Multiconfigurational Second-order Perturbation Theory Research Articles

Coulomb explosion of nitrogen and oxygen molecules through non-Coulombic states

We have systematically studied Coulomb explosion of nitrogen and oxygen molecules in intense 8 and 24 fs laser pulses. In the experiment, we explicitly separated all explosion pathways through coincident measurements. The high resolution kinetic energy releases (KERs) and the exotic angular distributions of atomic ions provide direct evidence that Coulomb explosion occurs through non-Coulombic states. In the theory, we calculated dissociation potential energy curves (PECs) of nitrogen and oxygen molecules and their multicharged molecular ions using multiconfiguration second-order perturbation theory. The results indicate that Coulomb potentials are close to the accurate PECs of multicharged molecular ions only when the internuclear distance is larger than 3 Å. In comparison with the experimental observations and the theoretical calculations, we determined the internuclear distance when Coulombic explosion occurs. It is near the equilibrium distance of the neutral molecules in the case of 8 fs laser pulses and expands gradually with the increase of the charge state of the molecular ions in the case of 24 fs laser pulses.

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 (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.

Benchmarks of electronically excited states: Basis set effects on CASPT2 results

Vertical excitation energies and one-electron properties are computed for the valence excited states of 28 medium-sized organic benchmark molecules using multistate multiconfigurational second-order perturbation theory (MS-CASPT2) and the augmented correlation-consistent aug-cc-pVTZ basis set. They are compared with previously reported MS-CASPT2 results obtained with the smaller TZVP basis. The basis set extension from TZVP to aug-cc-pVTZ causes rather minor and systematic shifts in the vertical excitation energies that are normally slightly reduced (on average by 0.11 eV for the singlets and by 0.09 eV for the triplets), whereas the changes in the calculated oscillator strengths and dipole moments are somewhat more pronounced on a relative scale. These basis set effects at the MS-CASPT2 level are qualitatively and quantitatively similar to those found at the coupled cluster level for the same set of benchmark molecules. The previously proposed theoretical best estimates (TBE-1) for the vertical excitation energies for 104 singlet and 63 triplet excited states of the benchmark molecules are upgraded by replacing TZVP with aug-cc-pVTZ data that yields a new reference set (TBE-2). Statistical evaluations of the performance of density functional theory (DFT) and semiempirical methods lead to the same ranking and very similar quantitative results for TBE-1 and TBE-2, with slightly better performance measures with respect to TBE-2. DFT/MRCI is most accurate among the investigated DFT-based approaches, while the OMx methods with orthogonalization corrections perform best at the semiempirical level.

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

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

The CASPT2 potential energy curves (PECs) for O-loss dissociation from the X2Π, A2Π, B2Σ+, C2Σ+, 14Σ−, 12Σ−, and 14Π states of the OCS+ ion were calculated. The PEC calculations indicate that X2Π, 14Σ−, 12Σ−, and 14Π correlate with CS+(X2Σ+) + O(3Pg); A2Π and B2Σ+ correlate with CS+(A2Π) + O(3Pg); and C2Σ+ probably correlates with CS+(X2Σ+) + O(1Dg). The CASSCF minimum energy crossing point (MECP) calculations were performed for the C2Σ+/14Σ−, C2Σ+/14Π, A2Π/14Σ−, A2Π/12Σ−, A2Π/14Π, and B2Σ+/12Σ− state pairs and the spin-obit couplings were calculated at the located MECPs. A conical intersection point between the B2Σ+ and C2Σ+ potential energy surfaces was found at the CASSCF level. Based on our calculations, seven O-loss predissociation processes of the C2Σ+ state are suggested and an appearance potential value of 7.13 eV for the CS+ + O product group is predicted. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

Low-lying electronic states of HNCS and its ions: a CASSCF/CASPT2 study

Complete active space self-consistent-field (CASSCF) and multiconfigurational second-order perturbation theory (CASPT2) calculations in conjunction with the ANO-L basis set were performed to investigate systematically the low-lying electronic states of HNCS and its ions in C s symmetry. Our highly accurate calculation indicated that theoretically determined geometric parameters and harmonic vibrational frequencies for the ground-state X 1A′ are in good agreement with observed experimental data. The geometry of triplet HNCS is clearly favored C 1 symmetry, and the relative energy is predicted to be 3.000 eV (69.2 kcal/mol). The vertical transition energies for the selected excited states of HNCS were calculated at CASSCF/CASPT2/ANO-L level of theory based on CASSCF optimized geometry. Except for a few linear states of X 2Π (12A′, 12A″), 14Σ− (14A″), and 12Σ+ (32A′) states of HNCS+, our results confirmed that the majority of excited states are twisted trans-bend structures. The existence of bound excited anion states has been found for the first time in HNCS−. A more elaborate examination of ionization potential of HNCS (AIP, VIP) than previous reports has been presented.

