J. CHEM. SOC. FARADAY TRANS., 1994, 90(21), 3205-3212 Non-reactive Interaction of Ammonia and Molecular Chlorine : Rotational Spectrum of the 'Charge-transfer' Complex H,N. GI, A. C. Legon," David G. Lister? and Joanna C. Thorn Department of Chemistry, University of Exeter, Stocker Road, Exeter, UK EX4 4QD The ground-state rotational spectra of five isotopomers of the 'charge-transfer' complex H,N- -.CI, have been observed by pulsed-nozzle, Fourier-transform microwave spectroscopy. The complex has C,, symmetry with the nuclei in the order H,N- .CI-CI. A detailed analysis of the CI nuclear quadrupole hyperfine structure in tran- sitions of H31 5N- * -35C12, H315N. 37CI, and H3l5N. . *37CI35CIgave the rotational constant, B,, the centrifu- gal distortion constants D, and D,, , and the nuclear quadrupole coupling constants x(CI,) and x(CI,) (i = inner, o = outer) in each case.Theodistance r(N. * .CI,) was obtained by an r,-type method and an r,-type method and lies in the range 2.73 k 0.03 A. A detailed analysis that allowed for bond shrinkage on isotopic substitution in the 35CI, subunit of H315N..-35CI, gave the r,-type coordinates of Cli and CI, and hence the distance rs (CI-CI) = 2.00 A. This value is very close to that in free CI, and indicates only a slight perturbation of this subunit when the complex is formed. The relatively small intermolecular stretching force constant, k, = 12.71(3) N m-' determined from D, and the weak perturbation of x(Cli) and x(CI,) from the value in free CI,, reinforce this conclusion.The observed difference x(~~CI,) -~(~~cl,)= 13.99 MHz can be interpreted in terms of a trans- fer of 0.064efrom Cli to CI, on formation of H,'5N-..35C12. It seems likely that the molecular interaction is mainly electrostatic in origin and charge-transfer effects are small. The nature of the initial non-reactive interaction of a pair of extent of electric charge redistribution attending complex for- simple molecules that can readily undergo a subsequent mation. mutual chemical reaction is of special interest in chemistry. One way to characterise a complex such as H,N- * -C1,is Ammonia and chlorine are examples of reactive substances through its rotational spectrum.' The spectroscopic proper- whose non-reactive interaction has received attention.Mulli- ties thereby obtained refer to the molecule in isolation and ken, in his theory of electron donor-acceptor interactions,' are therefore more appropriate for comparison with the classified complexes H,N-..X, as being of the n.ao type, results of ab initio calculations. The changes in the C1 nuclear where n signifies dative electrons from a non-bonding pair on quadrupole coupling constant of C1, induced by bringing N while aa indicates that an antibonding o orbital of X, acts NH, up to its equilibrium position in H,N. * eC1, will be of as the electron acceptor. In discussing chemical reactions in particular interest because the coupling constants in the systems such as NH, + I,, he further distinguished between complex give, by simple proportionality, the electric field gra- weak 'outer' complexes H,N- '1, and strong 'inner' com-dients at the nuclei to which they refer.The technique of plexes [H,NI]+I-, the latter postulated as favoured in, for pulsed-nozzle, Fourier-transform microwave (FTMW) spec- example, polar solvents.' The extent of charge transfer in troscopy," with its combination of high sensitivity for com- molecular complexes thereby became a topic of central sig- plexes and high resolution, is particularly appropriate here, nificance. but its application to mixtures of NH, and C1, is made diffi- Originally, Mulliken used the name 'charge-transfer cult by the chemical reaction between the two components. complexes' to describe the very wide range of systems that The reaction between ammonia and chlorine has been fell within the various classes of complex he identified.' Fol- known for many years.It was used, for example, by lowing the demonstration by Hanna3p4 that electrostatic Hofmann' in his classic demonstration of the composition forces made important contributions in at least some cases, of ammonia but the reaction is clearly not simple. Noyes and Mulliken and Persons conceded in 1969 that the extent of Lyon" argued that although the stoichiometry is 8NH3 charge transfer may have been overestimated in weak corn- + 3C1, = N, + 6NH4Cl for the reaction when aqueous plexes such as those in the bnaa class (ie.those with a n-ammonia drops into excess chlorine gas, nitrogen trichloride bonding orbital acting as donor to a o-antibonding orbital as is produced as an intermediate but subsequently decomposes.acceptor) and that a more descriptive name is electron When the gases are mixed under carefully controlled condi- chloramine (NH,CI) is a sig- donor-acceptor complexes. Nevertheless, the charge-transfer tions of relative compo~ition'~ interaction was still viewed as significant in n.ao complex- nificant product while NCl, results if C1, is in excess. To es of the H,N-..X, type, especially when X = I. Some theo- observe the rotational spectrum of H,N.