Ab initio study of PN electronic states – a qualitative interpretation of the perturbation and predissociation effects on observed transitions

Valence and high electronic states of PN have been calculated with accurate quantum chemistry methods. The variety of theoretical methods used includes complete active space self-consistent field, multireference configuration interaction and the newly developed explicitly correlated coupled cluster methods. The large correlation-consistent atomic orbitals basis sets AVQZ, AV5Z and AV(5+d)Z are used for the potential energy curves calculations in the bonding and long-range regions. The spectroscopic constants (R_e, B_e, ω_e, ω_ex_e, α_e, D_e, T_e) and the vibrational levels of the bound valence states (X¹Σ⁺, A¹Π, a³Σ⁺, d ³Δ, e³Σ^?, C¹Σ^?, b³Π, D ¹Δ and E¹Σ⁺ and some higher bound states) are determined and compared with experimental findings when available. Significant spin–orbit interactions between triplet states and A¹Π and E¹Σ⁺ excited states are found near the crossing points of the potential energy curves and could explain predissociation phenomena and the perturbations of the vibrational levels experimentally observed for PN in their A¹Π and E¹Σ⁺ states.     

The A 1Π ∼ D 1Δ rotation-electronic interaction in CO

All available experimental data pertinent to the A ¹Π (v = 0-4) and D ¹Δ state of CO have been used to derive five independent values for the rotation-electronic interaction parameter b(A ～D). The experimental values concern a narrow R centroïd region (1·21 < R < 1·32 Å). The mean value b(A ～D) = 0·12 ± 0·01 is much smaller than the value (0·48) predicted by ab initio SCF-CI calculations which have been carried out for several internuclear distances. The experimental and calculated values for the A ¹Π ～I ¹Σ^- and a ³Π ～ a′³Σ⁺, e ³Σ^-, d ³Δ rotation-electronic perturbations available in the literature are also discussed.     

On the cΠ (v = 0) state of carbon monoxide

A full analysis of the near infrared c³Π-b³Σ⁺ (0-0) band is given and term values for both states determined. The c³Π (v = 0) state was jointly analysed with the perturbing k³Π (v = 2) state and data from the c³Π-X¹Σ⁺ (0-0) transition and 3A band system were included. It is shown that the available data are consistent with the c³Π (v = 0) state having near Hund’s case b coupling with a spin-orbit constant of A = 0.45 ± 0.02 cm⁻¹, a homogeneous perturbation with the k³Π (v = 2) state, and Λ-type doubling arising predominantly from its interaction with the j³Σ⁺ state. A discrepancy with a more recent report of the 3A band system is identified and discussed. The perturbed b³Σ⁺ state term values are consistent with a previously reported five state interaction model.     

Fourier Transform Infrared Emission Spectroscopy of thebΠ–aΣSystem of BN

The emission spectrum of BN has been investigated in the 1800–9000 cm⁻¹region using a Fourier transform spectrometer. BN was formed in a microwave discharge of He with a trace of BCl₃and N₂. The bands observed in the 3000–7800 cm⁻¹interval have been assigned as theb¹Π–a¹Σ⁺transition, with the 0–0 band at 3513.99040(43) cm⁻¹. This transition is analogous to theA¹Π_u–X¹Σ⁺_g(Phillips) system of the isoelectronic C₂molecule. The rotational analysis of the 0–0, 1–1, 1–0, 2–1, 3–2, 2–0, 3–1, 4–2, and 4–1 bands has been obtained and the molecular constants for theb¹Π anda¹Σ⁺states have been determined. A local perturbation has been observed in thev= 1 vibrational level of theb¹Π state nearJ= 18 caused by the interaction with thev= 3 vibrational level of thea¹Σ⁺state. The principal equilibrium constants for thea¹Σ⁺state are: ω_e= 1705.4032(11) cm⁻¹, ω_ex_e= 10.55338(52) cm⁻¹,B_e= 1.683771(10), α_e= 0.013857(16) cm⁻¹, andr_e= 1.2745081(37) Å. Although theb¹Π–a¹Σ⁺transition has recently been seen in emission from boron nitride trapped in solid neon matrices [J. Chem. Phys.104,3143–3146 (1996)], our work represents the first observation of this transition of BN in the gas phase.     

