A CAS study on S‐loss and O‐loss dissociation mechanisms of the SO2+ ion in the C,D, and E states

In the present work, we mainly study dissociation of the C ²B₁, D²A₁, and E²B₂ states of the SO₂⁺ ion using the complete active‐space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) methods. We first performed CASPT2 potential energy curve (PEC) calculations for S‐ and O‐loss dissociation from the X, A, B, C, D, and E primarily ionization states and many quartet states. For studying S‐loss predissociation of the C, D, and E states by the quartet states to the first, second, and third S‐loss dissociation limits, the CASSCF minimum energy crossing point (MECP) calculations for the doublet/quartet state pairs were performed, and then the CASPT2 energies and CASSCF spin‐orbit couplings were calculated at the MECPs. Our calculations predict eight S‐loss predissociation processes (via MECPs and transition states) for the C, D, and E states and the energetics for these processes are reported. This study indicates that the C and D states can adiabatically dissociate to the first O‐loss dissociation limit. Our calculations (PEC and MECP) predict a predissociation process for the E state to the first O‐loss limit. Our calculations also predict that the E²B₂ state could dissociate to the first S‐ and O‐loss limits via the A²B₂ ← E²B₂ transition. On the basis of the 13 predicted processes, we discussed the S‐ and O‐loss dissociation mechanisms of the C, D, and E states proposed in the previous experimental studies. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Theoretical study on HBO+ and HOB+ cations using multiconfiguration second‐order perturbation theory

The HBO⁺ and HOB⁺ cations have been reinvestigated using the CASSCF and CASPT2 methods in conjunction with the contracted atomic natural orbital (ANO) basis sets. The geometries of all stationary points in the potential energy surfaces were optimized at the CASSCF/ANO and CASPT2/ANO levels. The ground and the first excited states of HBO⁺ are predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HOB⁺ is X²Σ⁺ state. The A²Π state of HOB⁺ has unique imaginary frequency. A bending local minimum M1 was found for the first time along the 1²A′′ potential energy surface and the A²Π state of HOB⁺ should be the transition state of the isomerization reactions for M1? M1. The CASPT2/ANO potential energy curves (PECs) of isomerization reactions were calculated as functions of the HBO bond angle. Many of the CASSCF and CASPT2 calculated results were different from the previously published QCISD(T) results. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Theoretical prediction on HAlS+ and HSAl+ cations using multiconfiguration second‐order perturbation theory

Some low‐lying states of the HAlS⁺ and HSAl⁺ cations have been studied for the first time by large‐scale theoretical calculations using three methods: complete active space self‐consistent field (CASSCF), complete active second‐order perturbation theory (CASPT2), and density functional theory Becke's three‐parameter hybrid function with the nonlocal correlation of Lee–Yang–Parr (B3LYP) with the contracted atomic natural orbital (ANO‐L) and cc‐pVTZ basis sets. The geometries of all stationary points along the potential energy surfaces (PESs) were optimized at the CASSCF/ANO‐L and B3LYP/cc‐pVTZ levels. The ground and the first excited states of linear HAlS⁺ are predicted to be X²Π and A²Σ⁺ states, respectively. For the linear HSAl⁺ structure, the first excited state is A²Σ⁺. The X²Π state of linear HSAl⁺ is a second‐order saddle point, because it has two imaginary frequencies. Two bent global minima M1 and M2 were found along the 1²A′ and 1²A″ PESs, respectively. The CASPT2/ANO‐L potential energy curves of isomerization reactions were calculated as a function of HAlS bond angle. According to our calculations, the ground‐state HAlS⁺ is linear, whereas the ground‐state HSAl⁺ is bent. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Dissociation of the OCS+ ion in low-lying electronic states studied using multiconfiguration second-order perturbation theory

