: generation by laser-ablation and characterization by rotational spectroscopy and ab initio calculations †

The new compound H 3 P (cid:2)(cid:2)(cid:2) AgI has been synthesized in the gas phase by means of the reaction of laser-ablated silver metal with a pulse of gas consisting of a dilute mixture of ICF 3 and PH 3 in argon. Ground-state rotational spectra were detected and assigned for the two isotopologues H 3 P (cid:2)(cid:2)(cid:2) 107 AgI and H 3 P (cid:2)(cid:2)(cid:2) 109 AgI in their natural abundance by means of a chirped-pulse, Fourier-transform, microwave spectrometer. Both isotopologues exhibit rotational spectra of the symmetric-top type, analysis of which led to accurate values of the rotational constant B 0 , the quartic centrifugal distortion constants D J and D JK , and the iodine nuclear quadrupole coupling constant w aa (I) = eQq aa . Ab initio calculations at the explicitly-correlated level of theory CCSD(T)(F12*)/aug-cc-pVDZ confirmed that the atoms P (cid:2)(cid:2)(cid:2) Ag–I lie on the C 3 axis in that order. The experimental rotational constants were interpreted to give the bond lengths r 0 (P (cid:2)(cid:2)(cid:2) Ag) = 2.3488(20) Å and r 0 (Ag–I) = 2.5483(1) Å, in good agreement with the equilibrium lengths of 2.3387 Å and 2.5537 Å, respectively, obtained in the ab initio calculations. Measures of the strength of the interaction of PH 3 and AgI (the dissociation energy D e for the process H 3 P (cid:2)(cid:2)(cid:2) AgI = H 3 P + AgI and the intermolecular stretching force constant F P (cid:2)(cid:2)(cid:2) Ag ) are presented and are interpreted to show that the order of binding strength is H 3 P (cid:2)(cid:2)(cid:2) HI o H 3 P (cid:2)(cid:2)(cid:2) ICl o H 3 P (cid:2)(cid:2)(cid:2) AgI for these metal-bonded molecules and their halogen-bonded and hydrogen-bonded analogues.


Introduction
A programme of systematic investigations of small molecules of the type BÁ Á ÁMX is being conducted, where B is a small Lewis base (e.g.N 2 , OC, H 2 O, H 2 S, HCRCH, H 2 CQCH 2 , cyclopropane or NH 3 ), M = Cu, Ag or Au, and X = F, Cl or I. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] The programme has both experimental and theoretical components.The experimental approach is to produce BÁ Á ÁMX by laser ablation of the metal M in the presence of a gas pulse composed of small amounts of B and a molecular source of halogen atoms X in a large excess of argon.Following supersonic expansion of the product BÁ Á ÁMX entrained in the carrier gas, its rotational spectrum is observed in isolation at a low effective temperature.Various properties of BÁ Á ÁMX are available through analysis of the rotational spectrum, namely the angular geometry, the distances r(BÁ Á ÁM) and r(M-X), the strength of the intermolecular bond BÁ Á ÁM, and the electric charge redistribution that accompanies formation of BÁ Á ÁMX.The theoretical component of the investigations involves ab initio calculations at the CCSD(T)(F12*) explicitly correlated level of theory, usually with the largest basis set affordable.These calculations have the advantage of providing accurate properties of the isolated molecule, which can be compared with the experimental results.
Several molecules H 3 NÁ Á ÁMX, where M = Cu or Ag and X = F, Cl or I, have been detected and characterised recently in the gas phase for the first time through their rotational spectra, [17][18][19] although H 3 NÁ Á ÁCuCl was identified in the solid state earlier. 20ach was established to be a symmetric-top molecule, with the NÁ Á ÁMX nuclei lying on the top (C 3 ) axis, in the order indicated.To date, analogues of H 3 NÁ Á ÁMX having phosphine instead of ammonia as the Lewis base B have not been identified experimentally, to the best of our knowledge, but several have been the subject of density functional calculations. 21,22We report here the rotational spectrum of H 3 PÁ Á ÁAg-I and some of its properties derived therefrom.

