The pure rotational spectra and hyperfine constants of SbN and SbP

The pure rotational spectra of antimony mononitride, SbN, and antimony monophosphide, SbP, have been recorded within the frequency range 6–26 GHz, using a cavity pulsed jet Fourier transform microwave spectrometer.

The molecules were prepared by laser ablation of Sb and reaction of the resulting plasma with suitable precursors in the backing gas of the jet.

For SbN the J = 1–0 transition was measured for the vibrational ground state of four isotopomers, two of which were also seen in the v = 1 excited state.

For SbP the J = 1–0 and 2–1 transitions have been observed for two isotopomers in the ground plus v = 1 and v = 2 excited vibrational states.

Accurate spectroscopic constants, including Born–Oppenheimer breakdown terms for Sb and N, have been obtained from the spectra.

Precise equilibrium bond lengths re have been determined.

Hyperfine constants including nuclear quadrupole coupling constants and nuclear spin-rotation constants have been evaluated for both molecules, and are compared with the results of density functional calculations.


The spectroscopic investigation of antimony mononitride, SbN, began in 1940 when Coy and Sponer1 observed band spectra from a 1Π–1Σ transition.

An electrical discharge through antimony metal and N2 vapor was used in the preparation of the carrier.

The spectral measurements obtained by Coy and Sponer were later used to show that SbN could also be prepared in the gas phase by flash heating antimony metal in the presence of N2.2

Later, Jenouvrier et al3. used a microwave discharge through SbCl5 in N2 and He or antimony metal in N2 to produce SbN and subsequently recorded rotationally resolved bands from the A 1Π–X 1Σ transition.

The authors obtained an equilibrium bond length re (SbN) of 1.8351 Å.

Antimony monophosphide has a similar history in the literature.

A group of bands attributed to the 1Π–X 1Σ transition of SbP was observed by Yee et al. in .19704

These bands were revisited by Jones et al. in 19745 this time with a higher resolution, and sets of vibrational and rotational constants for both the X 1Σ and 1Π electronic states were obtained.

A microwave discharge technique was used in both investigations to generate gas phase SbP.

No studies to date have been of sufficient resolution to enable observation of hyperfine structure in the gas phase spectra of SbN or SbP.

A common method for determining experimental nuclear quadrupole moments begins with obtaining experimental quadrupole coupling constants, eQq, typically from microwave spectroscopy, followed by the calculation ab initio of the molecular electric field gradient at the nucleus in question.6

The absence of these two pieces of information for any Sb-containing diatomic molecule may, in part, be the reason why the recent ‘year-2001’ compilation of quadrupole moments by Pyykkö6 shows that the values for the Sb-nuclei have the greatest proportional uncertainties among the main group elements (excepting the short-lived radioactive 209Pb isotope).

The hyperfine structure in the spectra of SbN and SbP will be rich and full of information concerning the electronic structures of the molecules.

Antimony has two naturally occurring isotopes, 121Sb and 123Sb, which have nuclear spin quantum numbers I = 5/2 and I = 7/2, respectively.

These will produce nuclear quadrupole hyperfine structure, which will also be generated by the coupling of the I = 1 14N nucleus.Magnetic hyperfine coupling is expected from all nuclei, including the I = 1/2 P and 15N nuclei.

It is also of interest to compare eQq (14N) in Sb14N with those values obtained for P14N7 and Bi14N.8

This article reports the hyperfine parameters for all of the atoms in SbN and SbP and also gives a considerable increase in the accuracy with which the rotational constants for both molecules in their X 1Σ electronic states are known.

This increase in accuracy has also allowed a measure of the Born–Oppenheimer breakdown, BOB, for these molecules.

The BOB parameters obtained for the nuclei in SbN and SbP are reported and found to be of similar magnitudes to those reported recently for BiN and BiP8.


The experiments were carried out using a cavity pulsed jet Fourier transform microwave (FTMW) spectrometer incorporating a laser ablation system.

Details have been published elsewhere.9,10

SbN and SbP were prepared in the following way.

Pieces of antimony metal were melted (mp 630.7 °C) and cast into a rod 5 mm in diameter and 30 mm in length.

This rod was then used as the ablation target within the spectrometer.

A Nd:YAG laser operating at 1064 nm was used as the ablation source.

Following ablation of the antimony rod, pulses of gas made up of either NH3 or N2 in argon (for SbN) or PH3 in argon (for SbP) were passed through the metal plasma.

These reaction mixtures then underwent supersonic expansion into the Fabry–Perot cavity of the spectrometer, where the molecule–radiation interaction took place.

Time-domain spectra were converted to frequency-domain spectra using a fast Fourier-transform (FFT).

