Robot Intelligent Grasp of Unknown Objects Based on Multi-Sensor Information.

Robots frequently need to work in human environments and handle many different types of objects. There are two problems that make this challenging for robots: human environments are typically cluttered, and the multi-finger robot hand needs to grasp and to lift objects without knowing their mass and damping properties. Therefore, this study combined vision and robot hand real-time grasp control action to achieve reliable and accurate object grasping in a cluttered scene. An efficient online algorithm for collision-free grasping pose generation according to a bounding box is proposed, and the grasp pose will be further checked for grasp quality. Finally, by fusing all available sensor data appropriately, an intelligent real-time grasp system was achieved that is reliable enough to handle various objects with unknown weights, friction, and stiffness. The robots used in this paper are the NTU 21-DOF five-finger robot hand and the NTU 6-DOF robot arm, which are both constructed by our Lab.

Photodissociation mechanisms of the CO2(2+) dication studied using multi-state multiconfiguration second-order perturbation theory.

Employing the multi-state multiconfiguration second-order perturbation theory (MS-CASPT2) and complete active space self-consistent field (CASSCF) methods, the geometries, relative energies (T(v)') to the ground state (X(3)Σg(-)), adiabatic excited energies, and photodissociation mechanisms and corresponding kinetic energy releases for the lower-lying 14 electronic states of the CO2 (2+) ion are studied. The T(v)' values are calculated at the experimental geometry of the ground state CO2 molecule using MS-CASPT2 method and highly close to the latest threshold photoelectrons coincidence and time-of-flight photoelectron photoelectron coincidence spectrum observations. The O-loss dissociation potential energy curves (PECs) for these 14 states are drawn using MS-CASPT2 partial optimization method at C(∞v) symmetry with one C-O bond length ranging from 1.05 to 8.0 Å. Those 14 states are confirmed to be correlated to the lowest four dissociation limits [CO(+)(X(2)Σ(+)) + O(+)((4)S(u)), CO(+)(A(2)Π) + O(+)((4)S(u)), CO(+)(X(2)Σ(+)) + O(+)((2)D(u)), and CO(+)(X(2)Σ(+)) + O(+)((2)P(u))] by analyzing Coulomb interaction energies, charges, spin densities, and bond lengths for the geometries at the C-O bond length of 8.0 Å. On the basis of these 14 MS-CASPT2 PECs, several state/state pairs are selected to optimize the minimum energy crossing points (MECPs) at the CASSCF level. And then the CASSCF spin-orbit couplings and CASPT2 state/state energies are calculated at these located MECPs. Based on all of the computational results, the photodissociation mechanisms of CO2(2+) are proposed. The relationships between the present theoretical studies and the previous experiments are discussed.

Synthesis and characterization of a singlet delocalized 2,4-diimino-1,3-disilacyclobutanediyl and a silylenylsilaimine.

The synthesis and characterization of a singlet delocalized 2,4-diimino-1,3-disilacyclobutanediyl, [LSi(µ-CNAr)(2)SiL] (2, L: PhC(NtBu)(2), Ar: 2,6-iPr(2) C(6) H(3)), and a silylenylsilaimine, [LSi(=NAr)-SiL] (3), are described. The reaction of three equivalents of the disilylene [LSi-SiL] (1) with two equivalents of ArN=C=NAr in toluene at room temperature for 12 h afforded [LSi(µ-CNAr)(2)SiL] (2) and [LSi(=NAr)-SiL] (3) in a ratio of 1:2. Compounds 2 and 3 have been characterized by NMR spectroscopy and X-ray crystallography. Compound 2 was also investigated by theoretical studies. The results show that compound 2 possesses singlet biradicaloid character with an extensive electronic delocalization throughout the Si(2)C(2) four-membered ring and exocyclic C=N bonds. Compound 3 is the first example of a silylenylsilaimine, which contains a low-valent silicon center and a silaimine substituent. A mechanism for the formation of 2 and 3 is also proposed.

The Bergman cyclizations of the enediyne and its N-substituted analogs using multiconfigurational second-order perturbation theory.

