Born Oppenheimer Breakdown Correction Research Articles

ExoMol line lists – XLVII. Rovibronic spectrum of aluminium monochloride (AlCl)

ABSTRACT A line list for two isotopologues of aluminium monochloride, Al35Cl and Al37Cl, is presented covering the wavelength range <0.2 µm, J up to 400, and applicable for temperatures up to 5000 K. The line lists are built using an empirical spectroscopic model consisting of potential energy curves, spin–orbit coupling curves, electronic angular momentum curves, and Born–Oppenheimer breakdown correction curves combined with ab initio dipole moments and cover the four lowest electronic states, ${X}\, ^1\Sigma ^+$, ${A}\, ^1\Pi$, ${a}\, ^3\Pi$, and ${b}\, ^3\Sigma ^+$. Considerable problems with the assignments of some laboratory rovibronic spectra are identified. Treatment of the states lying in the continuum is discussed. The YNAT line list is available from the ExoMol data base at www.exomol.com.

First fullyab initiopotential energy surface of methane with a spectroscopic accuracy

Full 9-dimensional ab initio potential energy surfaces for the methane molecule are constructed using extended electronic structure coupled-cluster calculations with various series of basis sets following increasing X cardinal numbers: cc-pVXZ (X = 3, 4, 5, 6), aug-cc-ACVXZ (X = 3, 4, 5), and cc-pCVXZ-F12 (X = 3, 4). High-order dynamic electron correlations including triple and quadrupole excitations as well as relativistic and diagonal Born-Oppenheimer breakdown corrections were accounted for. Analytical potential functions are parametrized as non-polynomial expansions in internal coordinates in irreducible tensor representation. Vibrational energy levels are reported using global variational nuclear motion calculations with exact kinetic energy operator and a full account of the tetrahedral symmetry of CH4. Our best ab initio surface including above-mentioned contributions provides the rms (obs.-calc.) errors of less than 0.11 cm−1 for vibrational band centers below 4700 cm−1, and ∼0.3 cm−1 for all 229 assigned experimentally determined vibrational levels up to the Icosad range <7900 cm−1 without empirically adjusted parameters. These results improve the accuracy of ab initio methane vibrational predictions by more than an order of magnitude with respect to previous works. This is an unprecedented accuracy of first-principles calculations of a five-atomic molecule for such a large data set. New ab initio potential results in significantly better band center predictions even in comparison with best available empirically corrected potential energy surfaces. The issues related to the basis set extrapolation and an additivity of various corrections at this level of accuracy are discussed.

Dissociation energies and potential energy functions for the ground X (1)Σ(+) and "avoided-crossing" A (1)Σ(+) states of NaH.

A direct-potential-fit analysis of all accessible data for the A (1)Σ(+) - X (1)Σ(+) system of NaH and NaD is used to determine analytic potential energy functions incorporating the correct theoretically predicted long-range behaviour. These potentials represent all of the data (on average) within the experimental uncertainties and yield an improved estimate for the ground-state NaH well depth of 𝔇e = 15797.4 (±4.3) cm(-1), which is ∼20 cm(-1) smaller than the best previous estimate. The present analysis also yields the first empirical determination of centrifugal (non-adiabatic) and potential-energy (adiabatic) Born-Oppenheimer breakdown correction functions for this system, with the latter showing that the A-state electronic isotope shift is -1.1(±0.6) cm(-1) going from NaH to NaD.

Non-adiabatic effects in thermochemistry, spectroscopy and kinetics: the general importance of all three Born-Oppenheimer breakdown corrections.

