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 The potential energy curve of the ground state of Mn$_2$ has beenstudied 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 thatan additional $\sigma_g$ orbital, originating from the atomic virtual$4p_z$ orbitals, is essential for a proper description of staticcorrelation in the $^1\Sigma_{g}^{+}$ state of Mn$_2$. The calculatedspectroscopic parameters of the $^1\Sigma_{g}^{+}$ state agree well withavailable experimental data. The calculated equilibrium bond lengthsare located between 3.24 and~3.50~{\AA}, the harmonic vibrationalfrequencies, 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 multistatemultireference perturbation theory (MS-MRPT) calculations on the groundstate of manganese dimer is presented. An enormous number of detectedintruder states ($>$5000) do not permit finding even an approximateshape of the $X^1\Sigma_{g}^{+}$ potential energy curve. The intruderstates are explicitly demonstrated to originate from quasidegeneraciesin the zeroth-order Hamiltonian spectrum. The electronic configurationsresponsible for appearance of the quasidegeneracies are identified assingle and double excitations from the active orbitals to the externalorbitals. It is shown that the quasidegeneracy problem can becompletely eliminated using shift techniques despite of its severity.The resultant curves are smooth and continuous. Unfortunately, strongdependence of the spectroscopic parameters of the $X^1\Sigma_{g}^{+}$state on the shift parameter is observed. This finding rises seriouscontroversies regarding validity of employing shift techniques forsolving the intruder state problem in multistate multireferenceperturbation theory.Prediction of a false ground state with popular variants ofmultireference perturbation theory (CASPT2 and MRMP) is reported. Thefailure occurs for a remarkably simple chemical system: the Sc$_2$molecule. Reasons for the failure are discussed and appropriateremedies are suggested. The presented finding has far-reachingconsequences for all the chemical community giving a serious warning onthe applicability of multireference perturbation theory in the presenceof intruder states.A systematic investigation of low-lying states of Sc$_2$ usingmultireference perturbation theory (NEVPT2 and NEVPT3) indicates thatthe 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. Thisstate 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 $^3\Sigma_u^-$ statesconfirms the recent MRCI results of Kalemos \textit{et al.}[\textit{J.Chem.Phys.} \textbf{132}, 024309 (2010)] and is at variancewith the earlier DMC predictions of Matxain \textit{et al.}[\textit{J.Chem.Phys.} \textbf{128}, 194315 (2008)]. An excellentagreement between the second- and third-order NEVPT results and betweenthe computed and experimental values of $\omega_e$ (241.8 vs.238.9~cm$^{-1}$) for the $^5\Sigma_u^-$ state suggests high accuracy ofour predictions.
 The potential energy curve of the ground state of Mn$_2$ has beenstudied 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 thatan additional $\sigma_g$ orbital, originating from the atomic virtual$4p_z$ orbitals, is essential for a proper description of staticcorrelation in the $^1\Sigma_{g}^{+}$ state of Mn$_2$. The calculatedspectroscopic parameters of the $^1\Sigma_{g}^{+}$ state agree well withavailable experimental data. The calculated equilibrium bond lengthsare located between 3.24 and~3.50~{\AA}, the harmonic vibrationalfrequencies, 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 multistatemultireference perturbation theory (MS-MRPT) calculations on the groundstate of manganese dimer is presented. An enormous number of detectedintruder states ($>$5000) do not permit finding even an approximateshape of the $X^1\Sigma_{g}^{+}$ potential energy curve. The intruderstates are explicitly demonstrated to originate from quasidegeneraciesin the zeroth-order Hamiltonian spectrum. The electronic configurationsresponsible for appearance of the quasidegeneracies are identified assingle and double excitations from the active orbitals to the externalorbitals. It is shown that the quasidegeneracy problem can becompletely eliminated using shift techniques despite of its severity.The resultant curves are smooth and continuous. Unfortunately, strongdependence of the spectroscopic parameters of the $X^1\Sigma_{g}^{+}$state on the shift parameter is observed. This finding rises seriouscontroversies regarding validity of employing shift techniques forsolving the intruder state problem in multistate multireferenceperturbation theory.Prediction of a false ground state with popular variants ofmultireference perturbation theory (CASPT2 and MRMP) is reported. Thefailure occurs for a remarkably simple chemical system: the Sc$_2$molecule. Reasons for the failure are discussed and appropriateremedies are suggested. The presented finding has far-reachingconsequences for all the chemical community giving a serious warning onthe applicability of multireference perturbation theory in the presenceof intruder states.A systematic investigation of low-lying states of Sc$_2$ usingmultireference perturbation theory (NEVPT2 and NEVPT3) indicates thatthe 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. Thisstate 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 $^3\Sigma_u^-$ statesconfirms the recent MRCI results of Kalemos \textit{et al.}[\textit{J.Chem.Phys.} \textbf{132}, 024309 (2010)] and is at variancewith the earlier DMC predictions of Matxain \textit{et al.}[\textit{J.Chem.Phys.} \textbf{128}, 194315 (2008)]. An excellentagreement between the second- and third-order NEVPT results and betweenthe computed and experimental values of $\omega_e$ (241.8 vs.238.9~cm$^{-1}$) for the $^5\Sigma_u^-$ state suggests high accuracy ofour predictions.