Accurate spectroscopic calculations of the 19 Λ-S states and 36 Ω states of the BC+ cation

This work computed the potential energy curves of 19 Λ-S states, which arose from the first five dissociation limits of BC⁺ cation, B⁺(¹S_g) + C(³P_g), B⁺(¹S_g) + C(¹D_g), B⁺(¹S_g) + C(¹S_g), C⁺(²P_u) + B(²P_u), and B⁺(¹S_g) + C(⁵S_u). The calculations were done for internuclear separations from 0.08 to 1.07 nm. The potential energy curves of 36 Ω states yielded from these Λ-S states were also calculated. Core-valence correlation and scalar relativistic correction, basis set extrapolation as well as Davidson correction were accounted for. Of these Λ-S states, the c¹Σ⁺, D³Π, 2¹Π, 2³Σ⁺, 2¹Δ, 3¹Σ⁺, and 4¹Σ⁺ had double wells; the 3³Π and 3¹Π states had three wells; the C³Σ^? and D³Π states were inverted with the spin-orbit coupling effect included; and the second wells of c¹Σ⁺, D³Π and 3¹Σ⁺ states, the second and the third wells of 3³Π state as well as the third well of 3¹Π state were very weakly bound, which well depths were smaller than 400 cm^?1. The spectroscopic parameters were determined for all the states. The vibrational properties were predicted only for some weakly bound states. The spin-orbit coupling effect on the spectroscopic parameters was evaluated.     

Observation of the c3Πu-X1Σg+ intersystem transition in the absorption spectrum of P2

The observation of the c³Π_u-X¹Σ_g⁺ intersystem transition of P₂ is reported. The 6-0 band of the system was identified on high resolution absorption plates teken on the NRC 10-m vacuum spectrograph at Ottawa. A rotational analysis of the band is given together with that of the adjacent 5-0 band of the C¹Σ_u⁺-X¹Σ_g⁺ system, the upper level of which is involved in a mutual perturbation with the c³Π_u, v = 6 level. The interaction parameters for the perturbation are derived. It is proposed that the appearance of the 6-0 band of the c³Π_u-X¹Σ_g⁺ transition is due to intensity borrowing from the strong, allowed C¹Σ_u⁺-X¹Σ_g⁺ system. Accurate values for the energies of the c³Π_u, b³Π_g, and a³Σ_u⁺ states relative to the ground state are given. The analysis of two other bands, 2-0 and 7-0, of the C¹Σ_u⁺-X¹Σ_g⁺ system whose upper levels likewise interact strongly with the c³Π_u state are also given.     

Anomalous isotope effects in indirect predissociations: An example in the spectrum of BeH

Measurements of the linewidths in the (3pπ) B²Π state of BeH and BeD which is predissociated by a ²Σ⁺ state show an anomalous isotope effect. Ab initio calculations of the five lowest excited ²Σ⁺ states of BeH show that the first excited ²Σ⁺ state is stable at a large inter-nuclear distance and is responsible for the observed predissociation. The anomalous isotope effect is explained by an indirect mechanism of predissociation involving this ²Σ⁺ state and the (3pσ) ²Σ⁺ state which is separated from the (3pπ) B²Π state by an energy of the order of magnitude of ω_e. A new method to calculate the widths and the shifts of predissociated levels is presented and calculations in the case of BeH and BeD give good agreement with the experimental data.     

A New Study of the Perturbations in theA1Π State of PN

TheA¹Π–X¹Σ⁺system of the PN molecule has been reexamined via high resolution conventional spectroscopy, at higher rotationalJ-values than those in previous studies. It is shown that perturbations occurring in theA¹Π (v= 0 to 3) levels give access to information concerning the (e³Σ⁻,a³Σ⁺,d³Δ,C¹Σ⁻,D¹Δ) valence states. Of particular interest are (1) the strong spin–orbit interaction between thee³Σ⁻andA¹Π (v_A= 2) levels, yielding 17 rotational energy levels of thee³Σ⁻state, and (2) the triple crossing occurring between theA¹Π (v_A= 3),d³Δ, andC¹Σ⁻levels.     

An ab initio investigation of the low-lying electronic states of BeH

Potential energy curves(PECs) for the ground state(X 2 Σ +) and the four excited electronic states(A 2 Π,B 2 Π,C 2 Σ +,4 Π) of a BeH molecule are calculated using the multi-configuration reference single and double excited configuration interaction(MRCI) approach in combination with the aug-cc-pVTZ basis sets.The calculation covers the internuclear distance ranging from 0.07 nm to 0.70 nm,and the equilibrium bond length R e and the vertical excited energy T e are determined directly.It is evident that the X2Σ+,A2Π,B2Π,C2Σ+ states are bound and 4Π is a repulsive excited state.With the potentials,all of the vibrational levels and inertial rotation constants are predicted when the rotational quantum number J is set to be equal to zero(J = 0) by numerically solving the radial Schr¨odinger equation of nuclear motion.Then the spectroscopic data are obtained including the rotation coupling constant ω e,the anharmonic constant ωexe,the equilibrium rotation constant Be,and the vibration-rotation coupling constant αe.These values are compared with the theoretical and experimental results currently available,showing that they are in agreement with each other.     