The Bergman cyclizations of the enediyne and its four N-substituted analogs [(Z)-pent-2-en-4-ynenitrile, 3-azahex-3-en-1,5-diyne, malenotrile, and 3,4-azahex-3-en-1,5-diyne] have been studied using the complete active space self-consistent field and multiconfigurational second-order perturbation theory methods in conjunction with the atomic natural orbital basis sets. The geometries and energies of the reactants, transition states, and products along both the S(0) (the ground state) and T(1) (the lowest-lying triplet state) potential energy surfaces (PESs) were calculated. The calculated geometries are in good agreement with the available experimental data. The distance between two terminal carbons in enediyne, which was considered as an important parameter governing the Bergman cyclization, was predicted to be 4.319 Å, in agreement with the experimental value of 4.321 Å. Our calculations indicate that the replacements of the terminal C atom(s) or the middle C atom(s) in the C=C bond by the N atom(s) increase or decrease the energy barrier values, respectively. There exist stable ring biradical products on the T(1) PESs for the five reactions. However, on the S(0) PESs the ring biradical products exist only for the reactions of enediyne, (Z)-pent-2-en-4-ynenitrile, and 3-azahex-3-en-1,5-diyne.

CASSCF and CASPT2 study on O- and Cl-loss predissociation mechanisms of OClO (A(2)A2).

For studying O- and Cl-loss predissociation mechanisms of OClO (A(2)A(2)), we calculated O- and Cl-loss dissociation potential energy curves (adiabatic minimum-energy dissociation paths) of several low-lying doublet and quartet states at the CASPT2 level and located the MECPs (minimum energy crossing points) for many pairs of the potential energy surfaces (PESs) at the CASPT2 and CASSCF levels. On the basis of our calculation results (including the spin-orbit couplings at the MECPs), we predict three processes for O-loss predissociation of A(2)A(2) and four processes for Cl-loss predissociation of A(2)A(2). The most favorable process for O-loss predissociation is OClO (A(2)A(2)) → A(2)A(2)/1 (2)B(2) MECP → 1 (2)B(2) (1 (2)A') → O ((3)P(g)) + ClO (X(2)Π) (the first O-loss limit), and the needed energy for this process from X(2)B(1) is 2.92 eV. The most favorable process for Cl-loss predissociation is OClO (A(2)A(2)) → A(2)A(2)/1 (2)B(2) MECP → TS1 (1 (2)B(2)) → 1 (2)B(2)/1 (2)A(1) MECP → Cl ((2)P(u)) + O(2) (X(3)Σ(g)(-)) (the first limit), and the needed energy is 3.08 eV. In the previously suggested mechanisms (processes), the A(2)A(2) state was considered to go to the important 1 (2)B(2) state via 1 (2)A(1) (A(2)A(2) → 1 (2)A(1) → 1 (2)B(2)). In the present study we have found that the A(2)A(2) state can directly go to 1 (2)B(2) (at the located A(2)A(2)/1 (2)B(2) MECP the CASPT2 energy (relative to X(2)B(1)) and CASSCF spin-orbit coupling are 2.92 eV and 61.3 cm(-1), respectively). We have compared our processes (A(2)A(2) → 1 (2)B(2) → ...) with the processes (A(2)A(2) → 1 (2)A(1) → 1 (2)B(2) → ...) suggested in the previous MRCI studies and rewritten by us using our calculation results. Energetically the MRCI process for O-loss predissociation (to the first limit) is only slightly (0.13 eV) more favorable than our process, and the MRCI processes for Cl-loss predissociation (to the first and second limits) need the same energies as our processes. By considering the probabilities of radiationless transitions, the MRCI processes are less favorable than our processes since the MRCI processes proceed via more PES/PES crossings (more MECPs). The experimental facts concerning the photodissociation are explained.

A CAS study on S-loss and O-loss dissociation mechanisms of the SO(2) (+) ion in the C, D, and E states.

In the present work, we mainly study dissociation of the C (2) B(1) , D(2) A(1) , and E(2) B(2) states of the SO(2) (+) 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 E(2) B(2) state could dissociate to the first S- and O-loss limits via the A(2) B(2) ← E(2) B(2) 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.

Theoretical study on the predissociation mechanism of CO(2)(+) (C (2)Sigma(g)(+)).

