# Interpreting the Microwave Spectra of Diatomic Molecules—Part II: Nuclear Quadrupole Coupling of One Nucleus

*Spectroscopy Journal*)

## Abstract

**:**

## 1. Introduction

_{e}) and vibration–rotation interaction (α

_{e}, γ

_{e}) via Equations (2)–(5) (Models 1–4):

## 2. Materials and Methods

## 3. Results

#### Sodium Iodide (NaI)

_{jk}. If k = 1, then the cluster average is just the average itself. If k = N, then each datum forms its own cluster and is equal to its cluster average. Typically, the optimal number of clusters corresponds to a break in slope of a plot of the sum of squared errors (difference between each datum and its assigned cluster average) versus the number of clusters.

_{e}only slightly improves the agreement (sum of squared errors (MHz

^{2}), SSE decreases by <10%, Table 1), and that most of the splitting from the average is still unaccounted for. The residuals in both models form a series of parabolic curves that seem to be consistently spaced. We must return to the theory to explain this.

## 4. Basic Theory of Nuclear Quadrupolar Coupling

^{3}and is therefore a sensitive probe of electron density near a nucleus. For example, it can be used to help predict the solid-state

^{51}V-NMR of vanadate compounds, which possess a very diverse structural chemistry [13].

## 5. Results

#### 5.1. Sodium Iodide (NaI, Reprise)

^{23}Na, I = 1.5, and for

^{127}I, I = 2.5. Both nuclei could potentially couple. The residual pattern suggests that there are at least eight sub-bands of this J = 2 transition. Which nucleus is responsible for the observed quadrupole splitting?

^{127}I). We can modify Models 1 and 2 by adding the nuclear quadrupole coupling term (Equations (9) and (10), Models 1-1 and 2-1, respectively):

_{e}is 2.711456 Å.

#### 5.2. Lithium Iodide (LiI)

_{e}= 2181.675 MHz, SSE = 476,090). Within each cluster, there appears to be a vibrational progression, assigned as v = 0–2 for the lower frequency cluster and v = 0, 1 for the higher frequency cluster (Model 1, B

_{e}= 2201.097 MHz, α

_{e}= 15.642 MHz, SSE = 157,984). The deviations for the two clusters (values of J) are predominantly opposite in sign (Figure 6), suggesting that there must be a huge centrifugal distortion constant (Model 3, B

_{e}= 2201.097 MHz, α

_{e}= 15.642 MHz, D

_{e}= −0.865 MHz, SSE = 8113). Further splitting is due to nuclear quadrupole effects. The lack of agreement between the predicted 2B and difference between clusters, along with the huge centrifugal distortion constant needed to fit the data (about 10

^{5}too big) suggests that the clustering is not due to different values of J.

_{e}ratio of 1.15736, SSE = 6050 (

^{7}Li

^{127}I) + 2058 (

^{6}Li

^{127}I), with a residual pattern suggesting that nuclear quadrupole effects are the next major source of variation (Figure 7). For lithium, I = 1 (

^{6}Li) or 1.5 (

^{7}Li), but it is iodine (

^{127}I, I = 2.5) that is responsible for the observed splitting, as the Casimir function differences for J = 0, I = 2.5 support this assignment. Model 1-1 gives a B

_{e}ratio of 1.157702, SSE = 7.820 (

^{7}Li

^{127}I) + 0.203 (

^{6}Li

^{127}I), approximately three orders of magnitude smaller. Comparisons of Models 2-1, 1-2, and 2-2 indicate that improving the description of the nuclear quadrupole model first is most advantageous (Table 2). The values for r

_{e}are 2.391920 (

^{7}Li

^{127}I, Model 2-2) and 2.391956 Å (

^{6}Li

^{127}I, Model 1-2), which is excellent agreement.

