Spin-rotation Interaction Research Articles

Investigation on the fine structure of the B 1∏ − c 3∑+ complex in KRb

The fine structure of the transitions in the (X, υ″ = 0 → (B, c), υ′ = 2) band system in K85Rb is studied by using selective Doppler-free spectroscopy techniques. Energy shifts of the perturbed levels due to spin-spin, spin-rotation and spin-orbit interactions were analyzed and modeled within the effective Hamiltonian approach. Molecular and coupling constants were determined, which successfully model the experimental observations.

Improved Theory of the Effective Dipole Moments and Absolute Line Strengths of the XY2 Asymmetric Top Molecules in the X2B1 Doublet Electronic States.

A new effective dipole moment model for the XY2 (C2v-symmetry) molecule in a doublet electronic state is derived that includes (as special cases) all currently known models of effective dipole moments for such types of molecules, and allows us to take into account the influence of spin-rotation interactions on the effective dipole moment operator that were not considered in the preceding studies. Necessary for the analysis of absolute line strengths, the matrix elements of this dipole moment operator are derived. A comparison with the previous analog models is made and discussed. The efficiency of the obtained results is illustrated, which have been applied to a set of the "forbidden" ΔKa=2 transitions of the ν3 band of the OClO free radical molecule.

Rate constants for saturation-recovery EPR and ELDOR of 14N-Spin labels

Saturation-recovery (SR)-EPR can determine electron spin–lattice relaxation rates in liquids over a wide range of effective viscosity, making it especially useful for biophysical and biomedical applications. Here, I develop exact solutions for the SR-EPR and SR-ELDOR rate constants of 14N-nitroxyl spin labels as a function of rotational correlation time and spectrometer operating frequency. Explicit mechanisms for electron spin–lattice relaxation are: rotational modulation of the N-hyperfine and electron-Zeeman anisotropies (specifically including cross terms), spin-rotation interaction, and residual frequency-independent vibrational contributions from Raman processes and local modes. Cross relaxation from mutual electron and nuclear spin flips, and direct nitrogen nuclear spin–lattice relaxation, also must be included. Both the latter are further contributions from rotational modulation of the electron-nuclear dipolar interaction (END). All the conventional liquid-state mechanisms are defined fully by the spin-Hamiltonian parameters; only the vibrational contributions contain fitting parameters. This analysis gives a firm basis for interpreting SR (and inversion recovery) results in terms of additional, less standard mechanisms.

Fourier-transform microwave spectroscopy of the s-trans-3-propenalyl (CH2CHĊO) and 3-propenolyl (ĊH2CHCO) radicals.

Pure rotational transitions of two conformers of the CH2CHCO radical have been observed by Fourier-transform microwave spectroscopy, where one conformer is called the s-trans-3-propenalyl radical and the other the 3-propenolyl radical. The observed two conformers have different electronic states. The former, the s-trans-3-propenalyl radical, has the 2A' electronic state and can be written as CH2CHĊO, where the unpaired electron resides mainly on the terminal CO carbon. On the other hand, the latter, 3-propenolyl radical has the 2A'' electronic state and can be written as ĊH2CHCO. We were able to observe pure rotational transitions of the two conformers. Since both of the species have an unpaired electron, there exist spin-rotation interactions due to the unpaired electron and the magnetic hyperfine interactions due to the three coupling protons. The observed very complicated spectra, caused by these interactions, were assigned, leading to detailed molecular constants including the fine and hyperfine coupling constants for both of the species. The determined molecular constants support the electronic structures of the two conformers. There exists a controversy as to which of the two conformers is the lowest energy one. Our present observation led to the conclusion that s-trans-3-propenalyl is the lowest energy conformer.

Frequency references based on molecular iodine for the study of Yb atoms using the 1S0 - 3P1 intercombination transition at 556 nm.

We used precision spectroscopy to analyze the R(53)24-1, P(49)24-1, and R(95)25-1 lines of molecular iodine (127I2) to establish optical frequency references for the laser cooling of Yb atoms using the 1S0 - 3P1 intercombination transition at 556 nm. A laser frequency instability of < 2 × 10-12 (for 0.01 s < τ < 3000 s, τ is the average time of the measurement) was attained using the observed Doppler-free hyperfine transitions of the iodine lines. The absolute frequencies of the observed 63 hyperfine transitions were determined with an uncertainty of 7 kHz (fractional uncertainty of 1.3 × 10-11). Highly accurate hyperfine constants were determined by fitting the measured hyperfine splittings to a four-term Hamiltonian that includes the electric quadrupole, spin-rotation, tensor spin-spin, and scalar spin-spin interactions with an uncertainty of approximately 1 kHz. The observed hyperfine transitions of molecular iodine provide new frequency references for research using atomic Yb, because these transitions are close to the intercombination transition of Yb at 556 nm.