The main purpose of the present theoretical work was to study predissociation mechanism of the C (2)Sigma(g)(+) state of the CO(2)(+) ion using the CAS methods. Since the X (2)Pi(g), A (2)Pi(u), B (2)Sigma(u)(+), 1 (4)Sigma(g)(-), and 1 (4)Pi(u) states are involved in the predissociation, we also studied these five states. The CASPT2 calculations indicate that Renner-Teller splitting in 1 (4)Pi(u) leads to two C(2v) states, 1 (4)A(1) and 1 (4)B(1). For the X (2)Pi(g), A (2)Pi(u), B (2)Sigma(u)(+), and C (2)Sigma(g)(+) states, the CASPT2 T(0) values and geometries are in good agreement with experiment. The CASPT2 calculations for the O-loss dissociation potential energy curves indicate that the 1 (4)Sigma(g)(-), X (2)Pi(g), 1 (4)Pi(u), A (2)Pi(u), B (2)Sigma(u)(+), and C (2)Sigma(g)(+) states correlate with the first, second, second, third, third, and fourth dissociation limits, respectively. The CASSCF minimum energy crossing point (MECP) calculations (in the C(infinityv), C(s), and C(2v) symmetries) were performed for selected state/state pairs, and the spin-orbit couplings were calculated at the MECPs. All the MECPs (including the C (2)Sigma(g)(+)/1 (4)Pi(u) (1 (4)B(1)) MECP), involved in the proposed predissociation mechanism of Praet et al. ( J. Chem. Phys. 1982 , 77 , 4611 - 4618 ), were found and the calculated spin-orbit couplings at these MECPs are not small. Our calculations support the mechanism of Praet et al. and indicate that an energy value of 8.9 eV from CO(2)(+) (X (2)Pi(g)) is needed. The C (2)Sigma(g)(+) state in the previous [1 + 1] photodissociation experiments ( J. Chem. Phys. 2008 , 128 , 164308. ) could predissociate through the mechanism of Praet et al. since the two-photon energy was around 8.9 eV, while the C (2)Sigma(g)(+) state in the previous VUV-PFI-PE experiments ( J. Chem. Phys. 2003 , 118 , 149 - 163 ) would predissociate through another mechanism via A (2)Pi(u).

A theoretical study on the electronic states and O-loss photodissociation of the NO2(+) ion.

CASPT2 (multiconfiguration second-order perturbation theory) calculations were performed at the molecular geometry for 17 low-lying singlet and triplet states of the NO(2)(+) ion. The CASPT2 vertical relative energies (T(v)') were obtained and the characters of these ionic states (primary or shake-up ionization states) were determined. For the eight low-lying states, we performed CASPT2 geometry optimization calculations and obtained the CASPT2 adiabatic relative energies (T(0)). We conclude that the 1(1)A(1), 1(3)B(2), 1(3)A(2), 1(1)A(2), 1(1)B(2), 1(3)A(1), 2(3)B(1), and 3(3)B(2) states of NO(2)(+) correspond to the X(1)Sigma(g)(+), a(3)B(2), b(3)A(2), A(1)A(2), B(1)B(2), c(3)A(1), d(3)B(1), and (3b(2))(-1) (3)B(2) states (the eight ionic states below 20 eV observed in the photoelectron spectra of Brundle et al.1 and Baltzer et al.2), respectively. The 1(1)A(1), 1(3)B(2), 1(3)A(2), 1(1)A(2), 1(1)B(2), 1(3)A(1), and 3(3)B(2) states are primary ionization states, and the CASPT2 T(v)' and T(0) values of these states are close to the corresponding experimental values from refs. [1] and [2]. The 2(3)B(1) state is not a typical primary ionization state, and the CASPT2 T(v)' and T(0) values for 2(3)B(1) are in reasonable agreement with the experimental values for d(3)B(1) from refs. [1] and [2] (the CASPT2 T(0) value for 1(3)B(1) is more than 2.5 eV smaller than the experimental values). Based on our CASPT2 T(0) calculations, we comment on the assignments of the d(3)A(1), C(1)B(1), and D(1)B(2) states below 20 eV observed by Jarvis et al. and on the MRCI T(0) values of Hirst for the 1(3)B(1), 1(1)B(1), and (3)A(1) states. On the basis of the CASPT2 potential energy curve (PEC) and CASSCF singlet/triplet minimum-energy crossing point (MECP) calculations, we reach the following conclusions concerning O-loss photodissociation from the X(1)Sigma(g)(+), a(3)B(2), b(3)A(2), A(1)A(2), and B(1)B(2) states, which are in line with the experimental facts. The adiabatic dissociation process of the X(1)Sigma(g) (+) state to the second limit [NO(+)(X(1)Sigma(+))+O((1)D)] cannot occur due to a high energy barrier (>5.0 eV) along the PEC, and the nonadiabitic process of X(1)Sigma(g)(+) to the first limit [NO(+)(X(1)Sigma(+))+O((3)P)] via the triplet states is unlikely since the MECPs lie very high above X(1)Sigma(g)(+). For the a(3)B(2) and b(3)A(2) states, adiabatic dissociation processes to the first limit may occur. Both the A(1)A(2) and B(1)B(2) states can undergo processes of predissociation to the first limit by a repulsive 2(3)A'' state, since the MECPs lie low above A(1)A(2) and B(1)B(2) and the calculated spin-orbit couplings at the MECPs are not small.