#### 5.3. Interhalogen Diatomics

#### 5.4. Chlorine Monofluoride (ClF)

^{35}Cl

^{19}F, whereas those at 30,001 and 30,255 are due to

^{37}Cl

^{19}F (due to a v = 0, 1 progression). The reduction in error on going from the one isotopologue and four vibrational states (SSE = 9777) to two isotopologue anf two vibrational states (SSE = 2687.4 + 4332.3 = 7020) is not large, however.

^{19}F will not give a nuclear quadrupole coupling because I = 0.5, but both

^{35}Cl and

^{37}Cl will because I = 1.5. For J = 0, F = 1.5 (one level), but for J = 1, F = 2.5, 1.5, and 0.5 (three levels). For each transition, a triplet of signals should be observed, consistent with experiment. The spacing of the triplets allows for unambiguous assignment (F’). The values for r

_{e}(Model 1-1), 1.628314 (

^{35}Cl

^{19}F) and 1.628313 Å (

^{37}Cl

^{19}F) are in excellent agreement with each other (Table 4) and the X-ray result of 1.628 Å. This makes an excellent student exercise (see Appendix A).

#### 5.5. Bromine Monofluoride (BrF)

_{e}= 1.77 Å, which is slightly shorter than the observed X-ray structure (Table 3), so this is a safe assumption (see Supplementary Materials, Excel file BrF.xlsx). Through trial and error, the spectrum of 12 frequencies can be assigned (Figure 10), but there is a more systematic way to assign this using knowledge of theory. Because of the lack of an obvious pattern, it is clear that splitting effects due to isotope shifts, vibrational progressions, and nuclear quadrupole effects are about the same.

^{79}Br

^{19}F, v = 0; Grouping 2 is

^{79}Br

^{19}F, v = 1; Grouping 3 is

^{81}Br

^{19}F, v = 0; and Grouping 4 is

^{81}Br

^{19}F, v = 1. The nuclear quadrupole splitting is somewhat smaller for the heavier

^{81}Br

^{19}F isotopologue. The values for r

_{e}(Model 1-2, Table 5) of 1.758940 (

^{79}Br

^{19}F) and 1.758933 Å (

^{81}Br

^{19}F) are in excellent agreement with each other and in good agreement with the X-ray result of 1.822 Å (Table 3).

#### 5.6. Iodine Monofluoride (IF)

_{e}is approximately 1.93 Å, which falls in line with the expected crystal structure distance of approximately 2.0 Å.

_{e}and/or γ

_{e}(Models 2-1, 3-1, and 4-1), but the lack of pattern in the variation of the residual with J and v indicates that there is a bigger reason for the discrepancy. The reason is evident when one compares the magnitude of eQq and B. The quadrupolar coupling can no longer be regarded as a small perturbation.

#### 5.7. Deuterium Iodide (DI)

^{2}H

^{127}I) was measured [22] and given in Figure 14 (Grouping 1). If we assume that J = 0, then the predicted r is 1.62 Å, in excellent agreement with the liquid neutron diffraction result [23] of 1.625 ± 0.015 Å (see Supplementary Materials, Excel file HI.xlsx). It is not immediately obvious whether the splitting around the average of 195,083 MHz is due to nuclear quadrupole effects or to a vibrational progression, v = 0, 1, 3 (with v = 2 missing). Fitting to Model 1 gives B

_{e}= 97,708, α

_{e}= 91 MHz, SSE = 114. Model 2 exactly reproduces the spectrum (B

_{e}= 97,699.5, α

_{e}= 77.3, γ

_{e}= −3.3 MHz, SSE = 0) but gives a negative γ

_{e}. Model 0-1 fits the spectrum to within the error but only requires two parameters (B

_{0}= 97,532.3, eQq = −1809.3 MHz, SSE = 14.58, r

_{0}= 1.61664 Å). A more precise spectrum was also measured [24] (Figure 14, Grouping 2) and the same gap for the purported v = 2 was noticed, suggesting that the splitting is actually due to nuclear quadrupole effects. The same models with the more precise spectrum gave: Model 1, B

_{e}= 97,711.4, α

_{e}= 91.8 MHz, SSE = 229; Model 2, B

_{e}= 97,698.8, α

_{e}= 72.2, γ

_{e}= −4.72 MHz, SSE = 0; Model 0-1, B

_{0}= 97,534.1, eQq = −1822.6 MHz, SSE = 0.264, r

_{0}= 1.61662 Å. These make excellent student exercises (Appendix B and Appendix C).