Complete active space self-consistent-field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) calculations with atomic natural orbital basis sets were performed to investigate the S-loss direct dissociation of the 1 2Pi(X 2Pi), 2 2Pi(A 2Pi), 1 2Sigma+(B 2Sigma+), 1 4Sigma-, 1 2Sigma-, and 1 2Delta states of the OCS+ ion and the predissociations of the 1 2Pi, 2 2Pi, and 1 2Sigma+ states. Our calculations indicate that the S-loss dissociation products of the OCS(+) ion in the six states are the ground-state CO molecule plus the S+ ion in different electronic states. The CASPT2//CASSCF potential energy curves were calculated for the S-loss dissociation from the six states. The calculations indicate that the dissociation of the 1 4Sigma- state leads to the CO + S+ (4Su) products representing the first dissociation limit; the dissociations of the 1 2Pi, 1 2Sigma-, and 1 2Delta states lead to the CO + S+(2Du) products representing the second dissociation limit; and the dissociations of the 2 2Pi and 1 2Sigma+ states lead to the CO + S+(2Pu) products representing the third dissociation limit. Seams of the 1 2Pi-1 4Sigma-, 2 2Pi-1 4Sigma-, 2 2Pi-1 2Sigma-, 2 2Pi-1 2Delta, and 1 2Sigma(+)-1 4Sigma- potential energy surface intersections were calculated at the CASPT2 level, and the minima along the seams were located. The calculations indicate that within the experimental energy range (15.07-16.0 eV) the 2 2Pi(A 2Pi) state can be predissociated by 1 4Sigma- forming the S+(4Su) ion and can undergo internal conversion to 1 2Pi followed by the direct dissociation of 1 2Pi forming S+(2Du) and that within the experimental energy range (16.04-16.54 eV) the 1 2Sigma+(B 2Sigma+) state can be predissociated by 1 4Sigma- forming the S+(4Su) ion and can undergo internal conversion to 2 2Pi followed by the predissociation of 2 2Pi by 1 2Sigma- and 1 2Delta forming the S+(2Du) ion. These indications are in line with the experimental fact that both the 4Su and 2Du states of the S+ ion can be formed from the 2 2Pi and 1 2Sigma+ states of the OCS+ ion.     

Theoretical study on HBC− and HCB− anions using multiconfiguration second‐order perturbation theory

The HBC^? and HCB^? anions have been studied using the complete active space self‐consistent field, CASPT2, and DFT/B3LYP methods with the contracted atomic natural orbital (ANO) and cc‐pVTZ basis sets. The geometries of all stationary points along the potential energy surfaces were optimized at the CASSCF/ANO and B3LYP/cc‐pVTZ levels. The ground state of HBC^? is predicted to be X²? state, which is different from the previously published results. The CASPT2/ANO potential energy curves (PECs) of isomerization reactions were calculated as a function of HBC bond angle and the PECs also show the ²? state is the ground state of HBC^? anion. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Theoretical prediction on HBeN− and HNBe− anions using multiconfiguration second‐order perturbation theory

The HBeN^? and HNBe^? anions have been investigated for the first time using the CASSCF, CASPT2, and DFT/B3LYP methods with the contracted atomic natural orbital (ANO) and cc‐pVTZ basis sets. The geometries of all stationary points along the potential energy surfaces were optimized at the CASSCF/ANO and B3LYP/cc‐pVTZ levels. The ground and the first excited states of HBeN^? are predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HNBe^? is X²Σ⁺ state. The A²Π state of HNBe^? has unique imaginary frequency. A bend local minimum M1 was found along the 1²A″ potential energy surface and the A²Π state of HNBe^? should be the transition state of the isomerization reactions for M1 ? M1. The CASPT2/ANO potential energy curves of isomerization reactions were calculated as a function of HBeN bond angle. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2010     

Low-lying electronic states and Cl-loss photodissociation of the C2H3Cl+ ion studied using multiconfiguration second-order perturbation theory