-.Cl, in an retical attempts to gauge the relative importance of the NH,-Cl, gas mixture, such reactions must be inhibited. various contributions (electrostatic, polarisation, exchange, In the work reported here, the ground-state rotational dispersion and charge-transfer) to the interaction energy fol- spectra of several isotopomers of H,N.-.Cl, have been con-observed by using a fast-mixing in our FTMW spec-lowed.6-8 For example, Morokuma and co-worker~~.~ cluded that H3N...C1, is a weak complex in which the trometer.This type of nozzle allows the components to electrostatic and charge-transfer terms make contributions of remain separate until the point of their simultaneous coaxial comparable importance. Others emphasised the importance supersonic expansion. Complexes H,N. --C1,produced in of electrostatics.8 It is clearly desirable to characterise this way achieve collisionless expansion in ca. 10 ps and their H,N. ..C1, experimentally and to seek evidence about the spectra can then be observed while progress along the reac- tion coordinate is temporarily frozen. Molecular properties t Permanent address : Dipartimento di Chimica Industriale, Uni- derived from the spectral analyses with the aid of suitable versita di Messina, Salita Sperone 31, Casella Postale 29, 98166 Sant' models of H,N- .-Cl, allow a reasonably detailed character- Agata di Messina, Italy. isation of this species which complements our identification 14 643.9 14 6U.1 14 644.3 frequency/M Hz Fig.1 Frequency-domain recording of three Cl nuclear quadrupole hyperfine components in the J = 4 t3, K = 0 t0 and K = 1 t1 transitions of H3’’N..-35C12.Points are spaced by 3.90625 kHz and have been joined by straight lines.The stick diagram indicates the relative intensities of the three components calculated by assuming an effective temperature of 300 K for the distribution between the K = 0 and K = 1 states. Observed relative intensities are unreliable because of the very high Q of the Fabry-Perot cavity. For assignment of quantum numbers, see Table 1. of this prototype system in the gas phase reported in a pre- liminary communication. ’ Experimental The ground-state rotational spectrum of H,N- * sC1, was observed with a pulsed-nozzle, FTMW spectrorneterl6 of the Balle-Flygare design’ operating in the conventional con- figuration with the axis of the nozzle perpendicular to the axis of the Fabry-Perot cavity. To avoid a reaction between NH, and Cl,, a fast-mixing nozzle14 was used.Chlorine gas (Aldrich) was flowed continuously through a glass capillary from a reservoir held at a pressure of ca. 200 Torr to give a nominal pressure of CQ. 1 x Torr in the evacuated Fabry-Perot cavity. The outlet of the capillary was coaxial and coterminal with an outer Teflon tube down which was pulsed a mixture of 2% ammonia (Argo International) in argon. The pulses were repeated at a rate of 2 Hz and the gas was held at a stagnation pressure of 3 atm. The two com- ponent gases were thus kept separate until they simulta- neously expanded into the cavity. Complexes H,N. .C1, formed at the interface between the concentric gas flows were then polarised by pulses of MW radiation in the usual way and the subsequent free-induction decay detected as described elsewhere.16 15NH3 (Aldrich) was used in order to J.CHEM.SOC. FARADAY TRANS., 1994, VOL. 90 simplify the hyperfine structure in transitions and make the spectral analysis more straightforward. Three nuclear quadrupole components of the J = 4 +3 transition of H315N. -35C12 are shown in Fig. 1. This illus- trates that no Doppler doubling is observed when the fast- mixing nozzle is used and that individual hyperfine components had a half-width at half maximum of 16 kHz. Accordingly, frequency measurements had an estimated accu- racy of approximately 2 kHz. Results Spectroscopic Analysis The initial search for H,N. -Cl, with isotopically normal NH, and C1, led to the observation of a very rich, rather weak spectrum.The richness arose from the presence of hyperfine splitting generated by the presence of three quadru- polar nuclei (14N and the two Cl nuclei) coupled with the near coincidence in frequency of the hyperfine patterns of the isotopomers H314N. ”Cl 35Cl and H314N- --37Cl ,’Cl that results from the closeness of the inner chlorine nucleus to the dimer centre of mass. This spectrum was not analysed in detail. Instead, the estimated unperturbed centres of two con- secutive J + 1+J transitions were used to obtain B, and this was fitted with a model of CJv symmetry in which monomer geometries were assumed unchanged to give r(N. XlJ. The frequencies of the transitions of the spectro- scopically more tractable species H315N- --C1, were then pre- dicted with this r(N.