#### 5.8. Deuterium Bromide (DBr)

^{2}HBr) was measured [25] and given in Figure 15. If we assume that J = 0, then the predicted r is 1.44 Å, in excellent agreement with the liquid neutron diffraction result [26] of 1.446 ± 0.002 Å (see Supplementary Materials, Excel file HBr.xlsx). Because the bromine isotopes are in nearly equal abundance, both isotopologues should be observable. While the isotopologues can be separated by trial and error, the calculated frequency ratios are instructive as well. The predicted reduced mass ratio is 1.000614. Of the frequency ratios, four are close: 1.000687 (254,812/254,638), 1.000527 (254,812/254,678), 1.000597 (254,678/254,526), and 1.000522 (254,572/254,439). Of these, the first, third, and fourth encompass all of the data points, and we can provisionally separate the higher and lower frequencies of these sets as belonging to two different isotopologues: 254,812, 254,678, and 254,678 MHz (Grouping 1) belong to

^{2}H

^{79}Br, and 254,638, 254,526, and 254,439 (Grouping 2) belong to

^{2}H

^{81}Br. In this case, the magnitude of the remaining splitting is small enough to keep the frequency ratios close to the mass ratio.

#### 5.9. Sodium Bromide (NaBr)

_{e}~4534.2 MHz, α

_{e}~27.3 MHz), with some fine structure.

_{e}= 4534.177, α

_{e}= 27.286 MHz, SSE = 1445). Examination of the residuals reveals no obvious pattern as a function of J, but there does seem to be a clustering of positive and negative residuals as a function of v. When the points corresponding to these residual clusters are fit to two separate models with the same J, v assignments (B

_{e}= 4533.367, α

_{e}= 27.529 MHz, SSE = 107; B

_{e}= 4537.004, α

_{e}= 27.698 MHz, SSE = 37.8), the error is reduced by an order of magnitude, but the B

_{e}ratio (1.0008) is too small for it to be due to isotopologues (1.0056).

_{e}ratio of 1.005601. For J = 1, there are six ratios within a 0.0002 tolerance, but at most, three of them correspond to isotopic pairs because three of the frequencies are common. There are four possible ways to do this (reassigning v of

^{23}Na

^{81}Br is required); the one with the lowest combined SSE is taken. This gives 18,080.13, 18,070.07, and 17,968.42 for

^{23}Na

^{79}Br, and 17,980.48, 17,971.00, and 17,868.49 for

^{23}Na

^{81}Br. The isotopic separation is about the same as the vibration–rotation interaction, which is what makes the assignment so difficult. When this is done, we try to assign the remaining J = 1 frequencies. Clearly the high frequency at 18,095.95 MHz belongs to

^{23}Na

^{79}Br, establishing it as part of a Casimir triplet v = 0. Similarly, the frequency at 17,982.50 MHz must belong to the same species for v = 1. The assignment of the lower frequency at 17,856.57 could arise from a Casimir grouping for

^{23}Na

^{81}Br, v = 1 or for

^{23}Na

^{79}Br, v = 2. The latter assignment is preferred because of the slightly lower SSE. Fortunately, the nuclear quadrupole coupling is small enough not to affect the frequency ratios too much. We carry out a similar procedure for the J = 2 frequencies and can assign 10 of the 11 frequencies. Fitting to the same model, starting with J = 1 B

_{e}and α

_{e}, resulted in no change to these parameters. The low frequency at 26,455.80 MHz could be assigned to either

^{23}Na

^{81}Br v = 3, or to

^{23}Na

^{79}Br, v = 4, with the latter giving a much better residual.