Using a simple model Hamiltonian, the three correction terms for Born-Oppenheimer (BO) breakdown, the adiabatic diagonal correction (DC), the first-derivative momentum non-adiabatic correction (FD), and the second-derivative kinetic-energy non-adiabatic correction (SD), are shown to all contribute to thermodynamic and spectroscopic properties as well as to thermal non-diabatic chemical reaction rates. While DC often accounts for >80% of thermodynamic and spectroscopic property changes, the commonly used practice of including only the FD correction in kinetics calculations is rarely found to be adequate. For electron-transfer reactions not in the inverted region, the common physical picture that diabatic processes occur because of surface hopping at the transition state is proven inadequate as the DC acts first to block access, increasing the transition state energy by (ℏω)(2)λ/16J(2) (where λ is the reorganization energy, J the electronic coupling and ω the vibration frequency). However, the rate constant in the weakly-coupled Golden-Rule limit is identified as being only inversely proportional to this change rather than exponentially damped, owing to the effects of tunneling and surface hopping. Such weakly-coupled long-range electron-transfer processes should therefore not be described as "non-adiabatic" processes as they are easily described by Born-Huang ground-state adiabatic surfaces made by adding the DC to the BO surfaces; instead, they should be called just "non-Born-Oppenheimer" processes. The model system studied consists of two diabatic harmonic potential-energy surfaces coupled linearly through a single vibration, the "two-site Holstein model". Analytical expressions are derived for the BO breakdown terms, and the model is solved over a large parameter space focusing on both the lowest-energy spectroscopic transitions and the quantum dynamics of coherent-state wavepackets. BO breakdown is investigated pertinent to: ammonia inversion, aromaticity in benzene, the Creutz-Taube ion, the bacterial photosynthetic reaction centre, BNB, the molecular conductor Alq3, and inverted-region charge recombination in a ferrocene-porphyrin-fullerene triad photosynthetic model compound. Throughout, the fundamental nature of BO breakdown is linked to the properties of the cusp catastrophe: the cusp diameter is shown to determine the magnitudes of all couplings, numerical basis-set and trajectory-integration requirements, and to determine the transmission coefficient κ used to understand deviations from transition-state theory.

Terahertz spectroscopy of N18O and isotopic invariant fit of several nitric oxide isotopologs

A tunable far-infrared laser sideband spectrometer was used to investigate a nitric oxide sample enriched in 18O between 0.99 and 4.75THz. Regular, electric dipole transitions were recorded between 0.99 and 2.52THz, while magnetic dipole transitions between the 2Π1/2 and 2Π3/2 spin-ladders were recorded between 3.71 and 4.75THz. These data were combined with lower frequency data of N18O (unlabeled atoms refer to 14N and 16O, respectively), with rotational data of NO, 15NO, N17O, and 15N18O, and with heterodyne infrared data of NO to be subjected to one isotopic invariant fit. Rotational, fine and hyperfine structure parameters were determined along with vibrational, rotational, and Born–Oppenheimer breakdown corrections. The resulting spectroscopic parameters permit prediction of rotational spectra suitable for the identification of various nitric oxide isotopologs especially in the interstellar medium by means of rotational spectroscopy.

Beryllium monohydride (BeH): Where we are now, after 86 years of spectroscopy

BeH is one of the most important benchmark systems for ab initio methods and for studying Born–Oppenheimer breakdown. However the best empirical potential and best ab initio potential for the ground electronic state to date give drastically different predictions in the long-range region between where the highest measurements have been made, and the dissociation energy; a region which is about ∼1000cm−1 for 9BeH, ∼3000cm−1 for 9BeD, and ∼13000cm−1 for 9BeT. Improved empirical potentials and Born–Oppenheimer breakdown corrections have now been built in this work for the ground electronic states X(12Σ+) of all three isotopologues. The predicted dissociation energy for 9BeH from the new empirical potential is now in agreement with the current best ab initio prediction in all 5 digits of the former’s precision, while the previous best empirical potential was in disagreement by 74cm−1. The previous best empirical potential predicted the existence of unobserved vibrational levels for all three isotopologues, and the current best ab initio study also predicted the existence of all of these levels, and 7 more in total. With the exception of two, the present empirical potential agrees with the existence of all of the ab initio potentials’ extra levels not predicted by the earlier empirical potential. With one exception, all energy spacings between vibrational energy levels for which measurements have been made, are predicted with an agreement of better than 1cm−1 between the new empirical potential and the current best ab initio potential, but some predictions for unobserved levels are still in great disagreement, and the equilibrium bond lengths are different by orders of magnitude.