Detection of the rotational spectrum
A chirped-pulse Fourier-transform microwave (CP-FTMW) spectrometer fitted with a laser ablation source was used to observe rotational spectra in the frequency range 6.5 to 18.5 GHz.Detailed descriptions of the spectrometer and laser ablation source are available elsewhere. 29,30A gas sample containing B4.0% PH 3 and B1.5% CF 3 I in argon was prepared at a total pressure of 6 bar.The sample was pulsed over the surface of a silver rod that was ablated by a suitably timed Nd:YAG laser pulse (wavelength 532 nm, pulse duration 10 ns, pulse energy 20 mJ).Subsequently, the gas pulse expanded supersonically into the vacuum chamber of the spectrometer.The rod was translated and rotated regularly at small intervals to allow each laser pulse (repetition rate of B1.05 Hz) to impinge on a fresh metal surface and thereby ensure shot-toshot reproducibility.
The sequence employed to record broadband microwave spectra involves repetition of two steps.The first is polarization of the sample by a microwave chirp that sweeps from 6.5 to 18.5 GHz within 1 ms and the second is recording of the subsequent free induction decay of the molecular emission over a 20 ms time period.This sequence is repeated eight times during the expansion of each gas sample pulse into the spectrometer chamber.The free induction decay (FID) of the polarization is mixed down with the signal from a 19 GHz local oscillator and then digitized by means of a 25 Gs s À1 digital oscilloscope.Each transition is observed as a single peak with full-width at half-maximum (fwhm) D 150 kHz after application of a Kaiser-Bessel digital filter.

Ab initio calculations
Structure optimizations and counter-poise corrected dissociation energies were calculated using the Turbomole package 31 at the CCSD(T)(F12*) level of theory, 32 a coupled-cluster method with single and double excitations, explicit correlation, 33 and a perturbative treatment of triple excitations. 34Only valence electrons were included in the correlation treatment.A basis set combination consisting of aug-cc-pVDZ on H and P atoms and aug-cc-pVDZ-PP on Ag and I atoms was used and will be referred to by AVDZ.ECP-10-MDF 35,36 and ECP-28-MDF 37 were used on Ag and I, respectively, to account for scalar relativistic effects.
For the density fitting approximation used to accelerate the CCSD(T)(F12*) calculation, the respective def2-QZVPP basis sets were employed for the MP2 38,39 and Fock 40 terms.For the complementary auxiliary basis required for the F12 treatment, 41 the aug-cc-pCVDZ MP2 density fitting basis sets were used. 39Quadratic force constants were also calculated at this level of theory.For comparison, the same force constants were calculated with the GAUSSIAN 09 package 42 at the MP2 level of theory.A basis set combination consisting of aug-cc-pVTZ on the H and P atoms, and aug-cc-pVTZ-PP on the Ag and I atoms was used in this case.

Determination of spectroscopic constants
The observed spectrum of H 3 PÁ Á ÁAgI showed evidence of the presence of the two isotopologues H 3 PÁ Á Á 107 AgI and H 3 PÁ Á Á 109 AgI, each exhibiting iodine nuclear quadrupole hyperfine structure, as may be seen from consideration of Fig. 1.An iterative least-squares fit of the observed hyperfine frequencies of each isotopologue was conducted using the program PGOPHER, written and maintained by Western. 43The Hamiltonian employed was of the form where H R is the usual energy operator appropriate to a semirigid symmetric rotor molecule and À 1 6 Q:=E is the iodine nuclear quadrupole energy operator, in which Q is the iodine nuclear electric quadrupole moment tensor and =E is the electric field gradient tensor at I. The matrix of H was constructed in the coupled symmetric-rotor basis I + J = F.The only determinable spectroscopic constants were the rotational constant B 0 , the quartic centrifugal distortion constants D J and D JK , and the iodine nuclear quadrupole coupling constant w aa (I) = ÀeQq 2 V/qa 2 = eQq aa (where q aa = Àq 2 V/qa 2 is the electric field gradient along the C a 3 axis direction).The magnetic coupling of the iodine nuclear spin to the molecular rotation can in principle be described by the spin-rotation constant C bb but this constant was too small to determine from the observed frequencies.Values of the spectroscopic constants from the final cycle of the least-squares fit with PGOPHER are given in Table 1 for the two isotopologues H 3 PÁ Á Á 107 AgI and H 3 PÁ Á Á 109 AgI investigated, together with s RMS , the RMS deviation of the fit, and N, the number of hyperfine components fitted.Spectra simulated using PGOPHER and the final set of spectroscopic constants are shown in Fig. 1.The detailed PGOPHER fits are available as Supplementary Material.The values of s RMS are satisfactory, given the estimated accuracy of frequency measurement (12 kHz) associated with the chirpedpulse F-T microwave spectrometer.