The o-, m-, and p-benzyne radical cations: a theoretical study.

On the basis of the CASPT2 (multiconfigurational second-order perturbation theory) geometry optimization calculations, the ground states of the o-C6H4+ (C2v), m-C6H4+ (C2v), and p-C6H4+ (D2h) radical cations were determined to be 1 2B1, 1 2A2, and 1 2B1u, respectively. For o-C6H4+ and m-C6H4+, the first excited states (1 2A2 and 1 2A1, respectively) lie very close to the respective ground states. The small distance value of 1.419 A between the two dehydrocarbons in the ground-state geometry of m-C6H4+ indicates that there is a real chemical bond between the two dehydrocarbons (the distance in the 1 2A1 geometry of m-C6H4+ is very long as in the m-C6H4 molecule). The (U)B3LYP isotropic proton hfcc (hyperfine coupling constant) calculation results imply that the ground and first excited states of o-C6H4+ will have similar ESR spectrum patterns while the ground and first excited states of m-C6H4+ will have completely different ESR spectrum patterns.

Two-way effects between hydrogen bond and intramolecular resonance effect: an ab initio study on complexes of formamide and its derivatives with water.

Ab initio calculations up to MP2/aug-cc-pVTZ//MP2/cc-pVTZ level, including natural charge population and natural resonance theory analyses, have been carried out to study the two-way effects between hydrogen bond (H-bond) and the intramolecular resonance effect by using the H-bonded complexes of formamide ( FAO) and its derivatives ( FAXs, X represents the heavy atoms in the substituent groups, CH 2, NH, SiH 2, PH, and S) with water as models. Unlike NH 3 and NH 2CH 3 which prefer being H-bond acceptors ( HA) to form H-bond with water, the amino groups in the six monomers, because of the resonance effect, prefer being H-bond donors ( HD) rather HA. Six monomers can all form HD complexes with water, and only two ( FAC and FASi) with the weakest resonance effect are able to form HA complexes with water. The HD H-bond and resonance effect enhance each other (positive two-way effects) whereas the HA H-bond and resonance effect weaken each other (negative two-way effects). The H-bond energies in the six HD complexes are nearly linearly correlated with the weights of the dipolar resonance in Pauling's model and the N-C bond lengths; the correlation coefficients are 0.91 and 0.93, respectively. The positive two-way effects also happens in FAO-water complex, in which the FAO CO group serves as HA ( HA co ). Interestingly, when the HD and HA co H-bonds are present in FAO H-bond complex simultaneously, the enhancements are much more significant, and the energies of the two types of H-bonds are much larger than those when only one type of H-bond is present, reflecting the cooperative effects. By using the knowledge to the two-way effects, we computationally designed a molecule ( FAO- BH 3 ) to increase H-bond energy. Because of the oxygen lone pair donation to the empty pi orbital of BH 3, FAO- BH 3 has a much stronger resonance effect than FAO. As a result, the H-bond energy (-5.55 kcal/mol) in HD H 2O ... FAO- BH 3 complex is much greater than the -3.30 kcal/mol in the HD H 2O...FAO complex. The two-way effects can be rationalized as follows: the resonance effect leads to intramolecular charge shifts in the monomers which facilitate or prevent the charge donation or acceptation of their H-bond partners. Therefore, the H-bonds are strengthened or weakened. In reverse, the charge donations or acceptations of their H-bond partners facilitate or prevent the intramolecular charge shifts in the monomer moieties, which enhance or weaken the resonance effect. The understanding to the two-way effects may be helpful in drug design and refinement by modulating the H-bond strength and in building empirical H-bond models to study large biological molecules. The study supports Pauling's resonance model.