-C1,) and the model.15 The ground-state rotational spectra of the isotopomers H315N.. .35C135Cl, H3’5N.. .37C135CI and H3’5N.. . ,’Cl ,’Cl were observed near to the predicted frequencies. Each was unmistakably that of a symmetric-top molecule carrying two Cl(I = 3) quadrupolar nuclei on the molecular symmetry axis. Frequencies of the observed nuclear quadru- pole hyperfine components in J + 1+J, K tK transitions having J = 1, 2 and 3 and K = 0 and 1 for the isotopomer H,”N. * -,’Cl are given in Table 1, while the same tran- sitions of the H315N. s. 35Cl 37Cl and H3I5N- -37Cl iso- topomers are collected in Table 2. Transitions having K > 1 were not observed, presumably as a result of collisional depopulation of higher K states in the supersonic expansion. No attempt was made to measure the weak transitions associated with the least abundant isotopomer (H,”N.--j7Cl wl) in the 15NH,-C1, mixture for reasons of cost. For each observed isotopomer, the hyperfine frequencies (as given in Tables 1 and 2) were fitted in an iterative least- squares analysis to give the rotational constant, B,, the cen- trifugal distortion constants, D, and DJK, and the nuclear quadrupole coupling constants, X(C1,) and ~(cl,), where i and o delineate the inner and outer chlorine nucleus, respectively. The Hamiltonian, H = H, -*Q(ClJ :VE(C1J -iQJC1,) :VE(C1,) (1) where H, is the familiar energy operator describing the rota- tion of a semi-rigid symmetric-top molecule, was constructed in the coupled basis Ii+ Z, = I; Z + J = F and diagonalised in blocks of F in the usual way.A convenient source of the matrix elements of the terms -&(Cl,) :VE(C1.J describing the interaction of the C1 nuclear electric quadrupole moment Q(C1,) with the electric field gradient VE(C1,) at nucleus x (x = i or 0)is given in the paper of Keenan et ~1.’~For a prolate symmetric-top molecule, only the component x(C1,) = -eQB2V/Bzzis observable. The residuals from the final cycle of the least-squares fits are given in Tables 1 and 2 while the corresponding sets of J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 1 Observed and calculated transition frequencies of H,l5N*..35Cl, 24-1 0 344-34 7287.1206 0.7 1 3 44-3 3 7293.0984 0.9 0 334-12 7308.4248 0.3 1 244-23 7321.0587 0.5 1 234-22 7321.1320 -0.3 0 234-22 7321.2282 -6.2 0 234-23 73 2 1.3703 9.4 0 244-23 7321.435 1 1.o 0 354-34 7326.072 1 0.9 1 354-34 7334.2598 1.8 3+-2 0 354-35 10948.1828 0.8 0 224-02 10953.3150 -1.9 0 234-23 10953.8482 -0.4 1 3 54-3 5 10959.9779 -1.1 0 324-31 10960.2965 -7.7b 1 234-23 10960.3 194 0.9 0 324-12 10966.5867 -0.3 0 334-32 10968.1439 0.8 1 344-34 10968.2712 -0.6 1 334-32 10970.901 1 0.0 1 3 44-3 3 10972.2265 -0.7 0 344-34 10972.4306 0.0 1 324-3 1 10974.6626 0.8 1 23+-22 10974.8323 0.2 0 314-31 10976.7090 0.1 1 124-1 1 10977.7386 -3.1 0 144-13 10978.3364 -1.1 1 354-34 10979.3309 -0.2 0 134-12 10979.3641 8.0b 0 344-33 10980.08 18 -0.7 1 144-13 10980.6039 -1.4 0 034-02 10980.9505 -0.5 1 224-21 10981.0643 -1.2 1 244-23 1098 1.2435 0.0 1 254-24 10981.4404 -0.9 0 244-23 10981.7753 0.2 0 254-24 10982.0335 -1.0 0 234-22 10982.9742 0.7 0 364-35 10984.5937 1.4 0 124-11 10984.6456 -6.1b 1 334-33 10986.6 193 0.3 0 354-34 10987.1324 -0.9 1 3 64-3 5 10987.2401 1.o 1 134-1 2 10987.2753 -1.0 1 034-02 10987.7027 -0.6 1 32t32 10993.5882 2.2 0 324-32 10998.3095 -1.0 0 334-33 10999.2569 0.8 0 22t22 11010.8823 -2.0 44-3 1 13t33 14635.3431 -1.1 1 344-33 1463 5.6670 -0.2 1 33t32 14636.9709 2.7 0 344-33 14637.0522 1.6 1 324-31 14637.0522 -1.7 1 35-34 14638.4578 -0.7 1 244-23 14639.1835 -0.7 1 134-1 2 14639.7238 -1.0 1 154-14 1464 1.0701 0.1 1 234-22 14641.405 1 4.6 1 254-24 14641.4779 0.7 1 264-25 14641.7414 1.3 0 144-13 1464 1.7936 -3.0 0 044-03 14642.2422 1.4 0 254-24 14642.2636 -0.6 0 264-25 1 4642.541 6 0.3 0 354-34 14642.5739 1.9 1 364-35 14642.6163 0.1 0 244-23 14642.8629 -1.0 1 144-1 3 14643.9967 1.4 0 374-36 14644.1 549 -0.3 1 044-03 14644.2074 -2.7 1 374-36 14644.9184 -0.1 0 364-35 14645.7608 0.2 a Av = vOb -vcalc.Omitted from fit, see text. spectroscopic constants are in Table 3. Certain transitions were omitted from the fits because of overlap with stronger transitions nearby which caused uncertainty in their fre- quency measurement. The standard deviations of the fits, included in Table 3, are of the same order as the estimated experimental error and are therefore satisfactory.Attempts to include terms describing the spin-rotation coupling of the C1 nuclei in the fit did not improve the residuals and led to inde- terminate coupling constants. Also included in Table 3 are the quantities x(~'C~,)(~~Q/"'Q) i.e. 37Cl nuclear quadrupole coupling constants scaled by the known ratio'' of the nuclear electric quadrupole moments of 35Cl and 37Cl. We note that for both H,15N. -* 37C1 35C1 and H315N-. .35C1 37C1 the scaled value agrees with that of the appropriate nucleus in the other (H,N, 35Cl 37Cl) isotopomer, indicating that the fitting procedure is in order. We note also that isotopic sub- stitution at one C1 nucleus in H,'5N-. .35Cl 35Cl leaves the coupling constant at the other C1 nucleus essentially unchanged. Rotational constants estimated from the approximate centre of the very rich hyperfine structure in two consecutive J + 1 tJ transitions of the isotopomers H314N..