Molecular geometry
The facts that the ground-state rotational spectrum of the detected complex of phosphine and argentous iodide is of the symmetric-top type and that the Ag atom is close to the complex centre of mass (see later) mean that the arrangement of the atoms is either H 3 PÁ Á ÁAgI or PH 3 Á Á ÁAgI.The second of these is unlikely because d+ Ag-I dÀ is dipolar in the indicated sense and it is expected that the positive end of the electric dipole would interact with the P non-bonding electron pair, which lies on the C 3 axis of phosphine.This expectation is confirmed by ab initio calculations at the CCSD(T)(F12*)/AVDZ level of theory, which predict that the optimised geometry of PH 3 Á Á ÁAgI lies higher in energy by 116 kJ mol À1 than that of the H 3 PÁ Á ÁAgI conformer.The higher energy conformer would not be populated at the low effective temperature (B2 K) of the supersonic expansion.The observed conformer is therefore of the general form shown in Fig. 2.
The rotational constants B 0 = C 0 for the two isotopologues H where the error is estimated from da = 0.0015/|a| as recommended by Costain. 46,47The corresponding values for this coordinate implied by the determined r 0 geometry and the ab initio r e geometry are 0.9017 Å and 0.9056 Å, respectively.

Strength of the interaction of H 3 P and AgI
There are two common measures of the strength of the interaction of phosphine and silver iodide in H 3 PÁ Á ÁAgI.Both are properties of the one-dimensional potential-energy function associated with variation of the distance r(PÁ Á ÁAg) when C 3v symmetry is maintained but with structural relaxation at each point (referred to as the dissociation coordinate).The first is the intermolecular stretching quadratic force constant F PÁ Á ÁAg .The second is the energy, D e , required to dissociate H 3 PÁ Á ÁAgI to give PH 3 and AgI at infinite separation, with reactants and products at their equilibrium geometries.The first can be obtained from the experimental centrifugal distortion constants D J but the second is not available from the present experiments.Both are available from the ab initio calculations.
For weakly bound complexes (such as most hydrogen-bonded complexes BÁ Á ÁHX, where B is a simple Lewis base and X is a halogen atom) it is a good approximation to assume that B and HX are rigid and unchanged in geometry on complex formation.Then F BÁ Á ÁH can be related to the equilibrium centrifugal distortion constant D e J or D e J (depending on molecular symmetry) of the complex and the various rotational constants of B, HX and BÁ Á ÁHX, as demonstrated by Novick 48 for the case where B is an atom and by Millen 49 for a wider range of molecules B. For complexes BÁ Á ÁMX, where M is a coinage metal atom, the intermolecular bond can be strong and the approximation that the force constant F BÁ Á ÁM is much smaller than all other stretching force constants is no longer appropriate.To deal with such cases, we have recently described a two-force constant model which relates the quadratic force constants F M-X and F BÁ Á ÁM (hereafter referred to as F 11 and F 22 , respectively) to either D e J or D e J under the assumption that the contribution of the cross term F 12 is negligible. 50The model applies to all complexes of a Lewis base B with any diatomic molecule (e.g. a hydrogen halide HX, a dihalogen XY, or a coinage metal halide MX) as long as the diatomic molecule lies along a C n (n Z 2) symmetry axis of B in the equilibrium geometry.Note that B is assumed rigid, but can be changed in geometry when subsumed into the complex.During the vibrational motion no further change is assumed, however.
The two-force constant model for a symmetric-top molecule such as H 3 PÁ Á ÁAgI leads (with numbering of the Ag and I atoms and internal coordinates r 1 and r 2 shown in Fig. 2) to the expression 50 hD e J ¼ 1 2 In eqn (3), I e bb is an equilibrium principal moment of inertia and the a n are equilibrium principal axis coordinates of atoms n = 1 and 2. The compliance matrix elements (F À1 ) nn are simply 1/F nn under the approximations described above.It was shown in ref.50 that zero-point constants and coordinates can be used in place of equilibrium values to a reasonable approximation.Least-squares fitting of (F À1 ) 11 and (F À1 ) 22 simultaneously to the D 0 J values of the two isotopologues H 3 PÁ Á Á 107 AgI and H 3 PÁ Á Á 109 AgI led to ill-conditioning, however, so instead a fixed value of F 11 was assumed and F 22 was fitted.Fig. 3 shows F 22 plotted as a function of F 11 for a wide range of values of the latter, with the equilibrium value of the force constant 145.8 N m À1 of the free diatomic molecule Ag-I indicated, as calculated from its equilibrium vibrational wavenumber. 51The result for free AgI at the same level is F 11 = 160.1 N m À1 , corresponding to 9.8% overestimation of the experimental equilibrium value.If F 11 for H 3 PÁ Á ÁAgI were also overestimated by a similar percentage, the corrected value would be F 11 = 153 N m À1 , which likewise represents a small increase relative to that of the free molecule.
It has been shown that in the limit of rigid, unchanged B and MX geometries, when F 11 becomes infinite, eqn (3) reduces to the corresponding Millen expression 49  J .Clearly, any reasonable F 11 must lead to a F 22 value that is considerably greater than that given by eqn (4).
The other measure of the strength of binding is the dissociation energy defined earlier; it takes the value D e = 116 kJ mol À1 when calculated at the CCSD(T)(F12*)/AVDZ level of theory, after counterpoise correction. 52The value for AgI = Ag + I at the same level of theory is 230 kJ mol À1 .It is therefore clear from the D e value and the force constant F 22 that the intermolecular bond in H 3 PÁ Á ÁAgI is by no means weak.In fact by either measure, the PÁ Á ÁAg bond is about an order of magnitude stronger than most hydrogen or halogen bonds, but is only about a factor of two weaker than the Ag-I bond itself.