Accurate High-N Rest Frequencies for CO+, an Ideal Tracer of Photon-Dominated Regions

The submillimeter-wave rotational spectra of CO(+), (13)CO(+) and C(18)O(+) in the v = 0 and 1 vibrational states were measured through a hollow cathode dc discharge in a cryogenic cell cooled to liquid nitrogen temperature. In addition, a few transitions of the main isotopic species have been measured between 1.1 and 1.3 THz. An updated isotopically invariant fit, including Born-Oppenheimer breakdown corrections, is presented: the derived set of independent molecular parameters, valid for all the isotopologues of the molecule included in the fit, allows to predict the rotational spectrum with calculated 1σ uncertainty of 280 kHz at 2 THz.

Quantum-chemical determination of Born–Oppenheimer breakdown parameters for rotational constants: the open-shell species CN, CO+ and BO

The quantum-chemical protocol for computing Born–Oppenheimer breakdown corrections to rotational constants in the case of diatomic molecules is extended to open-shell species. The deviation from the Born–Oppenheimer equilibrium rotational constant is obtained by considering three contributions: the adiabatic correction to the equilibrium bond distance, the electronic contribution to the moment of inertia requiring the computation of the rotational g-tensor, and the so-called Dunham correction. Values for the Born–Oppenheimer breakdown parameters of CN, CO+, and BO in their 2Σ+ electronic ground states are reported based on coupled-cluster calculations of the involved quantities and compared to available experimental data.

Accurate ab initio determination of the adiabatic potential energy function and the Born–Oppenheimer breakdown corrections for the electronic ground state of LiH isotopologues

High level ab initio potential energy functions have been constructed for LiH in order to predict vibrational levels up to dissociation. After careful tests of the parameters of the calculation, the final adiabatic potential energy function has been composed from: (a) an ab initio nonrelativistic potential obtained at the multireference configuration interaction with singles and doubles level including a size-extensivity correction and quintuple-sextuple ζ extrapolations of the basis, (b) a mass-velocity-Darwin relativistic correction, and (c) a diagonal Born-Oppenheimer (BO) correction. Finally, nonadiabatic effects have also been considered by including a nonadiabatic correction to the kinetic energy operator of the nuclei. This correction is calculated from nonadiabatic matrix elements between the ground and excited electronic states. The calculated vibrational levels have been compared with those obtained from the experimental data [J. A. Coxon and C. S. Dickinson, J. Chem. Phys. 134, 9378 (2004)]. It was found that the calculated BO potential results in vibrational levels which have root mean square (rms) deviations of about 6-7 cm(-1) for LiH and ∼3 cm(-1) for LiD. With all the above mentioned corrections accounted for, the rms deviation falls down to ∼1 cm(-1). These results represent a drastic improvement over previous theoretical predictions of vibrational levels for all isotopologues of LiH.

Studies on rotational spectra of the ground states of ZnO, ZnS, SiSe and SiTe isotopic molecules using an isotopic error compensation approach

Accurate rotational spectra of 28 isotopologues of the ground electronic states of ZnO, ZnS, SiSe and SiTe are studied using an effective isotopic error compensation (IEC) approach. More than 200 new rotational transition frequencies are predicted for 20 of the above isotopologues using high-precision experimental data of the relevant isotopologues. The results show that the IEC approach can produce far more accurate rotational transition frequencies than the semi-classical isotope relation if the Born–Oppenheimer breakdown correction coefficients are ignored.

