，而且数值大小也很接近．
A few open-shell molecules are taken as examples in order to examine the performance of the open-shell perturbation theory for electron correlation(J Chem Theory Comput,2009,5:931–936).The convergence of the perturbation series is shown to be stable for the doublet state of NH2 at both the equilibrium and stretched geometries.The equilibrium bond lengths,and harmonic and anharmonic vibrational frequencies are calculated for NO(X2),OH(X2),CH(X2)and NH(X2)with different second-order perturbation theories at the cc-pVDZ,cc-pVTZ and cc-pVQZ levels.The ground state energies of BeF(X2+), MgH(X2+)and the HCCl triplet state have also been computed with various perturbation theories and compared with configuration interaction with single and double excitations(CISD)and CISD+Davidson correction.The energy difference between the formaldehyde(H2CO + )and hydroxymethylene(HCOH+)radical cations has been computed.Our perturbation theory predicts correctly that H2CO + is more stable than HCOH+.However,calculations using UMP2,CASPT2,the Z-averaged perturbation theory and restricted Mφller–Plesset theory fail even to produce the correct sign of the energy difference.