Rotational distribution in simultaneously excited electronic states of NH

The rotational structures of the NH(A³Π→X³Σ^-) and (c¹Π→a¹Δ) bands were excited simultaneously in electrical discharges through NH₃ and NH₃ + Ar. The A³Π state exhibits higher rotational temperature than the c¹Π state. The NH (A³Π) excited in an NH₃ + Ar discharge showed non-Maxwellian distribution. Mechanisms for excitation of NH are discussed.     

The electronic spectrum of the SiC radical: A theoretical study

Electronic structure and spectroscopic properties of the low-lying electronic states of the SiC radical have been determined from the ab initio based configuration interaction calculations. Potential energy curves of 32 Λ-S states of singlet, triplet, and quintet spin multiplicities have been constructed. Spectroscopic constants (r_e, T_e, and ω_e) of 23 states within 6 eV are reported and compared with the existing data. The dipole moments (μ_e) of most of these states at their respective equilibrium bond lengths have been computed. Effects of the spin-orbit coupling on the spectroscopic properties of SiC have been studied. The E³Π state is found to be an important one which has not been studied before. A transition of the type E³Π-X³Π is predicted to take place in the range 25 000-26 000 cm⁻¹. The partial radiative lifetimes for several electric dipole allowed transitions such as A³Σ⁺-X³Π, B³Σ⁺-X³Π, C³Π-X³Π, D³Δ-X³Π, E³Π-X³Π etc. have been reported.     

Chemiluminescence of Si + N2O flames

Spectra of the chemiluminescent flame produced by the reaction of silicon vapor with N₂O have shown strong emission from the A¹Π-X¹Σ⁺, b³Π-X¹Σ⁺, and a³Σ⁺-X¹Σ⁺ systems of SiO with preferential excitation into the b³Π state. Bandhead measurements of 33 bands of the b-X system yielded the following constants for the b³Π state:

$T_e=33947.0\pm 1.9c{m}^{?1};{\omega }_e=1013.8\pm 1.1c{m}^{?1};{\omega }_e{x}_e=7.57\pm 0.12c{m}^{?1}$

. From partially resolved rotational structure in the a-X bands, an approximate value of B = 0.59 ± 0.01cm^?1 was obtained for the a³Σ⁺ state. The effect of adding active nitrogen and CO to the flame was investigated and the results were shown to be consistent with assigning the a and b states as triplets. The photon yield of the Si + N₂O reaction was measured and found to be small.     

Vibrational analysis of the a3Σ+-X1Σ+ and b3Π-X1Σ+ band systems of GeS

Spectra of GeS have been obtained in a chemiluminescent flame produced by the reaction Ge + OCS → GeS + CO. Neither of the known band systems, D¹Π-X¹Σ⁺ and E¹Σ⁺-X¹Σ⁺, was observed, but two new band systems in the regions 350–400 and 420–650 nm were obtained. By comparison with similar systems in isovalent molecules, these were assigned as b³Π₁-X¹Σ⁺ and a³Σ⁺-X¹Σ⁺, respectively. Vibrational assignments were made with the help of the germanium isotope effect and vibrational constants were obtained for the states involved. Approximate Morse potential Franck-Condon factors were computed and were shown to fit the general trend of the intensity distribution for both systems. Addition of active nitrogen to the flame was shown to increase the intensity of the b-X system by an order of magnitude while hardly affecting the a-X system. Constants (in cm^?1) obtained for the two new states are: a³Σ⁺: T_e = 21986.3 ± 2.3, ω_e = 388.9 ± 1.0, ω_ex_e = 1.35 ± 0.11; b³Π₁: T_e = 27192.0 ± 1.8, ω_e = 435.4 ± 1.1, ω_ex_e = 1.68 ± 0.20.     

Transition Probabilities in the BΣ-XΣ and the BΣ-AΠ Electronic Systems of MgO

Transition probabilities for the B¹Σ⁺-X¹Σ⁺ and the B¹Σ⁺-A¹Π electronic systems are presented for v=0-4 and J=0-150 in each electronic state. The functional form of the electronic transition moment for the B-X transition is taken from published ab initio results. The B-A moment is assumed to have the same form and is scaled using empirical branching ratio data. The R_e(r) are used with Rydberg-Klein-Rees (RKR) wavefunctions to calculate transition probabilities for v=0-4 and J=0-150. The RKR potentials were calculated based on empirical spectroscopic constants.     

Resonance-enhanced multiphoton ionization detection of a new 3Σ+-a3Π band system in CS

Resonance-enhanced multiphoton ionization has been used to detect absorption transitions from the nascent states of CS produced in the two-photon laser flash photolysis of CS₂. Transitions are seen from the a³Π state of CS to a previously unobserved ³Σ⁺ state. Rotational assignments of the (1, 0), (0, 0), (0, 1), and (0, 2) bands have been made; the derived constants for those bands are similar to those of the CS⁺ ion, in good agreement with the assumption that the upper electronic state is the 3sσ³Σ⁺ Rydberg state.     