Parity-violating contributions to nuclear spin-rotation interactions and to NMR shielding constants in tetrahedral molecules

In natural processes involving weak interactions, a violation of spatial parity conservation should appear. Although the parity-violation effects are expected to be observable in molecular systems, their tiny magnitude has prevented their detection to date. We present a theoretical analysis of four-component relativistic nuclear-spin-dependent parity-violating nuclear spin-rotation and NMR shielding tensors in a set of tetrahedral chiral molecules. This work emphasizes the significant contribution of the ligands and the electronic structure of the chiral center in enhancing these effects, paving the way for the targeted design of promising molecules for measurements.

A variational model for the hyperfine resolved spectrum of VO in its ground electronic state.

A variational model for the infra-red spectrum of vanadium monoxide (VO) is presented, which aims to accurately predict the hyperfine structure within the VO XΣ-4 electronic ground state. To give the correct electron spin splitting of the XΣ-4 state, electron spin dipolar interaction within the ground state and the spin-orbit coupling between XΣ-4 and two excited states, AΠ4 and 1Σ+2, are calculated ab initio alongside hyperfine interaction terms. Four hyperfine coupling terms are explicitly considered: Fermi-contact interaction, electron spin-nuclear spin dipolar interaction, nuclear spin-rotation interaction, and nuclear electric quadrupole interaction. These terms are included as part of a full variational solution of the nuclear-motion Schrödinger equation performed using program Duo, which is used to generate both hyperfine-resolved energy levels and spectra. To improve the accuracy of the model, ab initio curves are subject to small shifts. The energy levels generated by this model show good agreement with the recently derived empirical term values. This and other comparisons validate both our model and the recently developed hyperfine modules in Duo.

High resolution spectroscopy of the [formula omitted] band of the [formula omitted]ClO2 free radical: Spin–rotation–vibration interactions

The high resolution spectrum of the ν1+ν3 band of the 35ClO2 free radical was recorded with a Bruker IFS 125HR Fourier transform infrared spectrometer and theoretically analysed with an improved theoretical basis including the reduced effective spin–rotation Hamiltonian (which takes into account sixth order operators describing spin–rotational interactions) and a newly created computer code ROVDES for the ro–vibrational spectra of open–shell free radicals. About 2600 spin–ro–vibrational transitions with the values Nmax=59 and Kamax=17 (being about 2.4 times higher in comparison with the number of assigned transitions known in the literature) were assigned to the ν1+ν3 band of 35ClO2 and 1049 spin–ro–vibrational energies (produced only from unblended non–saturated and not very weak experimental lines) of the (101) upper vibrational state were obtained. A set of 30 varied parameters of the effective spin–rotation–vibration Hamiltonian of the (101) vibrational state (vibrational energy, 17 rotational and centrifugal distortion parameters and 12 are spin–rotational ones) was determined from the weighted fit of parameters of the effective spin–rotational Hamiltonian in A-reduction and Ir-representation. The obtained set of parameters reproduces the initial 1049 “experimental” upper state energies with the drms=2.5×10-4 cm−1 which is close to the experimental uncertainty of the recorded spectra and is almost 70 times higher in comparison with the analogous reproduction of the same initial upper energies with the use of parameters from (J.Mol.Spectrosc.,158,347-356(1993)).

Prediction of 1H Singlet Relaxation via Intermolecular Dipolar Couplings Using the Molecular Dynamics Method.

Dissolution dynamic nuclear polarization has been applied in various fields, including chemistry, biology, and medical science. To expand the scope of these applications, the nuclear singlet state, which is decoherence-free against dipolar relaxation between spin pairs, has been studied experimentally, theoretically, and numerically. The singlet state composed of proton spins is used in several applications, such as enhanced polarization preservation, molecular tagging to probe slow dynamic processes, and detection of ligand-protein complexes. In this study, we predict the lifetimes of the nuclear spin states composed of proton spin pairs using the molecular dynamics method and quantum chemistry simulations. We consider intramolecular dipolar, intermolecular dipolar between solvent and solute, chemical shift anisotropy, and spin-rotation interactions. In particular, the relaxation rate of intermolecular dipolar interactions is calculated using the molecular dynamics method for various solvents. The calculated values and the experimental values are of the same order of magnitude. Our program would provide insight into the molecular design of several NMR applications and would be helpful in predicting the nuclear spin relaxation time of synthetic molecules in advance.

A Method for the Variational Calculation of Hyperfine-Resolved Rovibronic Spectra of Diatomic Molecules.