* ,'Cl, and DH214N-..35Cl, are also included in Table 3. A detailed analysis of the species DH214N- ,'Cl, was not made for the -a reasons discussed above in connection with H, 14N. * * 35Cl,. Molecular Geometry and Nature of the Interaction The fact that H,N. ..Cl, is a symmetric-top molecule, coupled with the observed changes in the rotational con-stants, B,, on isotopic substitution in H315N. -.,'Cl 35Cl, is consistent only with a geometry of C,, symmetry with the order of the nuclei indicated, as discussed in more detail in ref.15. There is definite evidence that the interaction between NH, and C1, is not strong and leads to only a weak perturbation of the C1, bond length from its free molecule value. It has been shown" for weakly bound complexes that, in the quad- ratic approximation and with the assumption of rigid sub- units, the centrifugal distortion constant, D,, of a symmetric-top molecule like H,N. --Cl, is related to the intermolecular stretching force constant, k, ,by k, = (16n2pB~/D,)(1-B0/BNH3-B,/BC'Z) The k, values determined from the D, and B, values for each of the three isotopomers, H3I5N--* 35Cl ,'Cl, H315N...37C1 35C1 and H315N. -35Cl 37Cl, when used in eqn. (2) are given in Table 4. The ground-state rotational con- stants, BtH3and Bg'z, of the free molecules NH, and Cl,, which are collected with various other monomer properties in Table 5, were used in the evaluation.20*2' The conclusion from the k, values of H,N.-.Cl, is that the strength of binding, as gauged by the intermolecular stretching force constant, is reduced by about one third from that2' of the hydrogen-bonded species H,N.-.HCl and is similar in mag- nitude to that23 of H,O. * -HCl. On this basis H,N. * eC1, is a rather weak complex and large perturbations of the C1, bond length, for example, on its formation do not seem likely. In principle, the availability of rotational constants for H315N.. -35C135C1, H315N.. -37C135Cl and H3'5N.. . 35Cl 37CI allows the T, coordinates of the chlorine nuclei and hence the rs bond length of Cl,, within the complex, to be determined. The simplest possible approach is Costain's methodz4 which uses ground-state moments of inertia in Kraitchman's equation, a; = AI:/pL, (3) J.CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 2 Observed and calculated transition frequencies of H3”N. .* 37Cl ”Cl and H3l5N*. .”Cl j7CI H315N.. .37C135Cl H315N.. .35c1J7C1 Av/kHz“ v,,,$MHz Av/kHz“J’ 4-J” K I’ F’ 4-I” F” VobJMHz 24-1 1 244-23 73 18.7272 -0.5 7 161.4682 2.0 0 244-23 73 19.1 154 0.7 7 161 S927 0.3 0 35-34 7 3 2 3.2 39 8 0.9 7165.4933 0.6 1 354-34 73 30.4540 -0.5 7172.8433 -1.5 3+-2 3 054-35 10948.5730 -0.2 0 334-32 10966.2462 2.7 10729.4673 -0.6 1 344-34 10966.2907 -2.0 --1 334-32 10968.633 1 -0.3 10731.8987 -1.0 1 344-33 10969.8020 1.5 10733.051 7 1.1 1 234-22 10972.1237 1.7 10735.2769 -0.9 1 124-11 10974.7003 -4.2 10737.9719 1.5 1 324-12 --10738.0843 -0.5 0 034-12 --10738.7826 0.3 0 144-13 10975.26 18 2.3 10739.3684 -0.4 1 354-34 10976.1294 -0.8 107 39.0629 -0.8 0 344-33 10976.8399 -1.3 10740.2699 -0.8 1 144-13 10977.2104 0.7 10741.2269 -1.0 0 134-02 --10741.4326 2.3 0 034-02 10977.5917 -2.5 1 24-23 10977.8440 1.3 10740.3 770 0.5 1 254-24 10977.9680 -1.4 10741.6354 -0.3 0 224-21 10978.3951 3.4 0 244-23 10978.3951 -2.7 10740.6378 -1.0 0 254-24 10978.5685 0.9 10742.0995 0.4 0 214-21 10978.5685 -0.6 0 23-22 10979.4122 1.o 10742.7 169 0.5 0 364-35 10980.8473 0.6 10744.1706 0.6 0 12-11 --10744.4163 -1.7 1 334-33 10746.1700 1.9 0 354-34 10983.1078 -4.5 10746.2270 0.6 1 364-35 10983.1292 3.3 10746.5197 -1.2 1 134-12 10746.5720 -0.7 1 034-02 10983.5564 -1.3 10746.8955 -0.2 0 334-33 10993.8434 1.6 10757.7508 0.0 44-3 1 354-34 14634.2203 -0.5 14318.6330 -0.6 1 244-23 14634.8666 -0.9 143 19.2376 1.6 1 134-12 14635.3431 0.9 1 154-14 14636.4857 -10.5” 1 234-22 14636.8986 2.8 1 254-24 14636.9434 -2.4 0 154-14 14636.7619 -0.2 1 264-25 14637.1232 0.6 14321 3221 -1.1 -1 254-14 -14321S374 -1.6 1 224-21 14637.0522 7.9 0 264-25 14637.9271 0.5 14322.5327 1.3 0 354-34 --14322.3970 -3.5 1 364-35 14637.9271 2.1 14322.0935 2.4 0 374-36 14639.3681 0.2 14323.7828 0.8 1 04co3 14639.3151 -1.3 14323.9225 -0.3 1 374-36 14639.9542 0.4 14324.4256 0.4 0 364-35 14640.8003 -1.9 14325.0259 1.o ~~~ ~~ ~ ~ ~~ a Av = vObs -v,,,~.” Omitted from fit, see text. Table 3 Ground-state spectroscopic constants of five isotopomers of the ammonia-chlorine dimer H315N-..35Cl, 1830.355 1( 1) 1.347(4) 101.13(7) -115.785(7) .