_{e}ratio for all models with hyperfine splitting included is 1.00560 ± 0.00002, in excellent agreement with experiment, whereas without hyperfine splitting included, the values are slightly too high (1.0059–1.0063, Table 8). The equilibrium bond distances r

_{e}are 2.502037 (

^{23}Na

^{79}Br) and 2.502035 Å (

^{23}Na

^{81}Br), in excellent agreement.

#### 5.10. Lithium Bromide (LiBr)

^{7}Li isotopologues should be observed.

^{6}Li

^{79}Br,

^{6}Li

^{81}Br,

^{7}Li

^{79}Br, and

^{7}Li

^{81}Br. Examination of frequency ratios suggests that the frequency at 38,113 MHz is from

^{6}Li

^{81}Br (r

_{0}= 2.176390 Å), the three-frequency cluster at 33,130 MHz is due to

^{7}Li

^{79}Br, and the three-frequency cluster at 33,065 MHz is due to

^{7}Li

^{81}Br. Similarly, the bands at 32,462 and 32,397 MHz can be assigned to

^{7}Li

^{79}Br, and

^{7}Li

^{81}Br. The final cluster at 32,730 MHz is nearly in the middle of the two clusters due to

^{7}Li

^{81}Br, and these form a vibrational progression (the corresponding v = 1 cluster of

^{7}Li

^{79}Br was not observed, Figure 18 lower panel). The hyperfine structure is easily assigned, giving r

_{e}(Model 1-1) of 2.170483 Å (

^{7}Li

^{79}Br) and 2.170487 Å (

^{7}Li

^{81}Br). An order of magnitude SSE improvement is gained by including γ (Model 2-1), and the vibrational dependence of eQq, (Model 2-2), but these are somewhat dependent on one another.

## 6. Conclusions

_{e}, bond length r

_{e}, vibration–rotation interaction constant α

_{e}, and the nuclear quadrupole splitting eQq. (Model 1-1). In some cases, other spectroscopic constants (D

_{e}, γ

_{e}) can be determined.

## Supplementary Materials

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. Analysis of the Microwave Spectrum of Chlorine Monofluoride (ClF)

_{e}, α

_{e}, and eQq. (d) Give a precise value of r

_{e}.

^{19}F

^{37}Cl, v = 1;

^{19}F

^{37}Cl, v = 0;

^{19}F

^{35}Cl, v = 1;

^{19}F

^{35}Cl, v = 0 (b) Within each triplet, in order of increasing frequency, F’ = 1.5, 2.5, 0.5 (c)

^{19}F

^{37}Cl: B

_{e}= 15,189.169, α

_{e}= 126.959, eQq = −114.964;

^{19}F

^{35}Cl: B

_{e}= 15,483.628, α

_{e}= 130.666, eQq = −145.968 (d) r

_{e}= 1.62831 Å].

## Appendix B. Analysis of the Microwave Spectrum of Deuterium Iodide (DI)

_{0}and eQq. (c) Give a precise value of r

_{0}.

_{0}= 97,532.3, eQq = −1809.3 MHz (c) r

_{0}= 1.61664 Å].

## Appendix C. Analysis of the Microwave Spectrum of Deuterium Iodide (DI)

_{0}and eQq. (c) Give a precise value of r

_{0}.

_{0}= 97,534.1, eQq = −1822.6 MHz (c) r

_{0}= 1.61662 Å].

## Appendix D. Analysis of the Microwave Spectrum of Deuterium Bromide (DBr)

_{0}and eQq. (d) Give a precise value of r

_{0}.