Electric charge redistribution on formation of H 3 PÁ Á ÁAgI
The iodine nuclear quadrupole coupling constant w aa (I) = eq I aa Q I carries information about the electric charge distribution at I through the electric field gradient q I aa along the a-axis direction at the iodine nucleus.According to the Townes-Dailey model 53 for interpreting such coupling constants, the ionicity i c (or fractional ionic character) of the free AgI molecule is given by w aa ðIÞ eQ I q I ð5;1;0Þ ; (5) in which q I (5,1,0) is the contribution to the electric field gradient at I along the a-axis direction that arises from an electron in 5p a orbital.The quantity eQ I q I (5,1,0) has the value 2292.71MHz when described as a frequency. 54Eqn (5) leads to the result i c = 0.537 for 107 Ag 127 I (the values 51,55 of several properties of AgI, including w aa (I), are collected in Table 2) but has the value 0.680 for the complex H 3 PÁ Á Á 107 Ag 127 I. Evidently, the charge rearrangement within AgI on formation of the complex is significant, a result consistent with the similar magnitude of the values for the dissociation energies D e for the processes H 3 PÁ Á ÁAgI = H 3 P + AgI and AgI = Ag + I referred to earlier.Interestingly, there appears to be very little change in its bond length when AgI is subsumed into the complex.