Doppler doubled line widths were typically 7–10 kHz (FWHM).

The microwave spectra recorded were referenced to a Loran frequency standard which has an accuracy of 1 part in 1010.

The transition frequencies obtained are estimated to be accurate to ±1 kHz.

Theoretical calculations

All calculations have been performed using density functional theory with the Amsterdam Density Functional (ADF) package.11

Rather than use an exchange–correlation potential derived from the choice of functional a statistically averaged orbital potential (SAOP)12 has been used.

Relativistic effects were accounted for using the zeroth order regular approximation (ZORA).13,14

For the Sb, N and P atoms large all electron quadruple-zeta quadruply polarized (QZ4P) basis sets of Slater-type orbitals were used.

Results and analysis

For SbN a search was undertaken for the J = 1–0 transition in the region near 23 GHz using the rotational constant of Jenouvrier et al.3

A group of three lines was quickly found spread over ≈1 MHz.

Observation of these lines required ablation of the Sb-rod.

The 121Sb-nuclear quadrupole coupling constant, eQq(121Sb), in SbN was estimated using the field gradient, q, recorded at the Bi nucleus in BiN8 and the quadrupole moment of 121Sb.6

Using this estimate two further groups of three lines were predicted and found.

The carrier of these three groups was identified as being 121Sb14N by the observation of three more groups of lines shifted down in frequency by an amount consistent with that expected for the heavier 123Sb14N isotopomer.

An example group is in Fig. 1.

Further confirmation was obtained through the initial prediction and then observation of transitions from the 15N-containing isotopomers at the appropriate frequencies.

The spectra were sufficiently strong for these isotopomers to be observed in natural abundance.

Initially NH3 was used as a precursor in the preparation of SbN.

However, it was necessary to switch to N2 during the measurement of one of the hyperfine components of the 123Sb14N, v = 0, transitions because of a near coincidence with an inversion frequency for NH3 (J = 1, K = 1 at 23694.48 MHz) which was observed with sufficient intensity as to preclude the observation of any weaker lines nearby.

A similar procedure was performed for SbP using the rotational constant of Jones et al.5

Lines requiring ablation of the Sb-rod were soon found with a similar hyperfine pattern to that observed for SbN with the exception that for the J = 1–0 transition three groups of two lines were observed, as opposed to three groups of three lines in the Sb14N spectra.

The hyperfine structure for SbP arose from the coupling of the Sb nucleus to the molecular angular momentum followed by further coupling of the P nucleus (I = 1/2).

The measured transition frequencies are given with their quantum number assignments in Tables 1 and 2 for SbN and SbP, respectively.

The coupling scheme used was J + ISb = F1; F1 + IPn = F (Pn = N or P).

Spectroscopic constants for each isotopomer of each molecule in each vibrational state were determined using Pickett’s global least squares fitting program SPFIT.15

The Hamiltonian used was:Here Bv and Dv are the rotational constant and centrifugal distortion constant of vibrational state v.

The third and fourth terms represent the nuclear quadrupole coupling terms of Sb and N, with coupling constants eQqSb and eQqN, respectively; clearly the fourth term was needed only for Sb14N. Similarly, the fifth and sixth terms represent the nuclear spin-rotation coupling energies for Sb and Pn, with coupling constants CSb and CPn, respectively.

The resulting spectroscopic constants are in Tables 3 and 4 for SbN and SbP, respectively.

For SbN, since only the J = 1–0 transition could be measured, the distortion constant D0 was fixed at 17.09 kHz from the electronic spectrum.3

Molecular geometries

The bond lengths for both SbN and SbP have been determined previously.3,5

However an increase in the precision of these values is available from the newly recorded microwave data.

For 121Sb14N and 121SbP there are enough data to evaluate equilibrium (re) bond lengths.

First we use the following simple expression:in which Bv and Be represent the rotational constants for vibrational state v and at equilibrium, respectively and αe and γe are vibration–rotation constants.

In the case of 121Sb14N only αe was determined from the data set.

The resulting values are in Table 5; they agree well with those of refs. 3 and 5.

The equilibrium bond length re was then determined from the equation:where μ is the reduced mass of the isotopomer in atomic mass units (u), and C2 is given by:With the fundamental constants recommended by CODATA in 199816C2 = 710.9001379(25) Å MHz1/2 u1/2.

All the parameters determined by this procedure are in Table 5.

Because of the high precision of C2, the uncertainties in re, ≈ 5 × 10−7 Å, are dominated by the uncertainties in Be and in the 1993 atomic masses used.17

The values given agree well with those of refs. 3 and 5, but are more precise as shown in Table 5.

This table also shows the results of the DFT calculations, which are in moderate agreement with experiment.