^{2}H

^{79}Br, 254,572.2, 254,678.6, 254,812.9;

^{2}H

^{81}Br, 254,439.4, 254,526.7, 254,638.0 (b) F’ = 0.5, 2.5, 1.5 (c)

^{2}H

^{79}Br, B

_{0}= 127,352.87, eQq = +534.87;

^{2}H

^{81}Br, B

_{0}= 127,274.71, eQq = 441.49 (d) r

_{0}= 1.421464 Å].

## Appendix E. Some Relevant Isotopic Data

**Table A1.**Some relevant isotopic data. Z = atomic number, m = atomic mass, I = nuclear spin, Q = nuclear quadrupole.

Isotope | Z | m (amu) | Abundance (%) | I | Q (barn) |
---|---|---|---|---|---|

^{2}H | 1 | 2.014101777844 | 0.03 | 1 | +0.0028578 |

^{6}Li | 3 | 6.015122795 | 7.59 | 1 | −0.000806 |

^{7}Li | 3 | 7.016004550 | 92.41 | 1.5 | −0.0400 |

^{19}F | 9 | 18.998403220 | 100.00 | 0.5 | −0.0942 |

^{23}Na | 11 | 22.989769281 | 100.00 | 1.5 | +0.104 |

^{35}Cl | 17 | 34.968852721 | 75.76 | 2.5 | −0.0817 |

^{37}Cl | 17 | 36.965902590 | 24.24 | 2.5 | −0.0644 |

^{79}Br | 35 | 78.9183371 | 50.69 | 1.5 | +0.3087 |

^{81}Br | 35 | 80.9162906 | 49.31 | 1.5 | +0.2579 |

^{127}I | 53 | 126.904473 | 100.00 | 2.5 | −0.688 |

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**Figure 4.**The residual plots of Models 1-1, 1-2, 2-1, and 2-2 for the microwave spectrum of sodium iodide.

**Figure 5.**The microwave spectrum of lithium iodide (Grouping 0), and the cluster averages for k = 1–2.

**Figure 10.**The microwave spectrum of bromine monofluoride (Grouping 0), and the assignment via trial and error. Each grouping corresponds to a different isotopologue and vibrational state.

**Figure 11.**Tools for the assignment of bromine monofluoride. In the top plot, a histogram of frequency differences is shown, with 6 differences in the [150,160] bin. In the middle plot, the v = 0, 1 pairs are grouped together. In the lower plot, the v = 0 frequencies are grouped together along with the v = 1 frequencies.

**Figure 12.**The microwave spectrum of iodine monofluoride (Grouping 0) and the cluster averages for k = 1–2.

**Figure 15.**The microwave spectrum of deuterium bromide (Grouping 0), and its grouping into isotopologues.

**Figure 16.**The microwave spectrum of sodium bromide (Grouping 0), and the cluster averages for k = 1–2.

**Figure 17.**The clustering of the effective rotational constants (MHz) of sodium bromide. Grouping 0 is the original, Grouping 1 corrects the bad point (red), and Grouping 2 shows the clustering into 5 groups.

**Figure 18.**The microwave spectrum of lithium bromide. The original spectrum is in blue, and the separation into two isotopologues is in orange.

**Table 1.**Model parameters for sodium iodide (MHz) (

^{23}Na

^{127}I, n = 25). B

_{e}is the rotational constant at the equilibrium distance,

**α**and

_{e}**γ**are the first two terms of the rotation-vibration interaction, eQq is the nuclear electric quadrupole moment, and SSE is the sum of squared errors for the model. n/a = not applicable.