Conclusions
The new molecule H 3 PÁ Á ÁAg-I has been synthesized in the gas phase by a laser ablation method in which a pulse of gas mixture consisting of a few per cent each of PH 3 and ICF 3 , with the remainder Ar, interacts with the plasma produced when silver is ablated by a Nd-YAG laser operating at 532 nm.The product was detected and characterised by means of its rotational spectrum, as observed with a chirped-pulse, Fouriertransform microwave spectrometer.The molecule is a symmetric top of C 3v symmetry with the atoms P, Ag and I lying in that order on the symmetry axis a. Spectroscopic constants determined by fitting the observed transitions of the isotopologues H 3 PÁ Á Á 107 AgI and H 3 PÁ Á Á 109 AgI were interpreted to give the values r 0 (PÁ Á ÁAg) = 2.3488(20) Å and r 0 (Ag-I) = 2.5483(1) Å for the indicated bond lengths, after assuming changes to the r 0 geometry of free PH 3 when bound up in the complex were the same as the corresponding changes in the r e geometry, as predicted ab initio at the CCSD(T)(F12*)/AVDZ level of theory.It is of interest to note that the value of r 0 (Ag-I) is increased by only 0.0017 Å relative to the free AgI value of 2.54663 Å (see Table 2). 55Interpretation of the centrifugal distortion constants D 0 J and the iodine nuclear quadrupole coupling constants led to a value F 22 = 110 (5) N m À1 for the quadratic stretching force constant of the PÁ Á ÁAg bond and to a value di c = 0.14 for the increase in the Ag-I bond ionicity when H 3 PÁ Á ÁAgI is formed.Although the ionicity of AgI increases significantly when subsumed into the complex, we note that the  This journal is © the Owner Societies 2016 length of the bond and its force constant F 11 are effectively unchanged.
H 3 NÁ Á ÁCuI, synthesized and characterised recently by a similar method, 19 is isomorphic with H 3 PÁ Á ÁAgI and has r 0 (NÁ Á ÁCu) = 1.9357(13)Å and r 0 (Cu-I) = 2.3553(5) Å, the latter representing an increase of only 0.0147 Å relative to the free Cu-I value of 2.34059 Å.The NÁ Á ÁCu interaction strength, as measured by F 22 = 110(30) N m À1 , is similar to that 110(5) N m À1 of PÁ Á ÁAg in H 3 PÁ Á ÁAgI, but the ab initio value for the other measure of binding strength for H 3 NÁ Á ÁCuI (D e = 168 kJ mol À1 ) is significantly larger than that (116 kJ mol À1 ) of H 3 PÁ Á ÁAgI.The increase, di c = 0.14, in the ionicity of the Cu-I bond when H 3 NÁ Á ÁCuI is formed is identical to that observed for H 3 PÁ Á ÁAgI.We conclude that H 3 PÁ Á ÁAgI and H 3 NÁ Á ÁCuI are very similar in their properties: both are strongly bound, both have similar changes in the ionicity of the M-I bond when the free MI molecule is subsumed into the complex, but the bond length r 0 (M-I) is effectively unchanged in both by this process.
Several complexes involving hydrogen bonds and halogen bonds to ammonia and phosphine have been described elsewhere, namely H 3 PÁ Á ÁHI, 25 H 3 NÁ Á ÁHI, 26 H 3 PÁ Á ÁICl 27 and H 3 NÁ Á ÁICl. 28All have C 3v symmetry, with all atoms but the three H atoms of PH 3 or NH 3 lying on the C a 3 axis and therefore all are isomorphic with H 3 PÁ Á ÁAgI.The hydrogen-bonded analogues H 3 PÁ Á ÁHI and H 3 NÁ Á ÁHI have also been discussed in a detailed review, 56 where it is concluded, based on several indirect observations, that there is little evidence of significant charge rearrangement or HI bond lengthening in these two complexes.Both are weakly bound, having quadratic force constants F 22 = F PÁ Á ÁH or F NÁ Á ÁH of 3.4 N m À1 and 7.2 N m À1 , respectively.These values are more than an order of magnitude smaller than those of H 3 PÁ Á ÁAgI and H 3 NÁ Á ÁCuI when F PÁ Á ÁAg or F NÁ Á ÁCu are calculated from the centrifugal distortion constant D 0 J by means of eqn (3), the more accurate method for strongly bound complexes.The related halogen-bonded H 3 PÁ Á ÁICl 27 and H 3 NÁ Á ÁICl 28 have F 22 = F PÁ Á ÁI = 20.8N m À1 and F 22 = F PÁ Á ÁI 30.4 N m À1 , respectively, when obtained by means of eqn (4).As indicated earlier, the larger is F 22 relative to F 11 , the more serious will be its underestimation when eqn (4) is used.This underestimation is likely to be negligible for H 3 PÁ Á ÁHI and H 3 NÁ Á ÁHI, but it is possible that the values of F 22 for H 3 PÁ Á ÁICl and H 3 NÁ Á ÁICl will both be somewhat larger (but only by a few %) than those reported previously.Clearly, the halogen-bonded complexes H 3 PÁ Á ÁICl and H 3 NÁ Á ÁICl are significantly more strongly bound than the hydrogenbonded species H 3 PÁ Á ÁHI and H 3 NÁ Á ÁHI (when using the F 22 criterion) but less so than H 3 PÁ Á ÁAgI and H 3 NÁ Á ÁCuI.According to a method of estimating electric charge redistribution from the changes in the I and Cl nuclear quadrupole coupling constants, 27,28,57 there is a net movement of 0.15e (where e = electronic charge) from Cl to I in ICl when each of H 3 PÁ Á ÁICl and H 3 NÁ Á ÁICl is formed, thereby suggesting similar charge movement to that observed in each of H 3 PÁ Á ÁAgI and H 3 NÁ Á ÁCuI.