We studied the 1(2)A' '(X2A' '), 1(2)A' (A2A'), 2(2)A' ' (B2A' '), and 2(2)A' (C2A') states of the C2H3Cl+ ion using the complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) methods. For the four ionic states, we calculated the equilibrium geometries, adiabatic (T0) and vertical (Tv) excitation energies, and relative energies (Tv') at the geometry of the molecule at the CASPT2 level and the Cl-loss dissociation potential energy curves (PECs) at the CASPT2//CASSCF level. The computed oscillator strength f value for the X2A' ' <-- A2A' transition is very small, which is in line with the experimental fact that the A state has a long lifetime. The CASPT2 geometry and T0 value for the A2A' state are in good agreement with experiment. The CASPT2 Tv' values for the A2A', B2A' ', and C2A' states are in good agreement with experiment. The Cl-loss PEC calculations predict that the X2A' ', A2A', and C2A' states correlate to C2H3+ (XA1) and the BA' ' state to C2H3+ (1A' ') (the B2A' ' and C2A' PECs cross at R(C-Cl) approximately 2.24 A). Our calculations indicate that at 357 nm the X2A' ' state can undergo a transition to B2A' ' followed by a predissociation of B2A' ' by the repulsive C2A' state (via the B/C crossing), leading to C2H3+ (X1A1), and therefore confirm the experimentally proposed pathway for the photodissociation of X2A' ' at 357 nm. Our CASPT2 D0 calculations support the experimental fact that the X state does not undergo dissociation in the visible spectral region and imply that a direct dissociation of the A state to C2H3+ (X1A1) is energetically feasible.     

Theoretical study on low‐lying states of HAlO+ and HOAl+ cations

Some low‐lying states of HAlO⁺ and HOAl⁺ cations have been studied using the complete‐active‐space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) methods with the contracted atomic natural orbital (ANO) basis sets. The geometries of all stationary points along the potential energy surfaces were optimized at the CASSCF/ANO and CASPT2/ANO levels. The ground and the first excited states of HAlO⁺ are predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HOAl⁺ is X²Σ⁺ state. The A²Π state of HOAl⁺ has unique imaginary frequency. A bent local minimum M1 was found along the 1²A″ potential energy surface, and the A²Π state of HOAl⁺ should be the transition state of the isomerization reactions for M1 ? M1. The CASPT2/ANO potential energy curves of isomerization reactions were calculated as a function of HAlO bond angle. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Theoretical computation of low‐lying electronic states of HCNS: A CASPT2 study

Complete active space self‐consistent field (CASSCF) and complete active space second‐order perturbation theory (CASPT2) calculations in conjunction with the aug‐cc‐pVTZ basis set have been used to investigate the low‐lying electronic states of thiofulminic acid (HCNS), HCNS⁺, and HCNS^?. The result of geometry optimization using CASPT2/aug‐cc‐pVTZ shows that theoretically determined geometric parameters and harmonic vibrational frequencies for the HCNS ground state X¹Σ⁺(X¹A′) are in agreement with previous studies. The ionization energies, the electron affinity energies, the adiabatic excitation energies, and vertical excitation energies have been calculated and the corresponding cation and anion states are identified. By calculating adiabatic electron affinity, the states of HCNS^? have been identified to contain both π orbital states (X²A′ and 1²A″) and dipole‐bond states (1⁴A′ and 1⁴A″). © 2012 Wiley Periodicals, Inc.     

Cl-loss and H-loss dissociations in low-lying electronic states of the CH3Cl+ ion studied using multiconfiguration second-order perturbation theory

To examine the experimentally suggested scheme of the pathways for Cl- and H-loss dissociations of the CH(3)Cl(+) ion in the X(2)E (1(2)A', 1(2)A' '), A(2)A(1) (2(2)A'), and B(2)E (3(2)A', 2(2)A") states, the complete active space-self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) calculations with an atomic natural orbital (ANO) basis were performed for the 1(2)A' (X(2)A'), 1(2)A", 2(2)A', and 2(2)A'" states. The potential energy curves describing dissociation from the four C(s) states were obtained on the basis of the CASSCF partial geometry optimization calculations at fixed C-Cl or C-H distance values, followed by the CASPT2 energy calculations. The electronic states of the CH3(+) and CH(2)Cl(+) ions produced by Cl-loss and H-loss dissociation, respectively, were carefully determined. Our calculations confirm the following experimental facts: Cl-loss dissociation occurs from the 1(2)A' (X(2)A'), 1(2)A", and 2(2)A' states (all leading to CH3(+) (X(1)A(1)') + Cl), and H-loss dissociation does not occur from 2(2)A'. The calculations indicate that H-loss dissociation occurs from the 1(2)A' and 1(2)A' ' states (leading to CH(2)Cl(+) (X(1)A(1)) + H and CH(2)Cl(+) (1(3)A") + H, respectively). The calculations also indicate that H-loss dissociation occurs (with a barrier) from the 2(2)A" state (leading to CH(2)Cl(+) (1(1)A") + H), supporting the observation of direct dissociation from the B state to CH(2)Cl(+) and that Cl-loss dissociation occurs from the 2(2)A" state (leading to CH3(+) (1(3)A") + Cl), not supporting the previously proposed Cl-loss dissociation of the B state via internal conversion of B to A. The predicted appearance potential values for CH3(+) (X(1)A(1)') and CH(2)Cl(+) (X(1)A(1)) are in good agreement with the experimental values.     