 1 General Introduction 11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 The multiconfiguration self-consistent field approach . . . . . . . . . . 21.3 Multireference perturbation theory . . . . . . . . . . . . . . . . . . . 31.3.1 Rayleigh-Schr¨odinger perturbation theory . . . . . . . . . . . 41.3.2 The choice of ˆH0 . . . . . . . . . . . . . . . . . . . . . . . . . 61.4 Intruder states in multireference perturbation theory . . . . . . . . . 82 Ground state of Mn2 revisited 112.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . 132.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.3.1 Choice of active space . . . . . . . . . . . . . . . . . . . . . . 152.3.2 Bonding mechanism in Mn2 . . . . . . . . . . . . . . . . . . . 162.3.3 Spectroscopic constants . . . . . . . . . . . . . . . . . . . . . 202.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 Intruder states in MRPT: Mn2 303.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . 333.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 343.3.1 MCQDPT potential energy curves . . . . . . . . . . . . . . . . 343.3.2 CASPT2 potential energy curves . . . . . . . . . . . . . . . . 373.3.3 Analysis of intruder states in the MCQDPT calculations . . . 393.3.4 Failure of shift techniques . . . . . . . . . . . . . . . . . . . . 423.3.5 Alternative methods of removing intruder states . . . . . . . . 433.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534 Intruder states in MRPT: Sc2 594.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . 604.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 614.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655 The low-lying states of the scandium dimer 675.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.2 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . 735.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . 745.3.1 Atomic calculations . . . . . . . . . . . . . . . . . . . . . . . . 745.3.2 Low-lying states of Sc2 . . . . . . . . . . . . . . . . . . . . . . 755.3.3 NEVPT3 results for the 5−u and 3−u states . . . . . . . . . . 805.3.4 A comment on the applicability of reduced valence active spaces 815.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 846 General conclusions 91A Publications list 94A.1 Publications included in this dissertation . . . . . . . . . . . . . . . . 94A.2 Publications not included in this dissertation . . . . . . . . . . . . . . 94B Auxiliary material for: Chapter 2 96B.1 Deficiencies of the (12o,14e) active space . . . . . . . . . . . . . . . . 96B.2 PES with the (13o,14e) active space . . . . . . . . . . . . . . . . . . . 101B.3 Larger active spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103B.4 BSSE corrections and non-size consistency error . . . . . . . . . . . . 106B.5 How short can be the bond in Mn2? . . . . . . . . . . . . . . . . . . . 110B.6 ORMAS estimation of the full-valence CASSCF PES . . . . . . . . . 110C Auxiliary material for Chapter 3 116C.1 Note on deficiencies of H0 in MCQDPT . . . . . . . . . . . . . . . . . 116C.2 Note on multistate MCQDPT calculations . . . . . . . . . . . . . . . 116C.3 CASPT2 calculations with various values of the IPEA shift . . . . . . 118C.4 Excluding terms from the perturbation . . . . . . . . . . . . . . . . . 119D Auxiliary material for Chapter 4 121