Fig. 1
Fig. 1 Top panel: (a) broadband spectrum recorded while probing a sample containing CF 3 I, Ag and PH 3 (530k FIDs).Some transitions of CF 3 I are taken off-scale to allow weaker transitions to be distinguished from the baseline.(b) Expanded section of spectrum displayed in (a) to show J 0 À J 00 = 5-4 transitions of 107 AgI (B13 420 MHz) and 109 AgI (B13 280 MHz).Hyperfine splittings in each transition are evident.(c) Expanded section of the spectrum displayed in (a) to show J 0 À J 00 = 11-10 transition of H 3 PÁ Á Á 109 AgI (black).A simulated spectrum that uses the results of fitted parameters is displayed inverted (red).
3 31 PÁ Á Á 107 Ag 127 I and H 3 31 PÁ Á Á 109 Ag 127 I allow only a partial determination of the lengths of the H-P, PÁ Á ÁAg and Ag-I bonds and of the angle a = +HPAg (between the P-H bond and the C 3 axis) necessary to define the r 0 geometry.The quantities of most interest are r 0 (PÁ Á ÁAg) and r 0 (Ag-I).The ab initio calculations indicate that r e (P-H) decreases by 0.0114 Å when phosphine enters the complex and the angle a e decreases by 3.941.We shall assume that the r 0 geometry of phosphine (r 0 (P-H) = 1.420003Å and angle a 0 = 122.861obtained by fitting the accurately known 44 B 0 and C 0 using the STRFIT program of Kisiel 45 ) changes in the same way as does the r e geometry on formation of H 3 PÁ Á ÁAg-I.If so, r 0 (P-H) = 1.4086Å and a 0 = 118.921are appropriate to PH 3 in the complex.When these values were assumed in a fit of the ground-state principal moments of inertia of H 3 31 PÁ Á Á 107 Ag 127 I and H 3 31 PÁ Á Á 109 Ag 127 I, the values r 0 (PÁ Á ÁAg) = 2.3488 Å and r 0 (Ag-I) = 2.5483 Å resulted.No errors in these quantities are generated in the fit because two constants are fitted by two parameters.However, calculations reveal the following variations: qr(PÁ Á ÁAg)/qr(PÀH) = 0.065, qr(AgÀI)/qr(PÀH) = 0.005, qr(PÁ Á ÁAg)/ qa = 0.002 Å deg À1 .and qr(AgÀI)/qa = 0.0001 Å deg À1 .Thus, the length r 0 (Ag-I) is very insensitive to changes to the geometry of PH 3 that might occur when H 3 PÁ Á ÁAgI is formed.These partial derivatives lead, when the reasonable errors of dr 0 = 0.005 Å and da 0 = 11 are assumed, to r 0 (PÁ Á ÁAg) = 2.3488(20) Å and r 0 (Ag-I) = 2.5483(1) Å.The results from the CCSD(T)(F12*)/AVDZ optimisation of H 3 PÁ Á ÁAgI are 2.3387 Å and 2.5537 Å, respectively.The fact that spectroscopic constants have been determined for the isotopologues H 3 PÁ Á Á 107 AgI and H 3 PÁ Á Á 109 AgI allows the coordinate a Ag to be obtained by the substitution method from the expression a Ag 2 = DI 0 b /m s , (2) in which DI 0 b is the difference in the zero-point moments of inertia of the two isotopologues and m s ¼ MDm M þ Dm ; where M is the mass of the parent and Dm is the mass change accompanying the isotopic substitution at Ag.The result is |a Ag | = 0.9017(17) Å,