Electronic states of the C6H5CN+ ion studied using multiconfiguration wave functions

Electronic states of the C6H5CN+ ion have been studied within C2v symmetry 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 set. Adiabatic excitation energies (T 0), vertical excitation energies (T v), and relative energies () at the ground-state geometry of the C6H5CN molecule were calculated for eight electronic states of the C6H5CN+ ion. The CASPT2//CASSCF T 0 and CASPT2 T v and calculations all indicate that the 1 2B1, 1 2A2, 2 2B1, 1 2B2, 1 2A1, 2 2A1, 2 2B2, and 3 2B1 states are the eight lowest-lying states of C6H5CN+. In conjunction with the MS-CASPT2 T 0 and oscillator strength f calculations, we assigned the X, A, B, C, D, E, F, and G states of the C6H5CN+ ion to 1 2B1, 1 2A2, 1 2B2, 2 2B1, 1 2A1, 2 2A1, 2 2B2, and 3 2B1, respectively.

Theoretical studies on the low-lying electronic states of the diazomethyl (HCNN) radical and its ions

The diazomethyl (HCNN) radical has attracted considerable attention due to its great interest in interstellar chemistry and combustion processes. In this article, we have systemically studied the low-lying electronic states of the HCNN radical and its ions through complete active space self-consistent field and multiconfigurational second-order perturbation theory. For the ground state of HCNN, the calculated CH stretch ν 1, asymmetric NNC stretch ν 2, and NCH bend ν 4 are 3305, 1876, and 870 cm −1, respectively. The ν 4 is close to the experimental value of 871 cm −1. The adiabatic excitation energies of 1 2A′ and 2 2A″ of HCNN are shown to be in agreement with the experimental reports . Moreover, the first adiabatic detachment energy of HCNN − is 1.628 eV, which accords with the experimental value of 1.685 ± 0.006 eV. Our work might not only be helpful for deeply understanding the character of the low-lying electronic states of the HCNN radical and its ions, but also provide a theoretical guidance for further studying the photoelectron spectrum of HCNN and HCNN −.

CASSCF/CASPT2 Calculation of the Low-Lying Electronic States of the CH3Se Neutral Radical and Its Cation

Electronic states of the CH(3)Se and its cation CH(3)Se(+) have been studied using the complete active space self-consistent field (CASSCF) and multiconfiguration second-order perturbation theory (CASPT2) methods in conjunction with the ANO-RCC(TZP) basis set. To investigate the Jahn-Teller effect on the CH(3)Se radical, C(s) symmetry was used for CH(3)Se in calculations. The results show that the Jahn-Teller effect is very small (69 cm(-1)) and the 1(2)A' state is slightly more stable than the 1(2)A'' state (8 cm(-1)). The CH(3)Se has been found to have a 1(2)A' ground state with a C-Se bond distance of 1.975 A. The computed C-Se stretching nu(6)(a') frequency is 554.1 cm(-1), which is in good agreement with the experimental values of 600 +/- 60 cm(-1). The calculations for CH(3)Se at 3.621 and 5.307 eV are attributed to 1(2)A' --> 2(2)A'(1(2)A(1)) and 1(2)A' --> 2(2)A'', respectively. The vertical and adiabatic ionization energies were obtained to compare with the PES data.