In recent studies of some heavy metal-containing diatomic molecules using FTMW spectroscopy8,18–23 it was found necessary to consider the effect of Born–Oppenheimer breakdown (BOB) on the accuracy of determined re values.

BOB may be investigated using a multi-isotopomer Dunham-type analysis following the formalisms of Watson24,25 and Schlembach and Tiemann.18

The ro-vibrational energy of a particular isotopomer is given by:To the accuracy of the present work each Ykl, with the exception of Y01, is given by Ykl = Uklμ−(k + 2l)/2, where Ukl is a mass-independent Dunham parameter.

BOB is observed in the Y01 term, which is written for molecules AB containing relatively light atoms as:where MA and MB are the masses of atoms A and B, and me is the electron mass.

ΔA01 and ΔB01 are BOB terms, usually of similar magnitudes, incorporating adiabatic and non-adiabatic contributions plus the Dunham correction.18,24,25

For molecules containing heavier elements it may be necessary to modify eqn. (6) by adding terms accounting for the finite sizes of the nuclei.

These so-called “field-shift” terms were needed in the analysis of the rotational spectra of, for example, BiN8 and PtSi.22

For SbN and SbP, however, DFT calculations following the method of Cooke et al26. indicate that field shift effects are negligible, so the expression used for Y01 was that of eqn. (6).

For both SbN and SbP, line centers of the observed transitions were calculated to the same number of significant figures as the measurements, using the constants of Tables 3 and 4.

For SbN these frequencies were fit to U01, U11, ΔSb01, ΔN01, with U02 held fixed at −2.692 u2 MHz calculated from .ref. 3

The equation of Bunker27was then used to obtain rBOe which is given together with the fitted Ukl terms in Table 6.

Significant values for Δ01 were determined for both atoms.

For SbP the constants U01, U02, U11, U21 and ΔSb01 were fit to seven “unsplit” frequencies.

Because P has only one isotope ΔP01 could not be determined from the experimental data.

However, it will need to be accounted for in evaluating an accurate rBOe.

Since Δ01 is generally of similar magnitude for each atom25 (as is the case for SbN), ΔP01 was set to ΔSb01 ± 1 in the fitting procedure.

The resulting constants and reBO are also given in Table 6.

Estimates of vibration frequencies for SbP

In this work an experimental ground state distortion constant was only obtained for SbP.

If we make the approximation that DeD0 then we may use the equations of Kratzer28 and Pekeris29 to estimate the vibration frequencies.

The equations are:We find ωe = 506(18) cm−1 and ωexe = 1.56(20) cm−1 which compare very well with the experimental values of 500.07 cm−1 and 1.632 cm−1 respectively.5

A potential function was produced from the DFT calculations.

From it values of ωe (521.2 cm−1) and ωexe (1.82 cm−1) were obtained.30

An approximation for the dissociation energy De was obtained from31The value obtained was 491(72) kJ mol−1.

This value is considerably larger than the literature value D2980 = 359.6(38) kJ mol−1,32 and the value obtained from the DFT calculation, 362 kJ mol−1.

Although our experimental value relies on the approximation of a Morse potential, which may be suspect, the large uncertainty makes it unclear whether this is the source of the discrepancy.

Nuclear quadrupole coupling constants

Nuclear quadrupole coupling constants eQqv for both Sb isotopes in both SbN and SbP, and for 14N in Sb14N, have been evaluated in both the ground and at least one excited vibrational state.

Their values in Tables 3 and 4 were applied to:eQq″ was only considered for SbP.

However, the vibrational variation of eQq(Sb) in SbP was found to be sufficiently linear that this value was not required.

The resulting eQqe values are in Table 5.

From the results for both SbN and SbP we calculate: This may be compared to the ratio Q(123Sb)/Q(121Sb) = 1.274714 ∼ 1.274770 obtained by Wang33 from the pure nuclear quadrupole spectra of solid antimony chloride.

We note from Tables 3 and 4 that all the eQq values decrease in magnitude with increasing v (i.e. with increasing internuclear separation).

A corresponding result has been found for BiN and BiP.8

It was suggested in ref. 8 that an increase in internuclear separation for BiN may be considered a step toward the potential curve asymptote at which both atoms have the spherically symmetric electron distribution of their ground states, 4S3/2.34

In this configuration, which corresponds to a half-filled p-shell, the field gradient and hence eQq are zero.

It is therefore reasonable that eQq(Bi) and eQq(N) should decrease in magnitude with increasing internuclear separation as this asymptote is approached.

Since similar potential curve asymptotes may be expected for SbN and SbP the same arguments apply in these cases as well.

DFT has been used to calculate the eQq values at different internuclear distances.