_{e}Model | B_{e} | α_{e} | γ_{e} | eQq | SSE |
---|---|---|---|---|---|

1 | 3530.486 | 19.218 | n/a | n/a | 8741.1 |

1-1 | 3531.567 | 19.226 | n/a | −268.133 | 8.099 |

2 | 3532.010 | 21.298 | −0.452 | n/a | 8260.4 |

2-1 | 3531.736 | 19.465 | +0.052 | −266.624 | 2.033 |

1-2 | 3531.553 | 19.219 | n/a | −268.5 −271.9 −270.0 −267.2 −258.9 | 5.597 |

2-2 | 3531.715 | 10.450 | 0.050 | −265.7 −271.1 −267.3 −264.7 −259.9 | 0.187 |

Model | B_{e} | α_{e} | γ_{e} | eQq | SSE |
---|---|---|---|---|---|

^{6}Li^{127}I | |||||

1 | 15,377.363 | 142.544 | n/a | n/a | 2058 |

1-1 | 15,380.614 | 151.044 | n/a | −199.993 | 0.203 |

1-2 | 15,380.779 | 151.369 | n/a | −206.8 −199.4 | 0.0002 |

2-1 | 15,380.977 | 152.012 | 0.484 | −199.993 | 0.203 |

^{7}Li^{127}I | |||||

1 | 13,286.504 | 121.179 | n/a | n/a | 6050 |

1-1 | 13,285.474 | 121.179 | n/a | −206.141 | 7.820 |

1-2 | 13,285.532 | 121.218 | n/a | −213.9 −206.1 −198.4 | 2.101 |

2-1 | 13,286.240 | 122.632 | 0.484 | −206.140 | 5.945 |

2-2 | 13,286.303 | 122.678 | 0.486 | −213.7 −206.5 −198.2 | 0.218 |

MX | R (Å) ^{1} | T (K) | Ref. |
---|---|---|---|

ClF | 1.628(1) | 85 | [14] |

BrF | 1.822(2) ^{2} | 123 | [15] |

IF | 2.0 (est.) | ||

BrCl | 2.178(2) ^{3} | 133 | [15] |

2.205(1) ^{4} | |||

ICl | 2.37(4), 2.44(4) ^{5} | 195 | [16] |

2.351, 2.440 ^{6} | 253 | [17] | |

IBr | 2.521 | 293 | [18] |

^{1}X-ray diffraction.

^{2}CH

_{3}Cl solvate.

^{3}Ordered.

^{4}Disordered.

^{5}α-ICl.

^{6}β-ICl.

**Table 4.**Model parameters for chlorine monofluoride (MHz) (

^{35}Cl

^{19}F, n = 6;

^{37}Cl

^{19}F, n = 6).

Model | B_{e} | α_{e} | eQq | SSE |
---|---|---|---|---|

^{35}Cl^{19}F | ||||

1 | 15,486.061 | 130.666 | n/a | 4332 |

1-1 | 15,483.628 | 130.666 | −145.968 | 0.018 |

^{37}Cl^{19}F | ||||

1 | 15,191.085 | 126.958 | n/a | 2687 |

1-1 | 15,189.169 | 126.959 | −114.964 | 0.002 |

**Table 5.**Model parameters for bromine monofluoride (MHz) (

^{79}Br

^{19}F, n = 6;

^{81}Br

^{19}F, n = 6).

Model | B_{e} | α_{e} | eQq | SSE |
---|---|---|---|---|

^{79}Br^{19}F | ||||

1 | 10,649.717 | 78.267 | n/a | 241,356 |

1-1 | 10,667.875 | 78.267 | +1089.5 | 1.49 |

1-2 | 10,667.851 | 78.243 | +1090.2 +1088.8 | 1.39 |

^{81}Br ^{19}F | ||||

1 | 10,601.692 | 77.950 | n/a | 168,159 |

1-1 | 10,616.848 | 77.950 | +909.4 | 0.12 |

1-2 | 10,616.838 | 77.939 | +909.7 +909.1 | 0.10 |

**Table 6.**Model parameters for iodine monofluoride (MHz) (

^{127}I

^{19}F, n = 22). D

_{e}is the centrifugal distortion constant.

