VIBRONIC STRUCTURE OF THE NO3 X̃ 2A2′ SYSTEM

The $\tilde{X}$ $^2A_2'$ state of NO$_3$ under jet cooled conditions is investigated via laser induced fluorescence (~LIF~) and two-color resonant four-wave mixing (~2C-R4WM~) techniques. The electronic structure of NO$_3$ is thought to be similar to that of BF$_3$, and the latter has been well documented in the literatures\footnote{H.~B.~Gray, Electrons and Chemical Bonding, W.~A.~Benjamin Inc., New York (1965); Open Source Tex Books, https://archive.org/details/ost-chemistry-electrons\_chemical\_bonding (retrieved Feb. 26, 2019).}\footnote{F.~A.~Cotton, Chemical Applications of Group Theory, 2nd ed., Wiley-International, New York (1971).}. The BF$_3$ highest occupied molecular orbital (~HOMO~) possesses peculiar electronic structure with orbital localization on each of three F’s and no contribution on the center atom, B. For NO$_3$, the HOMO corresponds to a singly occupied molecular orbital (~SOMO~), and, in the $\tilde{X}$ $^2A_2'$ state (~$\tilde{A}$ $^2E''$ and $\tilde{B}$ $^2E'$, too~) of NO$_3$, the un-paired electron is localized on the three O’s and has no contribution on N. For this state, the degenerate vibrations are naturally expected to strongly affect the electron motion, which can be referred to as ”degenerate-vibrationally induced vibronic coupling” on the non-degenerate electronic state. The SOMO characteristics of NO$_3$ have been confirmed by high-level quantum chemical computation\footnote{W.~Eisfeld and K.~Morokuma, $J.~Chem.~Phys.$ 113, 5587 (2000).}. The characteristic features of the vibrational structure of the $\tilde{X}$ $^2A_2'$ state may possibly be understood by the vibronic coupling. One feature is an unexpectedly large spin splitting of $1_0$ (~= $N_K$~) of the 3$\nu_4$ ($a_1'$) level observed by 2C-R4WM\footnote{M.~Fukushima and T.~Ishiwata, 73rd ISMS, paper WD02 (2018).}, and this splitting can be understood as the good quantum number behavior of $P$ (~$= K_v + \Sigma = \Lambda + l + \Sigma$~) derived from the coupling

2C-R4WM spectroscopy of jet cooled NO3

We have generated NO$_3$ from pyrolysis of N$_2$O$_5$ following supersonic free jet expansion, and carried out two color resonant four wave mixing (~2C-R4WM~) spectroscopy of the $\tilde{B}$ $^2E'$ -- $\tilde{X}$ $^2A_2'$ electronic transition. One laser was fixed to pump NO$_3$ to a ro-vibronic level of the $\tilde{B}$ state, and the other laser (~probe~) was scanned across two levels of the $\tilde{X}$ $^2A_2'$ state lying at 1051 and 1492 cm$^{-1}$, the $\nu_1$ ($a_1'$) and $\nu_3$ ($e'$) fundamentals, respectively. The 2C-R4WM spectra have unexpected back-ground signal of NO$_3$ (~stray signal due to experimental set-up is also detected~) similar to laser induced fluorescence (~LIF~) excitation spectrum of the 0-0 band, although the back-ground signal was not expected in considering the 2C-R4WM scheme. Despite the back-ground interference, we have observed two peaks at 1051.61 and 1055.29 cm$^{-1}$ in the $\nu_1$ region of the spectrum, and the frequencies agree with the two bands, 1051.2 and 1055.3 cm$^{-1}$, of our relatively higher resolution dispersed fluorescence spectrum, the former of which has been assigned to the $\nu_1$ fundamental. Band width of both peaks, $\sim$ 0.2 cm$^{-1}$, is broader than twice the experimental spectral-resolution, 0.04 cm$^{-1}$ (~because this experiment is double resonance spectroscopy~), and the 1051.61 cm$^{-1}$ peak is attributed to a $Q$ branch band head (~a line-like $Q$ branch~) of the $\nu_1$ fundamental. The other branches are suspected to be hidden in noise of the back-ground signal. The 1055.29 cm$^{-1}$ peak is also attributed to a $Q$ band head. The $\tilde{B}$ $^2E'_{\frac{1}{2}}$ (~$J' = \frac{3}{2}$, $K' = 1$~) -- $\tilde{X}$ $^2A_2'$ (~$N'' = 1$, $K'' = 0$~) ro-vibronic transition was used as the pump transition. The dump (~probe~) transition to both $a_1'$ and $e'$ vibronic levels are then allowed as perpendicular transition. Accordingly, it cannot be determined from present results whether the 1055.29 cm$^{-1}$ band is attributed to $a_1'$ or $e'$ ($\nu_3$), unfortunately. The 2C-R4WM spectrum of the 1492 cm$^{-1}$ band region shows one $Q$ head at 1499.79 cm$^{-1}$, which is consistent with our dispersed fluorescence spectrum. By considering with the $\nu_3$ + $\nu_4$ - $\nu_4$ hot band\footnote{K.~Kawaguchi $et$ $al.$, $J.$ $Phys.$ $Chem.$ $A$ 117, 13732 (2013) and E.~Hirota, $J.$ $Mol.$ $Spectrosco.$ 310, 99 (2015).}, the present results suggest that both 1055.29 and 1499.79 cm$^{-1}$ levels are $a_1'$ level