The pure rotational spectrum of TeSe: Rotational parameters, Born–Oppenheimer breakdown corrections, and hyperfine constants

The characterization of tellurium selenide in its electronic ground state (X0 + ∑ − ) was possible by using LASER-ablation to isolate the diatomic in a pulsed molecular beam and by applying Fourier transform microwave spectroscopy to obtain the pure rotational spectrum. Employing a global multi-isotopologue analysis to transitions of 43 isotopologues of TeSe in seven vibrational states spectroscopic Dunham parameters Y ℓ , m , Born–Oppenheimer breakdown coefficients δ ℓ , m , the equilibrium bond lengths r e, as well as the vibration parameters ω e and ω e x e were obtained for all analysed isotopologues. For low vibrational states, the Morse-potential function describes the TeSe-potential very well and provides an estimate of the maximum dissociation energy for this semi-metal compound. In addition, the isotopologue independent molecular constants U ℓ , m and the corresponding Born–Oppenheimer breakdown coefficients Δ ℓ , m were determined. Quite large coefficients Δ 0 , 1 Te and Δ 0 , 1 Se were necessary for Watson's reference isotopologue independent analysis. This is rationalized by the interaction between the two sublevels of the electronic 3Σ-state. Also the magnetic spin–rotation coupling constants that were achieved for some of the isotopologues reflect this electronic ground state. Field shift effects are found to be negligible.

Multi-isotopologue analyses of new vibration–rotation and pure rotation spectra of ZnH and CdH

High resolution infrared emission spectra of ZnH, ZnD, CdH, and CdD have been recorded with a Fourier transform spectrometer. The v = 1 → 0 and v = 2 → 1 bands of ZnH, ZnD, CdH, and CdD, as well as the v = 3 → 2 band of ZnD were observed for the X 2Σ + ground electronic state. In addition, new rotational spectra have been recorded for CdH and CdD using a tunable far-infrared spectrometer, and pure rotational transitions in the v = 1 level of the ground state were measured. The new data were combined with the previous data from diode laser infrared spectra and pure rotation spectra of ZnH/ZnD and CdH/CdD available in the literature. The data from all isotopologues were fitted together using a Dunham-type energy level expression for 2Σ + states, and Born–Oppenheimer breakdown correction parameters were obtained. The equilibrium rotational constants ( B e) of 64ZnH, 64ZnD, 114CdH, and 114CdD were determined to be 6.691332(17), 3.402156(7), 5.447074(18), and 2.750761(6) cm −1, respectively, and the associated equilibrium internuclear distances ( r e) are 1.593478(2), 1.593001(2), 1.760098(3), and 1.759695(2) Å, respectively. Simple reduced mass scaling for the spin–rotation interaction constants of ZnH and CdH fully accounted for their isotopologue dependence, and no Born–Oppenheimer breakdown correction was required for these parameters.

Infrared and near infrared emission spectra of SbH and SbD

The X 3Σ − ground state vibration–rotation spectrum of SbH and the near infrared spectra of the b 1Σ +– X 3Σ − transitions of SbH and SbD have been measured at high resolution by Fourier transform spectroscopy. The SbH and SbD radicals were generated in a tube furnace with a D.C. discharge of a flowing mixture of argon, hydrogen (or deuterium), and antimony vapor. In the infrared region, the 1–0 and 2–1 bands of the three components (0 +, 1 e , and 1 f ) as well as the 0 + component of the 3–2 band were observed for 121SbH and 123SbH. In the near infrared region, the 0–0, 1–1, and 2–2 bands of the b 1Σ +– X 3Σ − system of both SbH and SbD as well as the 3–3 band of SbD were observed. Except for a few lines, the antimony isotopic shift was not resolved for these electronic spectra. The present data set was combined with the available ground state data on SbD and a 1Δ data for SbH and SbD from previous work, and a least-squares fit was performed for each of the four isotopologues: 121SbH, 123SbH, 121SbD, and 123SbD. Improved spectroscopic constants were obtained for the observed vibrational levels of the X 3Σ −, a 1Δ, and b 1Σ + states of these four isotopologues. In addition, all the above data were also fitted simultaneously to a multi-isotopologue Dunham model, which yielded Dunham constants and Born–Oppenheimer breakdown parameters for these three electronic states. Interestingly, we found that Born–Oppenheimer breakdown corrections were also required for some of the spin–spin and spin–rotation parameters of the X 3Σ − state.