-101.794(7) 1.9 ~,15N.. .35C137cl 1790.32625(8) 1.262( 3) 96.67(4) -115.810(6) -80.227(7) 1.3 -101.799* ~~15~...37C135cl 1829.7798( 1) 1.33 7(4) 101.12( 7) -9 1.27( 1) -101.8q1) 2.0 -115.812” H314N.*. 35Cl, 1889.6(3)’ H,D 14N. ..35C12 18 13.9(5)’ ~~ ~ ~~~~~ a The niare the standard deviations of the fits reported in Tables 1 and 2. ~(~~cl)multiplied by the ratio of 35Q/3’Q from ref. 18. Calculated from estimated v, values of the J = 3 4-2 and J = 4 +3 transitions, with D, held at 1.35 kHz.For the species H2D 14N. * .35C12 the reported quantity is ca. (B, + C,)/2. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 4 Molecular properties of three isotopomers of the ammonia+hlorine dimer ~~~ ~ ~~ H3"N.. .35C12 3.789(3) 2.730(3) 12.7 1( 3) H3"N*. .35C1 37C1 3.812(3) 2.73 l(3) 12.74(3)H315N** * 37Cl "Cl 3.761(3) 2.73 l(3) 12.74(3) appropriate to substitution of an atom, i, on the symmetry axis, a, of a symmetric-top molecule to give a change, AIF, in the principal moment of inertia, 1,. In eqn. (3) ,us= AmM/ (Am + M) and is the 'reduced mass' for the substitution. The results for a(C1,) and a(Cl,) when the rotational constants B, (=h/8z21,)from Table 3 are employed in eqn. (3), are given in the second column of Table 6.Physical sense dictates that a(Cli) and a(C1,) must be of opposite sign. The C1, subunit in the zero-point state of H,N. * .C1, will be undergoing an angular oscillation, B, of the type defined in Fig. 2. Since /I,, = COS-~(COS~/I)"' = 7.5" is available (see next section), an estimate of the Cl-Cl bond length in the zero-point state can be obtained from r(C1--1) = (a(C1,) -a(Cl,)>/cos #I,,and this value is also included in Table 6. Given that the value of rs(Cl-Cl) in the free chlorine mol- ecule is 1.9920 A (see Table S), this naive approach leads to the conclusion that the formation of the complex barely changes the chlorine molecule bond length. However, eqn. (3) leads to errors for two reasons. First, it is not well suited to application to weakly bound complexes and in any case a(C1,) Table 6 CI-C1 bond length in H315N.. .35C12, calculated by three methods modified r, method coordinate modifiedb + bond or distance/A rs method" rs method shrinkage' ~~ ~~ ~~~~ ~ 4c13 -0.2109 -0.1899 -0.2050 1.7780 1.7757 1.7766 4cij -4c1j 1.9889 1.9656 1.9882 r(C1-Cl) 2.006 1.9826 2.005 Calculated using eqn.(3). 'Calculated using eqn. (4), with pa, = c~s-~(cos'/3)"' = 7.5" (see text for discussion). 'Calculated as in but allowing the bond to the C1 atom to shrink by 5 x 8, on 37C1substitution (see text for discussion). Fig. 2 Model used to discuss the geometry and internal dynamics of H3N**C1* is small and Costain's method is known to underestimate small coordinates significantly.A more sophisticated approach to r, coordinates of atoms on the symmetry axis of weakly bound complexes like H,N...Cl, takes into account the fact that the C1, subunit undergoes an angular oscillation of the type shown schemati- cally in Fig. 2 even in the zero-point state. The atoms Cli and C1, execute a circular motion in the plane perpendicular to the line between the two subunit mass centres and the mass of each atom is assumed to be spread evenly over the circle. It can then be shown26 in the case of a linear molecule B...Cl, that the Q coordinate of each atom is given by a Kraitchman-like expression a; = (AI:/p,) -(AZf(sin2 /I)/2pL,) (4) where AI: and AIT are changes in the zero-point moments of inertia of the dimer and monomer, respectively, that accom- pany the isotopic substitution.It is assumed in the derivation of eqn. (4) that (sin2 #?)is insignificantly changed by isotopic substitution and that a similar equation to eqn. (4) applies to isotopic substitution of an atom on the symmetry axis of a symmetric-top molecule. We show in the next section that a reasonable estimate of /I,, = COS-~(COS~#?)'j2 is 7.5". When this is used in eqn. (4), the values of a(Cli) and &lo) that result are those given in column 3 of Table 6. Although the change in a(C1,) from the value estimated using eqn. (3) is very small, the smaller coordinate, u(ClJ, becomes consider- ably reduced in magnitude. We note also from Table 6 that r(C1--1) estimated from these modified r, coordinates is now smaller than in free Cl,.If the complex H,N. eC1, is of the n.aa type, electron donation to a a-antibonding orbital should weaken, and therefore presumably lengthen the C1, bond. This unexpected shortening arises, however, from a serious underestimate of