LIF SPECTROSCOPY OF LINEAR SiOSi

We have assigned spectral species of a LIF spectrum with $^1\Pi$ -- $^1\Sigma$ rotational structure to SiOSi with the aid of $ab$ $initio$ quantum chemical calculations\footnote{M.~Fukushima and T.~Ishiwata, 73rd ISMS, paper MJ09 (2018).}. Due to the spectrum's red-shaded structure, the $R$-branch forms a band head, and an analysis adopting the $P$- and $Q$-branches had not been satisfactory. As the $ab$ $initio$ calculations suggest the ground electronic state is 1$^1\Sigma_g^+$, we attempted a more precise analysis via combination differences and noted heavy irregularities exclusive to the upper levels of the $Q$-branch. Considering parities of the rotational levels of the upper $\Pi$ electronic state, we are investigating this irregularity with the aid of computation

LIF SPECTROSCOPY OF A 1Σ SPECIES CONTAINING Si: LINEAR SiOSi ?

In our past SiCN investigation\footnote{M.~Fukushima and T.~Ishiwata, J.~Chem.~Phys. 145, 124304 (2016).}, we found unknown bands with $^1\Sigma$ -- $^1\Sigma$ rotational structure in the laser induced fluorescence (~LIF~) excitation spectrum of SiCN. From the rotational constants, the spectral species may possibly be attributed to SiOSi. Although the most stable geometry of the ground electronic state is reported to be cyclic structure\footnote{S.~J.~Paukstis, et~al., J.~Chem.~Phys.~A 106, 8435 (2002).}, our CCSD(T) calculation with arg-cc-pCVTZ indicates the linear geometry, $^1\Sigma_g^+$, lying $\sim$2,000 cm$^{-1}$ above it. The potential energy surface calculated is very strange, and it indicates a barrier between the two geometries, $\sim$10,000 cm$^{-1}$ from the bottom. The dispersed fluorescence (~DF~) spectra from the single vibronic levels have fairly long progressions with very harmonic structure, but no hot-band structure. More precise computational works are underway, and we will discuss the assignment of the spectral species in this talk