Bromine-loss and hydrogen-loss dissociations in low-lying electronic states of the CH3Br+ ion studied using multiconfiguration second-order perturbation theory

Complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) calculations with an ANO-RCC basis were performed for the 1(2)A', 1(2)A", 2(2)A', and 2(2)A" states of the CH3Br+ ion. The 1(2)A' state is predicted to be the ground state. The 2(2)A' state is predicted to be a bound state. The adiabatic and vertical excitation energies and the relative energies at the molecular geometry were calculated, and the energetic results for 2(2)A' and 2(2)A" are in reasonable agreement with the experimental data. Potential energy curves (PECs) for Br-loss and H-loss dissociations from the four C(s) states were calculated at the CASPT2//CASSCF level and the electronic states of the CH3(+) and CH2Br(+) ions as the dissociation products were determined by checking the relative energies and geometries of the asymptote products along the PECs. In the Br-loss dissociation, the 1(2)A', 1(2)A", and 2(2)A' states correlate with CH3(+) (X1A1') and the 2(2)A" state correlates with CH3(+) (1(3)A"). The energy increases monotonically with the R(C-Br) value along the four Br-loss PECs. In the H-loss dissociation the 1(2)A', 1(2)A", 2(2)A', and 2(2)A" states correlate with the X(1)A(1), 1(3)A", 1(3)A', and 1(1)A" states (1(3)A' lying above 1(1)A") of CH2Br(+), respectively. Along the 2(2)A" H-loss PEC there is an energy barrier and the CASSCF wave functions at large R(C-H) values have shake-up ionization character. Along the 2(2)A' H-loss PEC there are an energy barrier and a minimum. At the end of the present paper we present a comprehensive review on the electronic states and the X-loss and H-loss dissociations of the CH(3)X(+) (X = F, Cl, and Br) ions on the basis of our previous studies and the present study.     

F-loss and H-loss dissociations in low-lying electronic states of the CH3F+ ion studied using multiconfiguration second-order perturbation theory

Complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) calculations with an atomic natural orbital basis were performed for the 1(2)A', 1(2)A', 2(2)A', 2(2)A', and 3(2)A' (X2E, A2A1, and B2E) states of the CH3F+ ion. The 1(2)A' state is predicted to be the ground state, and the C(s)-state energy levels are different from those of the CH3Cl+ ion. The 2(2)A' (A2A1) state is predicted to be repulsive, and the calculated adiabatic excitation energies for 2(2)A' and 3(2)A' are very close to the experimental value for the B state. The CASPT2//CASSCF potential energy curves (PECs) were calculated for F-loss dissociation from the five C(s) states and H-loss dissociation from the 1(2)A', 1(2)A', and 2(2)A' states. The electronic states of the CH3+ and CH2F+ ions as the dissociation products were carefully determined by checking the energies and geometries of the asymptote products, and appearance potentials for the two ions in different states are predicted. The F-loss PEC calculations for CH3F+ indicate that F-loss dissociation occurs from the 1(2)A', 1(2)A', and 2(2)A' states [all correlating with CH3+(X1A1')], which supports the experimental observations of direct dissociation from the X and A states, and that direct F-loss dissociation can occur from the two Jahn-Teller component states of B2E, 2(2)A' and 3(2)A' [correlating with CH3+(1(3)A') and CH3+(1(3)A'), respectively]. Some aspects of the 3(2)A' Cl-loss PEC of the CH3Cl+ ion are inferred on the basis of the calculation results for CH3F+. The H-loss PEC calculations for CH3F+ indicate that H-loss dissociation occurs from the 1(2)A', 1(2)A', and 2(2)A' states [correlating with CH2F+(1(3)A'), CH2F+(X1A1), and CH2F+(1(1)A'), respectively], which supports the observations of direct dissociation from the X and B states. As the 2(2)A' H-loss PEC of CH3Cl+, the 2(2)A' H-loss PEC of CH3F+ does not lead to H + CH2X+, but the PECs of the two ions represent different types of reactions.     