Model | B_{e} | α_{e} | γ_{e} | D_{e} ^{1} | eQq | SSE |
---|---|---|---|---|---|---|

0 | 8317.031 | n/a | n/a | n/a | n/a | 4,605,220 |

0-1 | 8326.929 | n/a | n/a | n/a | −3406.72 | 352,033 |

1 | 8371.848 | 51.862 | n/a | n/a | n/a | 4,309,414 |

1-1 | 8386.775 | 56.567 | n/a | n/a | −3430.00 | 335.828 |

2-1 | 8386.464 | 55.877 | 0.285 | n/a | −3430.15 | 332.485 |

3-1 | 8389.135 | 56.449 | n/a | 0.640 | −3429.45 | 294.911 |

4-1 | 8388.806 | 55.580 | 0.358 | 0.656 | −3429.64 | 289.642 |

^{1}Centrifugal distortion constants have been multiplied by 10

^{6}.

Model | B_{e} | α_{e} | γ_{e} | eQq | SSE |
---|---|---|---|---|---|

^{2}H^{79}Br | |||||

0 | 127,343.95 | n/a | n/a | n/a | 29,098 |

1 | 127,434.21 | 60.175 | n/a | n/a | 129.7 |

2 | 127,445.26 | 81.100 | 6.975 | n/a | exact |

0-1 | 127,352.87 | n/a | n/a | 534.87 | 0.222 |

^{2}H^{81}Br | |||||

0 | 127,267.35 | n/a | n/a | n/a | 19,817 |

1 | 127,341.82 | 49.65 | 96.0 | ||

2 | 127,351.33 | 67.650 | 6.000 | n/a | exact |

0-1 | 127,274.71 | n/a | n/a | 441.49 | 0.620 |

Model | B_{e} | α_{e} | γ_{e} | D_{e} ^{1} | eQq | SSE |
---|---|---|---|---|---|---|

^{23}Na^{79}Br | ||||||

1 | 4534.486 | 27.868 | n/a | n/a | n/a | 514.10 |

1-1 | 4533.933 | 27.718 | n/a | n/a | 55.351 | 12.89 |

2-1 | 4534.451 | 28.278 | −0.114 | n/a | 55.865 | 3.18 |

3-1 | 4534.148 | 27.672 | n/a | 0.042 | 54.983 | 10.95 |

4-1 | 4534.465 | 28.261 | −0.111 | 0.0048 | 55.812 | 3.15 |

^{23}Na^{81}Br | ||||||

1 | 4507.996 | 27.170 | n/a | n/a | n/a | 74.44 |

1-1 | 4508.673 | 27.454 | n/a | n/a | 43.525 | 5.06 |

2-1 | 4509.110 | 27.932 | −0.109 | n/a | 48.461 | 3.67 |

3-1 | 4508.992 | 27.402 | n/a | 0.052 | 46.984 | 4.01 |

4-1 | 4509.213 | 27.790 | −0.085 | 0.033 | 49.545 | 3.32 |

^{1}Centrifugal distortion constants have been multiplied by 10

^{6}.

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**MDPI and ACS Style**

Pye, C.C.
Interpreting the Microwave Spectra of Diatomic Molecules—Part II: Nuclear Quadrupole Coupling of One Nucleus. *Spectrosc. J.* **2024**, *2*, 82-104.
https://doi.org/10.3390/spectroscj2030006

**AMA Style**

Pye CC.
Interpreting the Microwave Spectra of Diatomic Molecules—Part II: Nuclear Quadrupole Coupling of One Nucleus. *Spectroscopy Journal*. 2024; 2(3):82-104.
https://doi.org/10.3390/spectroscj2030006

**Chicago/Turabian Style**

Pye, Cory C.
2024. "Interpreting the Microwave Spectra of Diatomic Molecules—Part II: Nuclear Quadrupole Coupling of One Nucleus" *Spectroscopy Journal* 2, no. 3: 82-104.
https://doi.org/10.3390/spectroscj2030006