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.

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.

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.

X, A, B, C, and D states of the C6H5F+ ion studied using multiconfiguration wave functions.

Electronic states of the C6H5F+ ion have been studied within C2v symmetry by using the complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) methods in conjunction with an atomic natural orbital basis. Vertical excitation energies (Tv) and relative energies (Tv') at the ground-state geometry of the C6H5F molecule were calculated for 12 states. For the five lowest-lying states, 1(2)B1, 1(2)A2, 2(2)B1, 1(2)B2, and 1(2)A1, geometries and vibrational frequencies were calculated at the CASSCF level, and adiabatic excitation energies (T0) and potential energy curves (PEC) for F-loss dissociations were calculated at the CASPT2//CASSCF level. On the basis of the CASPT2 T0 calculations, we assign the X, A, B, C, and D states of the ion to 1(2)B1, 1(2)A2, 2(2)B1, 1(2)B2, and 1(2)A1, respectively, which supports the suggested assignment of the B state to (2)(2)B1 by Anand et al. based on their experiments. Our CASPT2 Tv and Tv' calculations and our MRCI T0, Tv, and Tv' calculations all indicate that the 2(2)B1 state of C6H5F+ lies below 1(2)B2. By checking the relative energies of the asymptote products and checking the fragmental geometries and the charge and spin density populations in the asymptote products along the CASPT2//CASSCF PECs, we conclude that the 1(2)B1, 1(2)B2, and 1(2)A1 states of C6H5F+ correlate with C6H5+ (1(1)A1) + F (2P) (the first dissociation limit). The energy increases monotonically along the 1(2)B1 PEC, and there are barriers and minima along the 1(2)B2 and 1(2)A1 PECs. The predicted appearance potential value for C6H5+ (1(1)A1) is very close to the average of the experimental values. Our CASPT2//CASSCF PEC calculations have led to the conclusion that the 1(2)A2 state of C6H5F+ correlates with the third dissociation limit of C6H5+ (1(1)A2) + F (2P), and a preliminary discussion is presented.

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.

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.

The 1 (2)A(1), 1 (2)B(2), and 1 (2)A(2) states of the SO(2) (+) ion studied using multiconfiguration second-order perturbation theory.

The 1 (2)A(1), 1 (2)B(2), and 1 (2)A(2) electronic states of the SO(2) (+) ion have been studied using multiconfiguration second-order perturbation theory (CASPT2) and two contracted atomic natural orbital basis sets, S[6s4p3d1f]/O[5s3p2d1f] (ANO-L) and S[4s3p2d]/O[3s2p1d] (ANO-S), and the three states were considered to correspond to the observed X, B, and A states, respectively, in the previous experimental and theoretical studies. Based on the CASPT2/ANO-L adiabatic excitation energy calculations, the X, A, and B states of SO(2) (+) are assigned to 1 (2)A(1), 1 (2)B(2), and 1 (2)A(2), respectively, and our assignments of the A and B states are contrary to the previous assignments (A to (2)A(2) and B to (2)B(2)). The CASPT2/ANO-L energetic calculations also indicate that the 1 (2)A(1), 1 (2)B(2), and 1 (2)A(2) states are, respectively, the ground, first excited, and second excited states at the ground-state (1 (2)A(1)) geometry of the ion and at the geometry of the ground-state SO(2) molecule. Based on the CASPT2/ANO-L results for the geometries, we realize that the experimental geometries (determined by assuming the bond lengths to be the same as the neutral ground state of SO(2)) were not accurate. The CASPT2/ANO-S calculations for the potential energy curves as functions of the OSO angle confirm that the 1 (2)B(2) and 1 (2)A(2) states are the results of the Renner-Teller effect in the degenerate (2)Pi(g) state at the linear geometry, and it is clearly shown that the 1 (2)B(2) curve, as the lower component of the Renner splitting, lies below the 1 (2)A(2) curve. The UB3LYP/cc-pVTZ adiabatic excitation energy calculations support the assignments (A to (2)B(2) and B to (2)A(2)) based on the CASPT2/ANO-L calculations.