Fine structure of the close-lying A 2Π and B 2Σ+ states of BaH and BaD

Molecular parameters for the close-lying and strongly interacting A ²Π and B ²Σ states of BaH and BaD have been re-evaluated by means of a numerical matrix diagonalization procedure. The results obtained according to this exact method deviate considerably from the effective ones of previous investigations, particularly with respect to the A ²Π-B ²Σ⁺ interaction matrix elements which describe the large Λ-doubling and spin-splitting. The new values of the Λ-doubling and spin-splitting parameters are in excellent agreement with pure precession values for L = 2, and thus the present results form an interesting extension of the pure precession model which so far has been found applicable in a number of cases for which L equals one. The pure precession result L = 2 indicates that the outermost electron of the A ²Π and B ²Σ⁺ states must be a d-electron, and this requires a re-assignment of the configuration quantum numbers of these states. Strong local perturbations are observed in the rotational levels of the A ²Π state of both BaH and BaD, and the result L = 2 now yields a further confirmation of the previous assumption that a ²Δ state causes these perturbations. In the case of BaD the electronic + vibrational energy and the rotational constants (B_v , D_v ) of the perturbing level could be determined from the perturbed A ²Π term values, and in particular the value of the interaction matrix element leads to the conclusion that there is a A ²Π, v = 0 - ²Δ, v = 2 interaction. Finally the influence of the A ²Π - ²Δ, Δv = 0 interaction on the A ²Π and B ²Σ⁺ molecular parameters was investigated.     

The B2Σ+ → A2Πi system of silicon nitride,SiN

The 440-nm violet-degraded ${}^2\text{Σ →}{}^2\text{Π}$ bands of SiN, which were previously assigned to a $\text{“K” → A}$ system, have been reanalyzed. These bands are shown to be Δv = 0, ±1 sequence bands of the B²Σ⁺ → A²Π system of SiN. The first reliable value of T_e(A²Π) = 994.4(1) cm^?1 has been obtained, and this determines the location of the D²Π and L²Π states with respect to the ground state. The B²Σ⁺, v = 7 and D²Π, v = 3 levels are shown to be mutually perturbing. A detailed study has been made of the perturbed X²Σ⁺, v = 8 level. The 6–8 band of the B → X system has been photographed at high resolution. A deperturbation of this band confirms T_e(A²Π), and provides the first experimental verification of the inverted nature of the A state.     

Rotational energies of Hund's case (c) 3Π states in diatomic molecules: The a3Π state of InH and InD

The general theory of the rotational energies and fine structure of a case (c) and intermediate case (c)-case (e) ³Π state is investigated. The theoretical results are then applied to the a³Π state of InH and InD. Certain anomalies in the Λ-doubling of the ³Π₁ substate indicate that the ³Σ⁺ state derivable from the lowest level of the separate atoms is stable with a potential minimum below that of the a³Π state. The stability of this ³Σ⁺ state also yields a reasonable explanation for the predissociation observed for all the a³Π substates. The good agreement between observed and theoretical results regarding the centrifugal distortion in the multiplet splitting shows that the a³Π state is close to coupling case (a) in its lowest vibrational level. However, an increasing case (c) transition occurs with increasing vibrational quantum number.     

CrHn(n=0,+1,+2)分子及离子的势能函数

用原子分子反应静力学原理推导出CrHⁿ(n=0，+1，+2)的电子状态及其离解极限. 对H原子采用6-311++G^**基组，对Cr原子采用SVP(split valence polarization)全电子基组，用B3PW91方法计算了它们的平衡几何、电子状态，在此基础上分别计算CrH，CrH⁺的Murrell-Sorbie解析势能函数和CrH²⁺的解析势能函数及其对应的力常数、光谱参数，理论计算值与实验值和文献计算值符合较好. 从离解极限和通道解释了不同的势能函数形状. 计算表明：CrH⁺的势能曲线均具有对应于稳定平衡结构的极小点，说明CrH⁺可稳定存在. 而CrH²⁺离子的势能曲线对应于不稳定的排斥态，说明CrH²⁺是不稳定的. 关键词： n(n=0')" href="#">CrHⁿ(n=0 +2) 势能函数 光谱参数 稳定性     

Potential energy curves for the 48 lowest-lying molecular states of LiH+

The electronic energies of the 20 lowest lying ²Σ⁺ states, the 14 lowest lying ²Π states, and the 14 lowest lying ²Δ states of LiH⁺ have been calculated in the range 2 ≤ R ≤ 20 a.u. from a model potential approach and using truncated diatomic orbitals (TDO) as basis set. Results in very good agreement with the more recent literature were obtained for the spectroscopic constants, R_e and D_e, for the ground state X²Σ⁺.