VIBRONIC STRUCTURE OF THE X_ 2A2_ STATE OF NO3

We have measured dispersed fluorescence (~DF~) spectra from the single vibronic levels (~SVL's~) of the $tilde{B}$ $^2E'$ state of jet cooled $^{14}$NO$_3$ and $^{15}$NO$_3$, and found a new vibronic band around the $nu_1$ fundamentalfootnote{M.~Fukushima and T.~Ishiwata, paper WJ03, ISMS2013, and paper MI17, ISMS2014.}. This new band has two characteristics; (1) inverse isotope shift, and (2) unexpectedly strong intensity, i.e.~comparable with that of the $nu_1$ fundamental. We concluded on the basis of the isotope effect that the terminated (~lower~) vibrational level of the new vibronic band should have vibrationally $a_1'$ symmetry, and assigned to the third over-tone of the $nu_4$ asymmetric ($e'$) mode, $3 nu_4$ ($a_1'$). We also assigned a weaker band at about 160 cm$^{-1}$ above the new band to one terminated to $3 nu_4$ ($a_2'$). The $3 nu_4$ ($a_1'$) and ($a_2'$) levels are ones with $l = pm3$. Hirota proposed new vibronic coupling mechanismfootnote{E.~Hirota, $J. Mol. Spectrosc.$, in press.} which suggests that degenerate vibrational modes can induce electronic orbital angular momentum (~$L$~) even in non-degenerate electronic states. %It is thus thought the surprisingly wide splitting of $3 nu_4$, $a_1'$ and $a_2'$, is resulted from vibronic coupling, and the explanation we proposed is as follows. We interpret this as a sort of break-down of the Born-Oppenheimer approximation, and think that $pm l$ induces $mpbar{Lambda}$, where $bar{Lambda}$ expresses the pseudo-$L$; for the present system, one of the components of the third over-tone level, $| Lambda = 0; v_4 = 3, l = +3 rangle$, can have contributions of $| bar{Lambda} = -1; v_4 = 3, l = +2 rangle$ and $| -2; 3, +1 rangle$. Under this interpretation, it is expected that there is sixth-order vibronic coupling, $(q_+^3Q_-^3 + q_-^3Q_+^3)$, between $| 0; 3, +3 rangle$ and $| 0; 3, -3 rangle$. The sixth-order coupling is weaker than the Renner-Teller term (~the fourth-order term, $(q_+^2Q_-^2 + q_-^2Q_+^2)$~), but stronger than the eighth-order term, $(q_+^4Q_-^4 + q_-^4Q_+^4)$. It is well known in linear molecules that the former shows huge separation, comparable with vibrational frequency, among the vibronic levels of $Pi$ electronic states, and the latter shows considerable splitting, $sim$10 cm$^{-1}$, at $Delta$ electronic states. Consequently, the $sim$160 cm$^{-1}$ splitting at $v_4$ = 3 is attributed to the sixth-order interaction. The relatively strong intensity for the band to $3 nu_4$ ($a_1'$) can be interpreted as a part of the huge 0-0 band intensity, because the $3 nu_4$ ($a_1'$) level, $| 0; 3, pm3 rangle$, can connect with the vibrationless level, $| 0; 0, 0 rangle$. $3 nu_4$ ($a_1'$) has two-fold intensity because of the vibrational wavefunction, $| 0; 3, +3 rangle + | 0; 3, -3 rangle$, while negligible intensity is expected for $3 nu_4$ ($a_2'$) with $| 0; 3, +3 rangle - | 0; 3, -3 rangle$ due to the cancellation. To confirm these interpretations, experiments on rotationally resolved spectra are underway

2C-R4WM SPECTROSCOPY OF JET COOLED NO3 (II)