A Theoretical Study of the Low-Lying Electronic States of the AlCCH Radical and Its Ions

The AlCCH radical is a photolysis product of the aluminum-acetylene adducts and has been considered as a molecule with potential interest in astrophysics. In this study, the low-lying electronic states of the AlCCH radical, cation, and anion have been studied by using complete active space self-consistent field and multiconfigurational second-order perturbation theory. The geometrical parameters, electron configurations, excitation energies, oscillator strengths, and harmonic vibrational frequencies are calculated in C(S) symmetry. For the X(1)Sigma(+) state of AlCCH, the calculated C-C and C-Al stretching modes are in good agreement with experimental reports. Moreover, the vertical excitation energy (T(v)) of 1(1)Pi is 3.68 eV, which is close to the experimental value of 3.57 eV. The electron transitions of AlCCH(+), X(2)Sigma(+) --> 1(2)Pi, X(2)Sigma(+) --> 2(2)Sigma(+), and X(2)Sigma(+) --> 1(2)Sigma(-), are predicted at 2.57, 4.51, and 4.61 eV, respectively. For AlCCH(-), the transition X(2)Pi --> 1(2)Sigma(-) occurs at 3.02 eV. The ionization potentials of AlCCH are computed in order to provide a theoretical guidance to the photoelectron spectrum of the AlCCH radical.

Photoisomerization of Model Retinal Chromophores: Insight from Quantum Monte Carlo and Multiconfigurational Perturbation Theory

We present a systematic investigation of the structural relaxation in the excited state of model retinal chromophores in the gas phase using the complete-active-space self-consistent theory (CASSCF), multiconfigurational second-order perturbation theory (CASPT2), quantum Monte Carlo (QMC), and coupled cluster (CC) methods. In contrast to the CASSCF photoisomerization mechanism of bond inversion followed by torsion around formal double bonds, we find that the other approaches predict an initial skeletal relaxation which does not lead to bond inversion but to a rather flexible retinal chromophore with longer bonds and with the bond-length pattern of the ground state being partly preserved. The relaxation proceeds then preferentially via partial torsion around formal single bonds and does not reach a conical intersection region. Our findings are compatible with solution experiments which point to the existence of multiple minima and relaxation pathways, some of which are nonreactive, do not lead to photoproducts via conical intersection, and are dominant in solution. Our results also demonstrate the importance of a balanced description of dynamical and static correlation in the excited-state gradients and raise serious concerns on the common use of the CASSCF method to investigate structural properties of photoexcited retinal systems.

Cl-loss and F-loss dissociations in low-lying electronic states of the [formula omitted] 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 (ANO-L) basis were performed for Cl- and F-loss dissociations of the CF 2 Cl 2 + ion in the 1 2B 2 (X 2B 2), 1 2A 2, 1 2B 1, and 1 2A 1 states. The electronic states of the CF 2Cl + and CF Cl 2 + ions produced by Cl-loss and F-loss dissociation, respectively, were carefully determined. Our predicted appearance potential values are in good agreement with experimental findings for CF 2Cl + (X 1A 1) and CF Cl 2 + (X 1A 1).

CASPT2 and CASSCF studies on the low-lying electronic states of the HCCO radical and its anion

The complete active space self-consistent field and multiconfigurational second-order perturbation theory methods have been used to investigate the low-lying electronic states of the HCCO radical and its anion. The calculated geometrical structure and harmonic vibrational frequencies for the X 2A″ state of HCCO are in good agreement with experimental values. The barrier to 12П (12A′) is estimated to be 0.069 eV (554 cm−1), which is also close to experimental result (540 cm−1). Moreover, we find that the 22A′ state is bent, while 22П (22A″) is linear. By comparing the oscillator strengths and adiabatic excitation energies, we show that the 22П (22A″) ← X 2A″ transition is the most intense among these transitions. The unpaired electrons mainly locate on the C atoms in the 22A′ and 22П (22A″) states according to the Mulliken spin populations. On the other hand, for HCCO−, the first adiabatic and vertical detachment energies are 2.210 and 2.362 eV, respectively, which reasonably agree with experimental value of 2.338 ± 0.008 eV. Remarkably, we explore several higher excited states of the HCCO radical (14A′, 24A″ and cis-14A′) and its anion (13A″, 11A″ and 13A′), which have not been reported in previous studies.

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

What Active Space Adequately Describes Oxygen Activation by a Late Transition Metal? CASPT2 and RASPT2 Applied to Intermediates from the Reaction of O2 with a Cu(I)-α-Ketocarboxylate.

Multiconfigurational second-order perturbation theory calculations based on a complete active space reference wave function (CASPT2), employing active spaces of increasing size, are well converged at the level of 12 electrons in 12 orbitals for the singlet-triplet state-energy splittings of three supported copper-dioxygen and two supported copper-oxo complexes. Corresponding calculations using the restricted active space approach (RASPT2) offer similar accuracy with a significantly reduced computational overhead provided an inner (2,2) complete active space is included in the overall RAS space in order to account for strong biradical character in most of the compounds. The effects of the different active space choices and the outer RAS space excitations are examined, and conclusions are drawn with respect to the general applicability of the RASPT2 protocol.