CASPT2 study on low‐lying states of HMgO and HOMg

The HMgO and magnesium monohydroxide (HOMg) have been reinvestigated using the complete active space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) methods with the contracted atomic natural orbital (ANO) basis sets. The geometries of all stationary points along the potential energy surfaces (PESs) were optimized at the CASSCF/ANO levels. The ground and the first excited states of HMgO are predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HOMg is X²Σ⁺ state. The A²Π state of HOMg has unique imaginary frequency. A bent local minimum M1 was found for the first time along the 1²A″ PES and the A²Π state of HOMg should be the transition state of the isomerization reactions for M1 ? M1. The CASPT2/ANO potential energy curves of isomerization reactions were calculated as a function of HMgO bond angle. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

CASPT2 study on low‐lying states of HBN and HNB radicals

In this study, some low‐lying states of the HBN and HNB radicals have been studied using multiconfiguration second‐order perturbation theory. The geometries of all stationary points along the potential energy surfaces (PESs) were optimized at the CASPT2/cc‐pVQZ level. The ground and the first excited states of HBN were predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HNB is X²Σ⁺ state. The A²Π state of HNB has unique imaginary frequency, which was different from the previously published results. A bending local minimum M1 was found for the first time along the 1²A″ PES, and the A²Π state of HNB should be the transition state of the isomerization reactions for M1 ? M1. The CASPT2/ANO potential energy curves (PECs) of isomerization reactions for HBN ? HNB were calculated as a function of HBN bond angle. By comparing the CASPT2 and CASSCF calculated results, we concluded that the influence of the dynamic electron correlation on HBN ? HNB system is not large. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

A CASSCF/CASPT2 study on the low‐lying electronic states of the CH3SS and its cation

Complete active space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) calculations with contracted ANO‐RCC basis set were performed for low‐lying electronic states of CH₃SS and its cation in C_s symmetry. For the ground state X²A″ of CH₃SS, the calculated S‐S stretching mode is in good agreement with experimental reports. The electron transitions of CH₃SS⁺, X¹A′ → 1¹A″, X¹A′ → 2¹A′, and X¹A′ → 2¹A″, are predicted at 1.055, 3.247, and 3.841 eV. Moreover, the calculated adiabatic and vertical ionization potential and adiabatic affinity are in reasonable agreement with the experimental data. The CASSCF/CASPT2 potential energy curves (PECs) were calculated for S₂‐loss dissociation from the X²A″, 1²A′, and 2²A″ states. The electronic states of the CH₃ radical and S₂ molecule as the dissociation products were carefully determined by checking energies and geometries of the asymptote products. The S₂‐loss PEC for CH₃SS indicate that S₂‐loss dissociation occurs from the X²A″ state leading to CH₃ (1²A″) + S₂ (X³Σ), the 1²A′ and 2²A″ leading to CH₃ (1²A″) + S₂ (¹Δ_g). © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012.     