We have generated NO$_3$ in a supersonic free jet expansion, and observed laser induced fluorescence (~LIF~) and two-color resonant four-wave mixing (~2C-R4WM~) signals. We have measured dispersed fluorescence (~DF~) spectra from single vibronic levels. Among the vibrational levels observed in the DF spectrum from the vibration-less level, the $\nu_1$ and $\nu_3$ fundamental regions (~$\sim$1050 and $\sim$1500 cm$^{-1}$ regions, respectively~) are now active for discussion, and thus we have tried to measure the rotationally resolved 2C-R4WM spectra\footnote{M.~Fukushima and T.~Ishiwata, 71st ISMS, paper RF01 (2016).}. The 2C-R4WM spectrum of the $\nu_3$ fundamental region is consistent with a previous infra-red investigation\footnote{K.~Kawaguchi, et~al., J. Mol. Spectrosco. 268, 85 (2011).}, and that of $\nu_1$ leads to the identification of the $K$ = 0 and $N$ = 1 level of the $\nu_1$ fundamental for the first time. We have found an additional level near $\nu_1$\footnote{M.~Fukushima and T.~Ishiwata, 68th ISMS, paper WJ03 (2013).}, and the 2C-R4WM spectrum of the level shows two rotational transitions separated by 0.27 cm$^{-1}$. Although the 0.27 cm$^{-1}$ separation is about 10 times larger than the spin splitting, $\sim$0.025 cm$^{-1}$, of the $K$ = 0 and $N$ = 1 levels at the other $a_1’$ levels with $l$ = 0, such as vibration-less and $\nu_1$ (~the latter value of which, 0.025 cm$^{-1}$, cannot be resolved under our instrumental resolution~), the two transitions are thought to correspond to those terminating to spin sub-levels, $J$ = 0.5 and = 1.5, at the present. We have assigned the additional level to $3\nu_4$ ($a_1'$) with $l = \pm3$. For $\Sigma$ vibronic levels with $K$ = 0, such as $v_d$ = 1 and $l$ = 1, of a $^2\Pi$ electronic state, it is well known that $^2\Sigma^{(+)}$ and $^2\Sigma^{(-)}$ vibronic levels have relatively large $\Omega$- or $\rho$-type doubling due to non-zero $\Lambda$, in spite of the $\Sigma$ vibronic levels\footnote{J.~Hougen, J.~Chem.~Phys. 36, 519 (1964)}. It is thought that the unexpectedly large spin splitting, 0.27 cm$^{-1}$, is induced by spin-vibration interaction, which has been discussed for degenerate vibronic levels of non-degenerate electronic states, $^2\Sigma$ and $^3\Sigma$, of linear polyatomic molecules\footnote{A.~J.~Merer and J.~M.~Allegretti, Can.~J.~Phys. 49, 2859 (1971).}

DISPERSED FLUORESCENCE SPECTRA OF JET COOLED SiCN

The laser induced fluorescence (~LIF~) spectrum of $tilde{A}$ $^2Delta$ -- $tilde{X}$ $^2Pi$ transition was obtained for SiCN generated by laser ablation under supersonic free jet expansion. The vibrational structure of the dispersed fluorescence (~DF~) spectra from single vibronic levels (~SVL's~) was analyzed with consideration of Renner-Teller (~RT~) interaction. The usual analysis based on the perturbation approachfootnote{J.~M.~Brown and F.~Jo rgensen, Advances in Chemical Physics 52, 117 (1983).}, indicated considerably different spin splitting for the $mu$ and $kappa$ levels of the $tilde{X}$ $^2Pi$ state of SiCN, in contrast to identical spin splitting for general species based on the usual RT analysis. Further analysis of the vibrational structure is being carried out via direct RT diagonalization