An algorithm for the calculation of hyperfine structure and spectra of diatomic molecules based on the variational nuclear motion is presented. The hyperfine coupling terms considered are Fermi-contact, nuclear spin-electron spin dipole–dipole, nuclear spin–orbit, nuclear spin-rotation, and nuclear electric quadrupole interactions. Initial hyperfine-unresolved wave functions are obtained for a given set of potential energy curves and associated couplings by a variation solution of the nuclear-motion Schrödinger equation. Fully hyperfine-resolved parity-conserved rovibronic Hamiltonian matrices for a given final angular momentum, F, are constructed and then diagonalized to give hyperfine-resolved energies and wave functions. Electric transition dipole moment curves can then be used to generate a hyperfine-resolved line list by applying rigorous selection rules. The algorithm is implemented in Duo, which is a general program for calculating spectra of diatomic molecules. This approach is tested for NO and MgH, and the results are compared to experiment and shown to be consistent with those given by the well-used effective Hamiltonian code PGOPHER.

Спектроскопия высокого разрешения молекул типа асимметричного волчка в несинглетных электронных состояниях: полоса &amp;nu;_1+&amp;nu;-=SUB=-3-=/SUB=- молекулы ClO-=SUB=-2-=/SUB=-

Using a Bruker IFS 125 HR Fourier spectrometer, the high-resolution spectrum of $^{16}$O$^{35}$\text{Cl}$^{16}$O molecule was recorded in the region of the $\nu_1+\nu_3$ band, in in which more than 2000 transitions with maximum values \textit{N}$^{max}$=59 and \textit{K}$^{max}_a$ = 16 were interpreted. The analysis of the obtained experimental information was performed on the basis of the model from ( Phys. Chem. Chem. Phys. 2021. V. 23. N. 8. P. 4580--4596) which takes into account the presence of spin-rotation interactions in the molecule. The standard deviation was $d_{rms}$ = 2.5 $\cdot 10^{-4} \text{cm}^{-1}$ and is 35 times higher than the result known in the literature.

Conversion of ortho and para nuclear spin isomers of methanol studied by internal axis method

Quantum statistics of identical nuclei in molecules gives rise to nuclear spin isomers. Except for methanol (CH3OH) that has internal rotation (i.e., torsion), all the studied molecules so far have overall rotational symmetry. Methanol does not rotate around the overall rotational symmetry axis but the methyl group axis. The identical nuclei in the methyl group produce a specific type of nuclear spin isomers of the ortho-CH3OH and para-CH3OH in methanol. Conversions between these two spin isomers have been observed in the experiment and a theory based on the rho-axis method (RAM) for partially explaining their conversions has been developed by us recently. However, besides RAM the internal axis method (IAM) is a classical method commonly used by many researchers and the coupling of the angular momenta between torsion and overall rotation in methanol can be completely separated from each other in the IAM. In this paper, as a series work we present a general theoretical model about conversion of ortho–para methanol using the IAM based on quantum relaxation theory. The expressions of the ortho–para state-mixing strengths induced by the nuclear spin–spin and nuclear spin–rotation interactions have been analytically deduced and numerically calculated. We found that the ortho–para states-mixings and ortho–para conversion can be induced by all these two intramolecular interactions whereas the nuclear spin–rotation interaction plays a major role. The conversion rate at temperature 300 K and pressure 1 Torr summed over eight ortho–para level pairs with gaps less than 2.7 GHz is calculated to be 1.4 × 10−2 s−1, which is close to the measured value of 2.1 (3) × 10−2 s−1, indicating the quantum relaxation is the leading process in the spin isomers conversions of methanol and suggesting our theory to be valid for other gaseous methanol-like molecules having torsion tunneling of symmetrical group. The most probable gateways in methanol for collision-induced population transfers are found to be levels-pairs in the ground-state A–E species of (υtJ, K, p) = (0, 24, 4, 1)−(0, 25, 2, 1) by nuclear spin–spin coupling, (0, 22, 5, p)−(0, 21, 6, −1) and (3, 34, 1, 0)−(3, 35, 0, 1) by nuclear spin–rotation coupling.