Theoretical study of the low‐lying electronic states of the molecular ion KRb+

The potential energy curves of the molecular ion KRb⁺ have been investigated for the 60 lowest molecular states of symmetry ²Σ⁺, ²Π, ²Δ, and Ω = 1/2, 3/2, and 5/2. Using an ab initio method, the calculation has been done in a one active electron approach based on nonempirical pseudopotentials with core valence effects taken into account through parameterized l‐dependent polarization potentials. Using the canonicals functions approach a rovibrational study is done by calculating the eigenvalues E_v, the rotational constants B_v, the centrifugal distortion constants D_v (up to 135 vibrational levels), and the spectroscopic constants ω_e and B_e for the five electronic states (1)²Σ⁺, (3)²Σ⁺, (1)²Π, (1)Ω = 1/2, and (1)Ω = 3/2. No comparison of these values with other results is yet possible because they are given here for the first time. Extensive tables of energy values of E_v, B_v, and D_v are displayed at http://hplasim2.univ‐lyon1.fr/allouche . © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

Diagrammatic formulation of the second‐order many‐body multipartitioning perturbation theory

The second‐order multireference perturbation theory employing multiple partitioning of the many‐electron Hamiltonian into a zero‐order part and a perturbation is formulated in terms of many‐body diagrams. The essential difference from the standard diagrammatic technique of Hose and Kaldor concerns the rules of evaluation of energy denominators which take into account the dependence of the Hamiltonian partitioning on the bra and ket determinantal vectors of a given matrix element, as well as the presence of several two‐particle terms in zero‐order operators. The novel formulation naturally gives rise to a “sum‐over‐orbital” procedure of correlation calculations on molecular electronic states, particularly efficient in treating the problems with large number of correlated electrons and extensive one‐electron bases. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 395–401, 1999     

Spectroscopic parameter and molecular constant investigations for low‐lying electronic states of P ion

The potential energy curves (PECs) of three low‐lying electronic states of P ion, X²Π_u, A²Σ, and B²Σ, have been studied using the full valence complete active space self‐consistent field method followed by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach and MRCI with Davidson correction (+Q). The correlation‐consistent basis sets, aug‐cc‐pV5Z and aug‐cc‐pV6Z, are used and the total energies are extrapolated to the complete basis set limit. Using these PECs obtained with the MRCI+Q/56‐extrapolation, the spectroscopic parameters for these electronic states are determined and compared in detail with experimental data and those of previous studies reported in the literature. The comparison shows that excellent agreement exists between the present results and the available experiments. The first 40 vibrational states for the three electronic states are also computed when the rotational quantum number J equals zero. For each vibrational state, the vibrational level G(υ), inertial rotation constant B_υ, and centrifugal distortion constant D_υ are determined when J = 0, which are in good accord with the available measurements. © 2012 Wiley Periodicals, Inc.     

Properties and Structure of Spinel Li‐Mn‐O‐F Compounds for Cathode Materials of Secondary Lithium‐ion Battery

The spinel Li‐Mn‐O‐F compound cathode materials were synthesized by solid‐state reaction from calculated amounts LiOH‐H₂O, MnO₂(EMD) and LiF. The results of the electrochemical test demonstrated that these materials exhibited excellent electrochemical properties. It's initial capacity is ‐ 115 mAh.g¹ and reversible efficiency is about 100%. After 60 cycles, its capacity is still around 110 mAh.g¹ with nearly 100% reversible efficiency. The spinel Li‐Mn‐O‐F compound possibly has two structure models: interstitial model [Li]‐[Mn³⁺_xMn⁴⁺_2‐x]O₄F_δ, in which the fluorine is located on the interstice of crystal lattice, and substituted model [Li]‐[Mn³⁺_xMn⁴⁺_2‐x]O_4‐δF_δ, which the fluorine atom substituted the oxygen atom. The electrochemical result supports the interstitial model [Li][Mn³⁺_xMn⁴⁺_2‐x]O₄F_δ.     

Intruder states in multireference perturbation theory: the ground state of manganese dimer

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 MS-MRPT. Various alternative approaches of removing intruder states (e.g., modification of the basis set or changing the active space) are tested. None of these conventional techniques is able to fully avoid the quasidegeneracies. We believe that the MS-MRPT calculations on the three lowest A(g) states of manganese dimer constitute a perfect benchmark case for studying the behavior of MRPT in extreme situations.