NUMERICAL ANALYSIS OF VIBRONIC STRUCTURE OF THE SiCN X̃ 2Π SYSTEM

The laser induced fluorescence (~LIF~) spectrum of the $\tilde{A}$ $^2\Delta$ -- $\tilde{X}$ $^2\Pi$ transition was obtained for SiCN generated by laser ablation under supersonic free jet expansion. The vibrational structure, particularly that associated with the bending mode, of the dispersed fluorescence (~DF~) spectra from single vibronic levels (~SVL's~) is too complicated to analyze by the usual formulation derived from perturbational approach. Successful analysis requires us to numerically diagonalize the vibronic Hamiltonian, in which Renner-Teller (~R-T~), anharmonicity, spin-orbit (~SO~), Herzberg-Teller (~H-T~), Fermi, and Sears interactions have been considered, where the Sears resonance is a second-order interaction combined from SO and H-T interactions with $\Delta K = \pm1$, $\Delta \Sigma = \mp1$, and $\Delta P = 0$. Accurate results were obtained from this procedure reproducing experimental observations within the deviations of our instrumental resolution, $\sim$5 cm$^{-1}$. The mixing coefficients of the two vibronic levels are comparable to those obtained from computational studies\footnote{V.~Brites, A.~O.~Mitrushchenkov, and C.~L\'{e}onard, J.~Chem.~Phys. 138, 104311 (2013); C.~L\'{e}onard, Private communication.}

2C-R4WM spectroscopy of jet cooled NO3

We have generated NO$_3$ from pyrolysis of N$_2$O$_5$ following supersonic free jet expansion, and carried out two color resonant four wave mixing (~2C-R4WM~) spectroscopy of the $\tilde{B}$ $^2E'$ -- $\tilde{X}$ $^2A_2'$ electronic transition. One laser was fixed to pump NO$_3$ to a ro-vibronic level of the $\tilde{B}$ state, and the other laser (~probe~) was scanned across two levels of the $\tilde{X}$ $^2A_2'$ state lying at 1051 and 1492 cm$^{-1}$, the $\nu_1$ ($a_1'$) and $\nu_3$ ($e'$) fundamentals, respectively. The 2C-R4WM spectra have unexpected back-ground signal of NO$_3$ (~stray signal due to experimental set-up is also detected~) similar to laser induced fluorescence (~LIF~) excitation spectrum of the 0-0 band, although the back-ground signal was not expected in considering the 2C-R4WM scheme. Despite the back-ground interference, we have observed two peaks at 1051.61 and 1055.29 cm$^{-1}$ in the $\nu_1$ region of the spectrum, and the frequencies agree with the two bands, 1051.2 and 1055.3 cm$^{-1}$, of our relatively higher resolution dispersed fluorescence spectrum, the former of which has been assigned to the $\nu_1$ fundamental. Band width of both peaks, $\sim$ 0.2 cm$^{-1}$, is broader than twice the experimental spectral-resolution, 0.04 cm$^{-1}$ (~because this experiment is double resonance spectroscopy~), and the 1051.61 cm$^{-1}$ peak is attributed to a $Q$ branch band head (~a line-like $Q$ branch~) of the $\nu_1$ fundamental. The other branches are suspected to be hidden in noise of the back-ground signal. The 1055.29 cm$^{-1}$ peak is also attributed to a $Q$ band head. The $\tilde{B}$ $^2E'_{\frac{1}{2}}$ (~$J' = \frac{3}{2}$, $K' = 1$~) -- $\tilde{X}$ $^2A_2'$ (~$N'' = 1$, $K'' = 0$~) ro-vibronic transition was used as the pump transition. The dump (~probe~) transition to both $a_1'$ and $e'$ vibronic levels are then allowed as perpendicular transition. Accordingly, it cannot be determined from present results whether the 1055.29 cm$^{-1}$ band is attributed to $a_1'$ or $e'$ ($\nu_3$), unfortunately. The 2C-R4WM spectrum of the 1492 cm$^{-1}$ band region shows one $Q$ head at 1499.79 cm$^{-1}$, which is consistent with our dispersed fluorescence spectrum. By considering with the $\nu_3$ + $\nu_4$ - $\nu_4$ hot band\footnote{K.~Kawaguchi $et$ $al.$, $J.$ $Phys.$ $Chem.$ $A$ 117, 13732 (2013) and E.~Hirota, $J.$ $Mol.$ $Spectrosco.$ 310, 99 (2015).}, the present results suggest that both 1055.29 and 1499.79 cm$^{-1}$ levels are $a_1'$ level