Fourier-transform spectroscopy and relativistic electronic structure calculation on the [formula omitted] state of KCs

The Ti:Saphire laser operated within 13800 - 11800 cm−1 range was used to excite the c3Σ+ state of KCs molecule directly from the ground X1Σ+ state. The laser-induced fluorescence (LIF) spectra of the c3Σ+→a3Σ+ transition were recorded with Fourier-transform spectrometer within 8000 to 10000 cm−1 range. Overall 673 rovibronic term values belonging to both e/f-components of the c3Σ+(Ω=1±) state of 39KCs, covering vibrational levels from v = 0 to about 45, and rotational levels J∈[11,149] were determined with the accuracy of about 0.01 cm−1; among them 7 values for 41KCs. The experimental term values with v∈[0,22] were involved in a direct point-wise potential reconstruction for the c3Σ+(Ω=1±) state, which takes into account the Ω-doubling effect caused by the spin-rotational interaction with the nearby c3Σ+(Ω=0−) state. The analysis and interpretation were facilitated by the fully-relativistic coupled cluster calculation of the potential energy curves for the B1Π, c3Σ+, and b3Π states, as well as of spin-forbidden c−X and spin-allowed c−a transition dipole moments; radiative lifetimes and vibronic branching ratios were calculated. A comparison of relative intensity distributions measured in vibrational c→a LIF progressions with their theoretical counterparts unambiguously confirms the vibrational assignment suggested in [J. Szczepkowski, et al., JQSRT, 204, 133–137 (2018)].

Hyperfine structure of molecular iodine measured using a light source with a laser linewidth at the megahertz level

The hyperfine structure of the absorption lines of molecular iodine at 531 nm was measured using a low-cost, coin-sized light source with a laser linewidth at the megahertz level. The measured hyperfine splittings were found to be systematically smaller than those measured using a narrow-linewidth diode laser. The theoretical fit of the measured hyperfine splittings to a four-term Hamiltonian, including the electric quadrupole, spin-rotation, tensor spin-spin, and scalar spin-spin interactions, does not clarify the observed systematic deviation in the measurement, but instead results in deviated hyperfine constants from reliable literature values beyond the uncertainties. Therefore, the theoretical fit, which is usually used to validate the measurement, does not provide the validation function in the case of megahertz level laser linewidths.

Анализ спектра высокого разрешения молекул в дублетных электронных состояниях: фундаментальная полоса &amp;nu;-=SUB=-3-=/SUB=- диоксида хлора (-=SUP=-16-=/SUP=-O-=SUP=-35-=/SUP=-Cl-=SUP=-16-=/SUP=-O) в основном электронном состоянии X-=SUP=-2-=/SUP=-B-=SUB=-1-=/SUB=-

Vibration-rotation structure of the ν3 band of ClO2 was recorded with a Bruker IFS 125 HR Fourier spectrometer with a resolution of 0.0015 cm–1. Ro-vibrational analysis of the recorded experimental spectrum was made with an improved effective Hamiltonian and developed computer code for ro–vibrational spectra of open–shell free radical molecules including spin–rotation interactions. About 4200 transitions with the maximum values Nmax = 68 and Kamax = 21 belonging to the ν3 band were assigned and subsequently used to determine a set of 13 spectroscopic parameters of the vibrational state under study. The root-mean-square deviation of the results is drms = 2.4 ∙ 10-4 cm-1.

Nuclear spin conversion in gaseous methanol

Molecules with identical nuclei exist in nature in the form of nuclear spin isomers. Most known are the spin isomers in molecules having overall rotational symmetry. There are molecules that do not have overall rotational symmetry but instead contain symmetrical groups of atoms that perform torsion tunneling (i.e., internal rotation) around their local symmetry axes. Quantum statistics gives rise in such molecules to a specific type of spin isomers based on the torsion tunneling of symmetrical groups of atoms. Recently, enrichment and conversion of nuclear spin isomers in methanol (${\mathrm{CH}}_{3}\mathrm{OH}$) that has torsion tunneling of the methyl group was experimentally investigated by Z.-D. Sun et al. [Nat. Commun. 6, 6877 (2015)]. In the present paper a theoretical model for the methanol spin isomers and their conversion is developed. The model is based on the quantum relaxation theory confirmed to be valid for molecules with overall rotational symmetry. The methanol spin isomer conversion induced by hyperfine spin-spin and spin-rotation interactions is considered. The most important level pair for the methanol isomer conversion is found to be the $({J}^{\ensuremath{'}}=25,{K}^{\ensuremath{'}}=2,{\ensuremath{\sigma}}^{\ensuremath{'}}=1)--(J=24,K=4,p=1)$ pair in the ground torsion state ${v}_{t}=0$. The spin-rotation interaction in methanol is estimated to be equal to 1.6 kHz.