The results for 121Sb14N are depicted in Fig. 2; a similar trend for eQq(121Sb) is found for SbP.

The calculated values of eQq(121Sb) in both SbN and SbP are significantly underestimated.

In these calculations the value Q(121Sb) = −36(4) fm2, taken from the ‘year-2001’ set of quadrupole moments given by Pyykkö,6 has been used.

Agreement with experimental results may be obtained from the DFT calculations if a larger value for Q(121Sb) is used i.e.

Q(121Sb) ≈ −50 fm2.

A range of values of Q(121Sb) may be found in the literature.

Notably, Murakawa gives Q(121Sb) = −53(10) fm2,35 and Dembczynski gives Q(121Sb) = −45 fm2.36

The most recent calculation by Svane37 gives Q(121Sb) = −66.9(15) fm2.

It is hoped that our experimental eQq values will lead to “definitive” Q(121Sb) and Q(123Sb) values.

The eQq(14N) in SbN is well-reproduced by the DFT calculation.

Fig. 2 shows clear decreases in the magnitudes of both eQq(121Sb) and eQq(14N) with increasing internuclear separation, consistent with experiment.

The values for eQq(14N) in N2, PN, SbN and BiN are given in Table 7.

A clear decrease in magnitude is observed with increasing molecular mass.

This is likely a result of the increased electronegativity difference as the group is descended, giving increased A3+B3− ionic character for the heavier molecules.

Nuclear spin–rotation coupling constants

The values for the nuclear spin-rotation constants for all atoms in SbN and SbP are given in Tables 3 and 4.

The ratio CI(Sb)/B for SbN and SbP agree within ≈10% indicating that the Sb atoms are in very similar environments consistent with the eQq(Sb) values from both molecules.

Using a similar equation to that of eqn. (11) equilibrium values of CI have been obtained and these are given in Table 5.

The Ramsey–Flygare non-relativistic model of nuclear shielding38,39 provides a link between nuclear spin-rotation constants and nuclear magnetic shielding parameters.

It has allowed useful comparisons to be made between data obtained from microwave spectroscopy, nmr spectroscopy and theoretical calculations.40

In this model the shielding tensor, σ, is decomposed into diamagnetic, σd, and paramagnetic, σp contributions.

The former may be approximately related to a nuclear contribution to CI and depends only on the nuclear positions and the diamagnetic shielding in the free atom which is obtainable from tables.41–43

The paramagnetic part is proportional to the electronic contribution to CI.40

More recently several authors have revised Ramsey’s theory of shielding to take into account relativistic effects.44,45

The ZORA relativistic formalism for the shielding tensor given by Ziegler and co-workers46–48 has been implemented in the utility program “NMR” available with the ADF program.11

In this formalism the shielding tensor σ is decomposed into contributions from σd, σp49 and additionally σso a spin–orbit contribution.50

Using the ADF/NMR programs we have been able to obtain values for each term for all atoms of SbN and SbP; they are given in Table 8.

A useful quantity which in non-relativistic theory provides a link between CI and the shielding tensor is the span of the shielding, Ω.

The span is a measure of the asymmetry of the shielding tensor, defined by Ω = σ||σ where σ|| and σ are the components of the shielding tensor parallel and perpendicular to the molecular axis, respectively.

Rather than relating the various parts of the shielding tensor to the various parts of CI the span is closely related to the total CI by:51where mp and me are the proton and electron mass respectively, and gN is the g–factor of the nucleus in question.

Application of eqn. (13) using Ω obtained from the DFT calculations gives the CI constants shown in Table 8.

The experimental CI values (also in Table 8) are very close to the DFT values, implying that eqn. (13) remains a useful equation in the relativistic case.


The pure rotational spectra of SbN and SbP have been measured for the first time.

Improved rotational constants have been presented along with the most accurate equilibrium internuclear distances, re, to date.

The extent of Born–Oppenheimer breakdown has been examined and found to be small but non-negligible with respect to the determination of isotopically independent bond lengths, rBOe for both molecules.

Nuclear quadrupole coupling constants and nuclear spin rotation constants for all relevant atoms have been obtained from the spectra of SbN and SbP for the first time.

The constants show that the electronic structures are very comparable for both molecules.

The vibrational dependence of the quadrupole coupling constants is consistent with the potential curve asymptotic values.

Although DFT calculations have reproduced the bond lengths and the trends of the nuclear quadrupole coupling constants with bond length, they have only poorly reproduced the magnitudes of eQq(Sb), partly because the nuclear quadrupole moments of Sb are only poorly known.

High level ab initio calculations similar to those used for Sc and Zr52,53 should permit comparable accuracy to be obtained for eQq(Sb).

Density functional theory has reproduced the experimental nuclear spin-rotation constants.