Fig. 2
Fig. 2 The molecular geometry of H 3 PÁ Á ÁAgI drawn to scale.The internal coordinates r 1 and r 2 used in the discussion of how to obtain force constant F 22 from the centrifugal distortion constants D 0 J are indicated.The experimental zero-point values of r 1 and r 2 are r 0 (Ag-I) = 2.5483(1) Å and r 0 (PÁ Á ÁAg) = 2.3488(20) Å, respectively.
It is also possible to calculate F 11 and F 22 ab initio.At the CCSD(T)(F12*)/AVDZ level of theory the results are F 11 = 151.1 N m À1 and F 22 = 106.8N m À1 .When the D 0 J values are fitted by using eqn (3) with F 11 fixed at 151.1 N m À1 , the result is F 22 = 110(5) N m À1 , where the error is that implied by the error in the D 0 J values, and is the best present experimental estimate for this quantity.For free AgI at the same level of theory, F 11 = 145.9N m À1 is obtained, in excellent agreement with the experimental equilibrium value of 145.8 N m À1 .Thus.F 11 increases by 3.5% when AgI is incorporated into H 3 PÁ Á ÁAgI.For comparison, the lower level of theory MP2/aug-cc-pVTZ-PP gives F 11 = 168.8N m À1 and F 22 = 130.1 N m À1 when using the GAUSSIAN package.
) in which B BÁ Á ÁMX , B B and B MX are equilibrium rotational constants of the complex and its components, but zero-point values are used of necessity.In eqn (4), m = m B m MX /(m B + m MX ).When B = H 3 P and MX = AgI, a fit of the centrifugal distortion constants D 0 J of H 3 PÁ Á Á 107 AgI and H 3 P 109 AgI (using zero-point rotational constants given in Tables 1 and 2) leads to F 22 = 31.3(5)N m À1 , which is a very serious underestimate.The reason why becomes clear when the plot of F 22 as a function of F 11 is extended to cover a wider range of F 11 values and unphysical solutions for which F 22 is negative are included.The result is the rectangular hyperbola shown in Fig. 4. The

Fig. 3
Fig. 3 Values of the quadratic intermolecular stretching force constant F 22 obtained by fitting the centrifugal distortion constants D 0 J of the isotopologues H 3 PÁ Á Á 107 AgI and H 3 PÁ Á Á 109 AgI using eqn (3) at fixed values of the AgI stretching force constant F 11 in the range 130 to 220 N m À1 .Eqn (3) is valid only if the offdiagonal force constant F 12 is assumed to be zero.The CCSD(T)(F12*)/AVDZ-F12 value of F 11 , the experimental equilibrium value for the free AgI molecule and the F 22 values they correspond to are indicated.

Fig. 4
Fig.4The rectangular hyperbola obtained by following the procedure described in the caption to Fig.3, but with the range of assumed F 11 values extended from À100 to +300 N m À1 .The negative values of F 22 and F 11 are unphysical.The asymptote at F 11 = 108.39N m À1 represents the value of that force constant below which a negative, unphysical value of F 22 is required to fit the centrifugal distortion constants D 0 J .The asymptote at F 22 = 31.26N m À1 is the value of this force constant in the limit F 11 = N N m À1 , that is when the MX molecule is rigid.It can be shown50 that if both PH 3 and AgI were rigid and unperturbed on formation of H 3 PÁ Á ÁAgI eqn (3) leads to the Millen eqn (4), when equilibrium spectroscopic constants are used in the latter.

Table 1
Observed spectroscopic constants a of H 3 PÁ Á Á 107 AgI and H 3 PÁ Á Á 109 AgI a Numbers in parentheses are one standard deviation in units of the last significant digits.b Standard deviation of the fit.c Number of hyperfine frequencies included in the fit.

Table 2
Some properties of H 3 P and Ag-I Ref. 44. b Ref. 55. c Calculated by fitting the zero-point rotational constants using the program STRFIT (ref.45).d Calculated from the equilibrium vibrational wavenumber o e given in ref. 51 by using the expression F AgI = 4p 2 o e 2 c 2 m AgI , where m AgI = m Ag m I /(m Ag + m I ).