A comparison between the CISD[TQ] wave function and other highly correlated methods: Molecular geometry and harmonic vibrational frequencies of MgH2

Abstract

The linear MgH2 molecule was selected as a model system to compare the total electronic energy (ETOT), equilibrium bond length (re), and vibrational frequency (ωn) predictions from six different configuration interaction (CI) and coupled-cluster (CC) methods using three large correlation consistent basis sets. The three CI procedures employed incorporated all single and double substitutions (CISD) as well as all triple and quadruple substitutions (CISDTQ) or limited triple and quadruple substitutions (CISD[TQ]). The remaining three CC schemes included all single and double excitations (CCSD) as well as all triple excitations (CCSDT) or a perturbative approximation of the triple excitations [CCSD(T)]. Within the frozen core approximation employed in the study, the CISDTQ method constituted a full CI wave function. With the largest basis set this approach included 1.79 million configuration state functions and predicted re=1.711 Å, ω1=1602 cm−1, ω2=438 cm−1 and ω3=1628 cm−1. At the equilibrium geometry predicted by each method, agreement with the CISDTQ properties was observed to improve systematically in the following manner for all three basis sets: ETOT: CISD≪CISD[TQ]≈CCSD<CCSD(T)<CCSDT≈CISDTQ, re: CISD≪CCSD<CISD[TQ]<CCSD(T)<CCSDT≈CISDTQ, ωn: CISD≪CCSD<CISD[TQ] ≈CCSD(T)<CCSDT≈CISDTQ. With the largest basis set, ETOT was also computed after the Mg–H bond had been stretched to 3.0 Å. At this nuclear configuration the CISD[TQ] wave function outperformed the CC methods and recovered 99.8% full CI correlation energy while including over 100 times fewer configurations in the CI expansion. At this stretched geometry, agreement with the full CI correlation energy improved as follows: ETOT: CISD≪CCSD≪CCSD(T)≈CCSDT <CISD[TQ]≈CISDTQ.