New Fourier transform infrared emission spectra of CaH and SrH: combined isotopomer analyses with CaD and SrD

In a search for the infrared spectra of gaseous CaH2 and SrH2, we obtained new Fourier transform infrared emission spectra of CaH and SrH, but no evidence of the metal dihydrides. The vibration-rotation bands from v=1→0 to v=4→3 of 40CaH and 88SrH, and the v=1→0 band of 87SrH and 86SrH were observed in the X2Σ+ ground electronic states. The new data were combined with the previous ground state data, obtained from diode laser infrared and pure rotational spectra, and the spectroscopic constants for v=0 to 4 of 40CaH and 88SrH were determined. In addition, the Dunham constants and the Born–Oppenheimer breakdown correction parameters were obtained using the previous ground state data for CaD and SrD in combined isotopomer fits. The equilibrium vibrational constants (ωe) for CaH and SrH were found to be 1298.400(1) and 1207.035(1) cm−1, respectively, while the equilibrium rotational constants (Be) are 4.277043(4) and 3.673495(4) cm−1. The equilibrium bond distances (re) were determined to be 2.0023603(9) Å for CaH and 2.1460574(10) Å for SrH.

Fourier transform infrared emission spectra of MgH and MgD.

High resolution Fourier transform infrared emission spectra of MgH and MgD have been recorded. The molecules were generated in an emission source that combines an electrical discharge with a high temperature furnace. Several vibration-rotation bands were observed for all six isotopomers in the X (2)Sigma(+) ground electronic state: v=1-->0 to 4-->3 for (24)MgH, v=1-->0 to 3-->2 for (25)MgH and (26)MgH, v=1-->0 to 5-->4 for (24)MgD, v=1-->0 to 4-->3 for (25)MgD and (26)MgD. The new data were combined with the previous ground state data, obtained from diode laser vibration-rotation measurements and pure rotation spectra, and spectroscopic constants were determined for the v=0 to 4 levels of (24)MgH and the v=0 to 5 levels of (24)MgD. In addition, Dunham constants and Born-Oppenheimer breakdown correction parameters were obtained in a combined fit of the six isotopomers. The equilibrium vibrational constants (omega(e)) for (24)MgH and (24)MgD were found to be 1492.776(7) cm(-1) and 1077.298(5) cm(-1), respectively, while the equilibrium rotational constants (B(e)) are 5.825 523(8) cm(-1) and 3.034 344(4) cm(-1). The associated equilibrium bond distances (r(e)) were determined to be 1.729 721(1) A for (24)MgH and 1.729 157(1) A for (24)MgD.

New Fourier transform infrared emission spectra of CaH and SrH: combined isotopomer analyses with CaD and SrD

In a search for the infrared spectra of gaseous CaH 2 and SrH 2, we obtained new Fourier transform infrared emission spectra of CaH and SrH, but no evidence of the metal dihydrides. The vibration-rotation bands from v=1→0 to v=4→3 of 40CaH and 88SrH, and the v=1→0 band of 87SrH and 86SrH were observed in the X 2 Σ + ground electronic states. The new data were combined with the previous ground state data, obtained from diode laser infrared and pure rotational spectra, and the spectroscopic constants for v=0 to 4 of 40CaH and 88SrH were determined. In addition, the Dunham constants and the Born–Oppenheimer breakdown correction parameters were obtained using the previous ground state data for CaD and SrD in combined isotopomer fits. The equilibrium vibrational constants ( ω e) for CaH and SrH were found to be 1298.400(1) and 1207.035(1) cm −1, respectively, while the equilibrium rotational constants ( B e) are 4.277043(4) and 3.673495(4) cm −1. The equilibrium bond distances ( r e) were determined to be 2.0023603(9) Å for CaH and 2.1460574(10) Å for SrH.