High-resolution laser spectroscopy of the linear SiC2Si molecule and its astrophysical implications

Small silicon-carbon clusters are important gas-phase constituents of stellar atmospheres, and are thought to play a role as potential seeds of the interstellar dusts formed in the envelopes of evolved carbon stars. Here we present the high-resolution optical spectra of the linear SiC2Si molecule (l-Si2C2) studied via laboratory experiments. The l-Si2C2 molecules are generated in a supersonically expanding planar plasma by discharging a silane-acetylene-argon gas mixture. The optical absorption spectra in the 5000−5300 Å region are recorded using sensitive pulsed cavity ring-down spectroscopy. In total, five optical absorption bands belonging to the $ \tilde{C} ^{3}\Sigma_{u} ^{-} $ – $ \tilde{X} ^{3}\Sigma_{g} ^{-} $ electronic transition system of l-Si2C2 are measured with fully resolved spin splitting fine structures in individual rotational transitions. Accurate spectroscopic constants for both $ \tilde{X} ^{3}\Sigma_{g} ^{-} $ and $ \tilde{C} ^{3}\Sigma_{u} ^{-} $ states of l-Si2C2, including the spin-spin interaction constants and spin-rotation interaction constants, are determined from the experimental spectra, which can be used to simulate these optical bands with different temperatures. Using the determined spectroscopic constants, optical spectra of l-Si2C2 simulated with different rotational excitation temperatures are compared to the stellar spectra of evolved carbon stars V Hya and IRAS 12311−23509, where the triatomic SiC2 are known to be abundant. Tentative assignments of the l-Si2C2 spectral features in the stellar spectra are discussed.

Water ortho–para conversion by microwave background radiation in space

ABSTRACT A theoretical model of water ortho–para conversion induced by blackbody radiation in space is developed. The model is based on two main ingredients: the mixing of water ortho and para states by a hyperfine spin-rotation interaction in the molecule and the interruption of this mixing by surrounding blackbody radiation. The model predicts the lifetime of water spin isomers τ = 2.7 Myr for radiation with a temperature of 100 K and τ = 1.3 Gyr for microwave background radiation. The time dependence of the ortho-to-para ratio (OPR) of water molecules interacting with microwave background radiation is determined. The temperature dependence of the stationary OPR predicted by the model is found to be different from the usually accepted OPR for water spin isomers.

Fourier-transform spectroscopy, relativistic electronic structure calculation, and coupled-channel deperturbation analysis of the fully mixed A1Σu+ and b3Πu states of Cs2

The 4503 rovibronic term values belonging to the mutually perturbed $A^1\Sigma^+_u$ and $b^3\Pi_u$ states of Cs$_2$ were extracted from laser induced fluorescence (LIF) $A\sim b\rightarrow X^1\Sigma^+_g$ Fourier transform spectra with the 0.01 cm$^{-1}$ uncertainty. The experimental term values of the $A^1\Sigma^+_u\sim b^3\Pi_u$ complex covering the rotational levels $J\in [4,395]$ in the excitation energy range $[9655,13630]$ cm$^{-1}$ were involved into coupled-channel (CC) deperturbation analysis. The deperturbation model takes explicitly into account spin-orbit coupling of the $A^1\Sigma^+_u(A0^+_u)$ and $b^3\Pi^+_{0_u}(b0^+_u)$ states as well as spin-rotational interaction between the $\Omega=0$, $1$ and $2$ components of the $b^3\Pi^+_{\Omega_u}$ state. The \emph{ab initio} relativistic calculations on the low-lying electronic states of Cs$_2$ were accomplished in the framework of Fock space relativistic coupled cluster (FSRCC) approach to provide the interatomic potentials of the interacting $A0^+_u$ and $b0^+_u$ states as well as the relevant $A\sim b$ spin-orbit coupling function. To validate the present CC deperturbation analysis solely obtained by energy-based data, the $A\sim b \to X(v^{\prime\prime}_X)$ LIF intensity distributions were measured and compared with their theoretical counterparts obtained by means of the non-adiabatic vibrational wave functions of the $A\sim b$ complex and the FSRCC $A\sim b \to X$ transition dipole moments calculated by the finite-field method.

Pressure effect on hyperfine CPT resonance of ground-state Li atoms in glass hot-vapor cell

We report the hyperfine splitting frequency of ground-state lithium atoms. The frequency shift is induced by the collisions to helium and xenon buffer gases. Coherent population-trapping resonance between the hyperfine levels enables the frequency measurements in the range of pressure from 2 to $$54\,\hbox {kPa}$$ and temperature from 260 to $$400\,^{\circ }\hbox {C}$$ in borosilicate-glass cells. The buffer-gas density is self-consistently calibrated from the hyperfine splitting in the sealed cells. The resonance frequency and the line width provide an insight into collision-induced spin dynamics, where hyperfine-shift, spin-rotation, and spin-exchange interactions play an important role in atomic lithium vapor and buffer gas.