the coordinate a(C1,) when either eqn. (3) or (4) is used to estimate it. It is well known that substitution of an atom by a more massive isotope leads to an effective shrinkage of the bonds in which the substituted atom is involved. For example, iso- topic substitution of "C by 13C in CO, leads to a decrease27 in 1, in the zero-point state and hence to an imaginary rs coordinate of C. By assuming that each C-0 bond shrinks by 5 x lo-' A as a result of the isotopic substitution, the correct values AI, = 0 and a(C)= 0 are obtained.To investi- gate the effects of bond shrinkage in H,N--.Cl,, we assume that both r(N.aC1) and r(C1-Cl) shrink by 5 x lo-' A when 37Clreplaces ,%l. This value is the difference in ro between 3'C179Br and 37C179Br, i.e. the shrinkage in BrCl that attends the corresponding isotopic substitution." The reason for using BrCl is that the necessary rotational con- stants are better characterised for this molecule than for C1,. The procedure is to find a value of r(N.*.Cl) for H, "N-. -,'C12 that reproduces the observed B, when unchanged monomer geometries2'V2' (see Table 5) are assumed and use it to calculate B, for H315N.--37C135Cl. The bonds N.-.Cl and Cl-CI are then allowed to shrink and the new value, Bb, for H3"N. -,'Cl ,'Cl calculated.The correction AXF = 1; -1, is then added to Iibs and the corrected moment of inertia used in eqn. (4) to give a(C1,) Table 5 Molecular properties of the monomers NH, and C1, B,/MHz C,/MHz ro/A -= HNHldegrees XoIMHZ 35~135~1 7287.95(60)" -1.99 15( 1)" 1.992od --11 1.7904(38)' 35~137~1 7090.99(60)" -1.991 7( 1)" ---"NH3 297388.12' 187W 1.0156' -107.28b -I4NH3 298 11 5.37' 187W -" Ref. 21. * Ref. 20. 'Calculated from the geometry given in ref. 20. Estimated from the B, values using eqn. (3). Ref. 29. corrected for shrinkage effects. A similar procedure was applied to correct a(Cl,), except that only shrinkage of the Cl-Cl bond was assumed. The results are given in column 4 of Table 6.We note that r(C1--1) is now only very slightly in excess of the free molecule r,-bond length of chlorine. It has to be admitted that the assumption of the same shrinkage in the r(N...Cl) and r(Cli-Clo) distances on iso- topic substitution at Cli is somewhat arbitrary. Fortunately, however, the results given in column 4 of Table 6 are not very sensitive to the shrinkage assumed for r(N.-.Cli). For example, when this shrinkage is taken as zero while a shrink- age of 5 x A is assumed for r(Cli-Clo), the result is r(C1--1) = 1.9917 A. Thus, the arguments in the preceding paragraphs, when taken together, provide some evidence that the geometry of the Cl, molecule is only slightly perturbed when it is incorporated in the weak complex H,N.sC1,. Although the change AZb accompanying isotopic substitu- tion by 14N in H315N-. . 35Cl, is not well determined because of the crude method of estimation of B, for the species H314N.. .35Cl, (see above), it is still possible to use eqn. (4), but replacing 8 by a, to obtain a value for the rs coordinate of 15N in the principal inertial axis system of H,'5N.-.35Cl,. We assume a,, = sin-'(sin2 = 15", a reasonable choice that is justified below and to which the conclusions are rela- tively insensitive. The necessary rotational constants are in Tables 3 and 5. The result is then 4N) = -2.96(3) A, where the relatively large error follows from that in the Bo value of H314N.1 .j5CI,. This coordinate is sufficiently large that the correction for bond shrinkage is negligible compared with the other sources of error.The corresponding value of a(N) -a(C1,) is 2.75(3) 8, but this is the distance between the two rings described by the N and Cli atoms. An estimate of the equilibrium distance r,(N. .C1) (i.e. that corrected for the angular oscillations a and fi),is then r,(N. * .Cl) = Ia(N)I -r(1 -cos a,,) -Ia(C1Jl + r'(1 -cos Pa,) (5) where r and r' are the distances of the N and Cli nuclei from their respective subunit mass centres measured along the molecular symmetry axis and are available from the geomet- ries in Table 5. The value r,(N. -.C1) = 2.74 (3) A is obtained in this way. Once it can be assumed that the NH, and Cl, subunit geometries are not significantly perturbed by formation of H2N...C1,, it is possible to estimate r(N-..Cl) by another route.When rigid subunits are assumed to execute angular oscillations a and pivoted at their mass centres, as described in Fig. 2, and the separation rcmof the mass centres is assumed fixed, it is readily shown that IF of the dimer is given in good approximation by 1: (Ibb) = p(I,?m)1'2+ 31rH3(i+ (COS' a)) + +IrH3(sin2a) + 3ZF'2(1 + (cos2 8)) (6) where IFH3,ZFH3 and Ip2are principal moments of inertia of the monomers (available from the rotational constants20J1-f in Table 5), IF refers to the dimer (Table 3) and ,u = + mNH3). Using pa, = COS-~<COS~(mC12mNH3)/(mC12 /3)"2 = 7.5", the vdues of (r,?,,,)'/2shown in Table 4 are obtained for the three isotopomers of H3l5N.