A multiconfigurational perturbation theory study of the electronic structure and EPR g values of an oxomolybdenum enzyme model complex

We have studied the electronic structure (ground and excited states) and g matrix of a model compound for oxomolybdenum enzymes featuring the MoO–dithiolate moiety in Cs symmetry, by means of multiconfigurational second-order perturbation theory (CASPT2) for a range of fold angles (5–29°), i.e. the angle between the S–Mo–S and S–C–C–S planes of the dithiolate ligand. We found no evidence of a suggested 3-center pseudo-σ bonding interaction between the singly occupied orbital of the ground state and the symmetric in-plane dithiolate orbital (Inscore et al. in Inorg Chem 38:1401–1410, 1999). This is complemented with our alternative assignment of band 4 in the electronic spectrum as the transition out of the a″ instead of the a′ dithiolate in-plane orbital into the singly occupied ground-state orbital, believed to probe the dominant hole superexchange pathway (Inscore et al. in Inorg Chem 38:1401–1410, 1999; Burgmayer et al. in J Inorg Biochem 101:1601–1616, 2007). Principal g values of 1.9652, 1.9090, 2.0003 were obtained at a fold angle of 21°. The latter value is so close to the free electron ge factor is due to an important positive contribution from the LMCT transition corresponding to band 4, counteracting the negative contributions from the ligand field transitions.

Electronic Structure and Chemical Bonding in the Lowest Electronic States of TcN

Multiconfiguration second-order perturbation theory, with the inclusion of relativistic effects and spin-orbit coupling, was employed to investigate the nature of the ground and low-lying Lambda-S and Omega states of the TcN molecule. Spectroscopic constants, effective bond order, and potential energy curves for 13 low-lying Lambda-S states and 5 Omega states are given. The computed ground state of TcN is of Omega = 3 symmetry (R(e) = 1.605 A and omega(e) = 1085 cm(-1)), originating mainly from the (3)Delta Lambda-S ground state. This result is contrasted with the nature of the ground state for other VIIB transtion-metal mononitrides, including X(3)Sigma(-) symmetry for MnN and Omega = 0(+) symmetry for ReN, derived also from a X(3)Sigma(-) state.

Electronic structure and chemical bonding in the ground states of Tc2 and Re2

Multiconfiguration second-order perturbation theory, including relativistic effects and spin–orbit coupling, has been employed to investigate the nature of the chemical bonding in the ground state of Tc2 and Re2. The Tc2 ground state is found to be a state, with an effective bond order (EBO) of 4.4, and a dissociation energy of 3.25 eV. The Re2 ground state is a 1 g state, with EBO = 4.3. Almost degenerate to it, is a state (T e = 77 cm−1), with EBO = 4.1. Experimental evidence also indicates that the ground state is of 1 g nature. The dissociation energy is computed to be 5.0 eV in agreement with an experimental estimate of 4 ± 1 eV.

Theoretical Study of the Chemiluminescent Decomposition of Dioxetanone

The unimolecular chemiluminescent decomposition of unsubstituted dioxetanone was studied at the complete active space self-consistent field level of theory combined with the multistate second-order multiconfigurational perturbation theory energy correction. The calculations revealed interesting features. Two transition states, two conical intersections, and one intermediate stable biradical structure along the lowest energy reaction path were identified. It was noted that the conical intersections are found at or in very close proximity to the transition states. The first and second transition states correspond to O-O and C-C cleavages, respectively. In particular, a planar structure is supported by the (1)(sigma,sigma*) state during the O-O dissociation up to the first transition state and conical intersection. At this point the (1)(sigma,sigma*) state dissociation path bifurcates, corresponding to a torsion of the O-C-C-O angle. Simultaneously, the (1)(n,sigma*) state becomes lower in energy while still favoring a planar structure. As the lowest-energy reaction path proceeds toward the second transition state and conical intersection, the (1)(n,sigma*), (3)(n,sigma*), and (1)(sigma,sigma*) states are close in energy. This work suggests that the vibrational distribution at the first conical intersection and the interactions among the states as the reaction proceeds between the two transition states are the origin of the population of the chemiluminescent (n,sigma*) states.

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.