標題: 小型過渡金屬簇之精確電子結構計算Accurate electronic structure calculations on small transition metal clusters 作者: 凱富Cristopher Camacho Leandro魏恆理Henryk Witek應用化學系碩博士班 關鍵字: Perturbation theory;Intruder states;Transition metals;CASSCF;Perturbation theory;Intruder states;Transition metals;CASSCF 公開日期: 2010 摘要: The potential energy curve of the ground state of Mn$_2$ has been studied using a systematic sequence of complete active spaces. Deficiencies of the routinely used active space, built from atomic $4s$ and $3d$ orbitals, has been identified and discussed. It is shown that an additional $\sigma_g$ orbital, originating from the atomic virtual $4p_z$ orbitals, is essential for a proper description of static correlation in the $^1\Sigma_{g}^{+}$ state of Mn$_2$. The calculated spectroscopic parameters of the $^1\Sigma_{g}^{+}$ state agree well with available experimental data. The calculated equilibrium bond lengths are located between 3.24 and~3.50~{\AA}, the harmonic vibrational frequencies, between 44 and~72~cm$^{-1}$, and the dissociation energies, between 0.05 and~0.09~eV. A detailed analysis of a severe intruder state problem in the multistate multireference perturbation theory (MS-MRPT) calculations on the ground state of manganese dimer is presented. An enormous number of detected intruder states ($>$5000) do not permit finding even an approximate shape of the $X^1\Sigma_{g}^{+}$ potential energy curve. The intruder states are explicitly demonstrated to originate from quasidegeneracies in the zeroth-order Hamiltonian spectrum. The electronic configurations responsible for appearance of the quasidegeneracies are identified as single and double excitations from the active orbitals to the external orbitals. It is shown that the quasidegeneracy problem can be completely eliminated using shift techniques despite of its severity. The resultant curves are smooth and continuous. Unfortunately, strong dependence of the spectroscopic parameters of the $X^1\Sigma_{g}^{+}$ state on the shift parameter is observed. This finding rises serious controversies regarding validity of employing shift techniques for solving the intruder state problem in multistate multireference perturbation theory. Prediction of a false ground state with popular variants of multireference perturbation theory (CASPT2 and MRMP) is reported. The failure occurs for a remarkably simple chemical system: the Sc$_2$ molecule. Reasons for the failure are discussed and appropriate remedies are suggested. The presented finding has far-reaching consequences for all the chemical community giving a serious warning on the applicability of multireference perturbation theory in the presence of intruder states. A systematic investigation of low-lying states of Sc$_2$ using multireference perturbation theory (NEVPT2 and NEVPT3) indicates that the ground state of this system is $^5\Sigma_u^-$ with $r_e=2.611$~{\AA}, $\omega_e=241.8$~cm$^{-1}$, and $D_e=1.78$~eV. This state is closely followed by other low-lying states of Sc$_2$: $^3\Sigma_u^-$, $^5\Delta_u$, $^3\Pi_g$, $^1\Pi_g$, and $^1\Sigma_u^-$. Our energy ordering of the $^5\Sigma_u^-$ and $^3\Sigma_u^-$ states confirms the recent MRCI results of Kalemos \textit{et al.} [\textit{J.Chem.Phys.} \textbf{132}, 024309 (2010)] and is at variance with the earlier DMC predictions of Matxain \textit{et al.} [\textit{J.Chem.Phys.} \textbf{128}, 194315 (2008)]. An excellent agreement between the second- and third-order NEVPT results and between the computed and experimental values of $\omega_e$ (241.8 vs. 238.9~cm$^{-1}$) for the $^5\Sigma_u^-$ state suggests high accuracy of our predictions.The potential energy curve of the ground state of Mn$_2$ has been studied using a systematic sequence of complete active spaces. Deficiencies of the routinely used active space, built from atomic $4s$ and $3d$ orbitals, has been identified and discussed. It is shown that an additional $\sigma_g$ orbital, originating from the atomic virtual $4p_z$ orbitals, is essential for a proper description of static correlation in the $^1\Sigma_{g}^{+}$ state of Mn$_2$. The calculated spectroscopic parameters of the $^1\Sigma_{g}^{+}$ state agree well with available experimental data. The calculated equilibrium bond lengths are located between 3.24 and~3.50~{\AA}, the harmonic vibrational frequencies, between 44 and~72~cm$^{-1}$, and the dissociation energies, between 0.05 and~0.09~eV. A detailed analysis of a severe intruder state problem in the multistate multireference perturbation theory (MS-MRPT) calculations on the ground state of manganese dimer is presented. An enormous number of detected intruder states ($>$5000) do not permit finding even an approximate shape of the $X^1\Sigma_{g}^{+}$ potential energy curve. The intruder states are explicitly demonstrated to originate from quasidegeneracies in the zeroth-order Hamiltonian spectrum. The electronic configurations responsible for appearance of the quasidegeneracies are identified as single and double excitations from the active orbitals to the external orbitals. It is shown that the quasidegeneracy problem can be completely eliminated using shift techniques despite of its severity. The resultant curves are smooth and continuous. Unfortunately, strong dependence of the spectroscopic parameters of the $X^1\Sigma_{g}^{+}$ state on the shift parameter is observed. This finding rises serious controversies regarding validity of employing shift techniques for solving the intruder state problem in multistate multireference perturbation theory. Prediction of a false ground state with popular variants of multireference perturbation theory (CASPT2 and MRMP) is reported. The failure occurs for a remarkably simple chemical system: the Sc$_2$ molecule. Reasons for the failure are discussed and appropriate remedies are suggested. The presented finding has far-reaching consequences for all the chemical community giving a serious warning on the applicability of multireference perturbation theory in the presence of intruder states. A systematic investigation of low-lying states of Sc$_2$ using multireference perturbation theory (NEVPT2 and NEVPT3) indicates that the ground state of this system is $^5\Sigma_u^-$ with $r_e=2.611$~{\AA}, $\omega_e=241.8$~cm$^{-1}$, and $D_e=1.78$~eV. This state is closely followed by other low-lying states of Sc$_2$: $^3\Sigma_u^-$, $^5\Delta_u$, $^3\Pi_g$, $^1\Pi_g$, and $^1\Sigma_u^-$. Our energy ordering of the $^5\Sigma_u^-$ and $^3\Sigma_u^-$ states confirms the recent MRCI results of Kalemos \textit{et al.} [\textit{J.Chem.Phys.} \textbf{132}, 024309 (2010)] and is at variance with the earlier DMC predictions of Matxain \textit{et al.} [\textit{J.Chem.Phys.} \textbf{128}, 194315 (2008)]. An excellent agreement between the second- and third-order NEVPT results and between the computed and experimental values of $\omega_e$ (241.8 vs. 238.9~cm$^{-1}$) for the $^5\Sigma_u^-$ state suggests high accuracy of our predictions. URI: http://140.113.39.130/cdrfb3/record/nctu/#GT079425816http://hdl.handle.net/11536/40850 Appears in Collections: Thesis