* .C1, investigated. A partial equilibrium distance r(N. * .ClJ (i.e. that corrected for the angular oscillations a and /3) is then given by r(N*. *Cli) = (r:m)1'2 -r' -r (7) t The rotational constant, C, for NH, isotopomers was calculated from the geometry given in ref. 20. J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 where r and I' are as defined previously. The results for r(N. -.Cli)so obtained are included in Table 4 and are seen to agree, within experimental error, with the value rs(N. -ClJ = 2.74 (3) A estimated from eqn. (5). The justification of the choice fi,, = 7.5"is made in the next section. The value a*, = 15" is that2, appropriate to H,N...HCl . In fact, the results in Table 6 are not strongly dependent on ct,,, a change of 2" in this angle corresponding to a change of only 0.003 8, in r(N.-*Cli). C1 Nuclear Quadruple Coupling and the Nature of the Interaction The intermolecular interaction in H,N- * .C1, is relatively weak, as established in the previous section by consideration of the force constant, k,, and the small perturbation of the C1-C1 bond length. Further evidence about the nature of the interaction is available from the Cl nuclear quadrupole coup- ling constants. We note from Table 3 that x(Cli) and x(C1,) for H,'5N..-35C12 are changed from the value of the coupling constant in free 35C1, (Table 5), but not greatly.28 This is further evidence of a weak interaction. Several factors contribute to the change in x(C1) on complex formation.First, when NH, is brought up to its equilibrium position along the C1, molecular axis its electric charge distribution will cause x(C1,) to increase in magnitude but x(C1,) to decrease in magnitude from the free molecule value, xo(Cl). This change arises from the additional electric field gradients at the C1 nuclei along the z axis resulting from the response of the Cl, electronic distribution to the electric field and its gradients due to NH,. To model the changes, the various response tensors of Cl, and the electric charge distribution of NH, are required and are being calc~lated.~~ Secondly, the x(C1) will change if there is any charge transfer between H3N and C1, . Thirdly, in the absence of any electri- cal effects, both x(Cli) and x(C1,) in the zero-point state of the complex would be reduced from the free molecule value through the angular oscillation /3 of the C1, subunit (see Fig.2) alluded to in the previous section. The necessary expres- sion in that case would be x(C1,) = +x0(c1)(3 cos2 /3 -1) (x = i or 0) (8) A deconvolution of the various effects contributing to the difference x(ClJ -x(C1,) must await a satisfactory modelling of the response of the C1, electronic distribution to the NH, subunit but some progress is possible with the aid of some recent ab initio calculati~ns.~~~~~These have shown that in molecules such as H,N. -.35Cl, and 14N2. -.HX (X = CN, CSCH) the mean value of the two 35Cl or 14N nuclear quadrupole coupling constants of or 14N, in the equi- librium conformation of the complex differs by less than 1% from the coupling constant of the free molecule 35Cl, or 14N2, even though the inner and outer atom coupling con- stants are changed by several percent.In H,"N. * -,%12, the observed mean value of the zero-point coupling constants is $(x(Cli)+ x(C1,)) = -108.790(7) MHz. If all of the difference of this quantity from the free molecule value,29 x0(35Cl) = -111.7904(38) MHz, is then attributed to the zero-point angular oscillation /3 of the C1, subunit (see Fig. 2), eqn. (8) leads to pa, = COS-~(COS~/3)'/2 = 7.5", which constitutes the justification for the assumption of this value of /la,in the dis- cussions of molecular geometry in the previous section.Another important property can be derived under the assumption that ${x(Cl,) + x(C1,)) is unaffected by the electric charge distribution of the NH, and hence differs from xo(Cl) only through zero-point averaging. The property in question is the mean fractional change,f, in the electric field gradient J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 (efg) of the inner and outer Cl nuclei as a result of bringing NH, up from infinity to its equilibrium position in the complex and is given by f = [Xe(Cli) -~e(C1o)l/[~e(C1J+ xe(C1o)I += Cx(Cli) -~(Clo)l/C~(Cli)~(Cl0)l (9) In eqn. (9), xe(C1,) = -eQa2V/di? is the equilibrium value of the C1 nuclear quadrupole coupling constant at the nucleus, x, and -a2V/dz2is the equilibrium efg along the dimer sym- metry axis z.The second equality in eqn. (9) holds in the approximation that the effects of zero-point averaging cancel between the terms in the numerator and denominator. The resulting value off for H,N. . ,'Cl, is 0.064 and indicates only a small electronic charge redistribution on formation of the complex. Discussion The ground-state rotational spectra of five isotopomers of the complex H,N..