The rotational spectrum, nuclear field shift effects, 195Pt nuclear spin–rotation constant, and electric dipole moment of PtSi

The pure rotational spectrum of the X 1 Σ + ground electronic state of platinum monosilicide has been measured for nine isotopomers. For the most abundant isotopomer, 194Pt 28Si, the J=1–0 and the J=2–1 transitions were recorded up to the fourth vibrationally excited state. The data set obtained enabled a multi-isotopomer fit to a Dunham-type expression and the constants Y 01, Y 02, Y 11, Y 21, and Y 31 were determined. In the process of fitting the data it was necessary to include Born–Oppenheimer breakdown correction terms and the values and significance of these terms are discussed. Strong evidence is presented indicating within the rotational spectrum the presence of field shift effects due to the finite size of the Pt nucleus. The nuclear spin–rotation constant, C I ( 195Pt) is found to be 30.98(157) kHz in the ground vibrational state. Hyperfine structure arising from the 29Si nucleus was not observed. The measurement of Stark shifts in the rotational spectrum of PtSi has enabled the determination of the dipole moments for the 194Pt 28Si and 196Pt 28Si isotopomers.

Threshold ion-pair production spectroscopy of HCl/DCl: Born–Oppenheimer breakdown in HCl and HCl+ and dynamics of photoion-pair formation

Threshold ion-pair production spectroscopy (TIPPS) has been applied to two isotopomers, HCl and DCl. From the high-resolution TIPP spectra the ion-pair thresholds of the two molecules have been precisely measured. Combined with the known ionization energy of H(D) and the electron affinity of Cl, the difference between their bond dissociation energies is calculated, and therefore an experimental determination of the effect of Born–Oppenheimer breakdown on the dissociation limit of the ground state potential curve has been obtained. The difference in De for the two isotopomers was found to be: De(H–Cl)−De(D–Cl)=3.2±1.0 cm−1. The bond energy for HCl was in agreement with our previous determination, D0(H–Cl)=35748.2±0.8 cm−1. These results are compared to a recent study of Born–Oppenheimer breakdown in HCl by Coxon and Hajigeorgiou, where high resolution spectroscopic data was used to fit Born–Oppenheimer breakdown correction terms for the intramolecular potential function. The present study also measured the high resolution spectra for photoion-pair production for HCl and DCl in the threshold region for ion-pair production (∼86 nm). Although there is qualitative agreement between the current results and previous experimental and theoretical work, there are some important differences. The possible mechanism for ion-pair formation in HCl and DCl is discussed in light of these high resolution results.

Born–Oppenheimer breakdown in a combined-isotopomer analysis of the A 1Σu+–X 1Σg+ system of Li2

New high resolution polarization data have been obtained for the A–X band system of Li2 6,7, and new Fourier transform data for the homonuclear lithium dimers. They are combined with earlier data for Li26,6 and Li2 7,7 in the first systematic combined-isotopomer analysis of data for Li2 . This analysis of 8445 rovibrational transitions yields an improved and internally consistent set of molecular constant for the three Li2 isotopomers, and determines the electronic isotope shift and leading vibrational and rotational Born–Oppenheimer breakdown correction terms for both electronic states.

The Pure Rotational Spectrum, Geometry, and Hyperfine Constants of Hafnium Monosulfide, HfS

The pure rotational spectra of seven isotopomers of hafnium monosulfide have been measured for several vibrational states. For the most abundant isotopomer, 180Hf 32S, the J=1 - 0, J=2 - 1, and J=3 - 2 transitions were recorded up to the sixth vibrationally excited state. The constants Y 01, Y 02, Y 11, Y 21, and Y 31 were determined via a multi-isotopomer fit to a Dunham-type expression. In the process of fitting the data it was necessary to include Born–Oppenheimer breakdown correction terms. The equilibrium internuclear distance has been evaluated. For both the 177Hf 32S and 179Hf 32S isotopomers, nuclear hyperfine structure due to the hafnium nucleus was observed and notably large Hf nuclear quadrupole coupling constants, eQq, were determined.