-Cl, have been observed by the pulsed-nozzle, FTMW technique. The symmetric-top nature of the spectrum and the changes in the rotational constant, B,, of the species H,I5N. --,'Cl, accompanying isotopic substitu- tion at each inequivalent atom in turn are consistent only with a geometry of C,, symmetry in which the atoms lie in the order indicated.The distance r(N...ClJ has been obtained by two different methods, one of the r, type and the other of the ro type, and lies in the range 2.73(3) A. Ab initio calculations lead to values ranging from 2.57 A to 2.93 A for this A detailed analysis that allowed for the effects of bond shrinkage on r,-type coordinates gave a value r,(Cl-Cl) = 2.00 A,establishing that the geometry of the Cl, subunit is only slightly perturbed when the complex is formed. This conclusion is reinforced by the relatively small value of the intermolecular stretching force constant, k, , and the weak perturbation of the C1 nuclear quadrupole coupling constants that attends complex formation. The observed dif- ference ~(Cli) -x(C1,) in fact corresponds to a mean frac- tional change of only f= 0.064 in the efgs at the inner and outer nuclei.This also suggests that the extent of any charge transfer between the NH, and C1, subunits is likely to be small. It has been indicated elsewhere31 that for all complexes B...Cl, so far investigated in detail by rotational spectros- copy, the angular geometry for a given B is identical with that of the corresponding member of the series B. * -HCl. In addi- tion there is a systematic relationship of the distances r(B. . .C1) and of the k, between the two series. This parallel behaviour has been interpreted31 as indicating that the empirical rules3' and the electrostatic model3, used suc-cessfully to describe the series B...HCl also apply to the series Be eC1,.Of course, the simple electrostatic model implies that polarisation of one molecule by the other is unimportant in determining, for example, angular geometry. In fact, the small value of f= 0.064 in the most strongly bound member of the series Be. .Cl, so far investigated (B = NH,) provides evidence of, at most, only small reorganisation of electric charge and hence further support for the electro- static model. The quantity,f, can be interpreted in terms of the extent of electric charge redistribution within the C1, subunit on the basis of the Townes-Dailey if charge transfer from NH, to C1, is assumed negligible. According to the Townes- Dailey model in its simplest form, a transfer of a 3p electron from Cli to C1, to give Cli+.-eC1,-would lead to C1 nuclear quadrupole coupling constants of ~(Cli) = -223 MHz and x(C1,) = 0 MHz. These values in eqn. (9) would then give 3211 0.07-0.06-0.05-0.04-0.03-0.02-I 1 2 4 6 8 10 12 14 kJN m-I Fig. 3 Variation of the fractional change,f, in efg between Cli and C1, on formation of B.. .C1, with intermolecular stretching force constant, for the n.an complexes where B = CO, HF, PH,, HCN and NH, f= 1 and it is obvious thatfis therefore also a direct measure of the fraction of electronic charge transferred from Cli to C1, when Be * aC1, is formed. The result,f= 0.064, for H,N. -.C1, indicates only minor electric charge reorganisation. Fig. 3 shows a plot off vs.k, for all Be -.C1, complexes of the n.ac type so far investigated7 in this way, namely B = CO, HF, PH,, HCN and NH,. We note that f is a monotonically increasing, nearly linear function of the strength of the inter- molecular interaction as measured by k, . Although f is very small in all cases, the polarisation of C1, by B increases as the interaction strength increases, as might be expected. We thank the SERC, MURST (60% funds) and the EC (contract no. ERBCHRX 9301 57) for research grants in support of this work and the Ruth King Trust of the Uni- versity of Exeter for a studentship (for J.C.T.). References 1 R. S. Mulliken and W. B. Person, Molecular Complexes, Wiley-Interscience, New York, 1969 and references therein.2 R.S. Mulliken, J. Phys. Chem., 1952,56,801. 3 M. W. Hanna, J.Am. Chem. SOC., 1968,90,285. 4 M. W. Hanna and D. E. Williams, J. Am. Chem. SOC., 1968,90, 5358. 5 R. S. Mulliken and W. B. Person, J. Am. Chem. SOC., 1969, 91, 3409. 6 K. Morokuma and K. Kitaura, in Molecular Interactions, ed. H. Ratajczak and W. J. Orville-Thomas, Wiley, New York, 1980, vol. 1, ch. 2. 7 H. Umeyama, K. Morokuma and S. Yamabe, J. Am. Chem. SOC., 1977,99,330. 8 I. Rnreggen and T. Dahl, J. Am. Chem. SOC., 1992,114,511. 9 See,for example, A. C. Legon, Chem. SOC.Rev., 1990,19, 197. 10 T. J. Balle and W. H. Flygare, Rev. Sci. Instrum., 1981,52, 33. 11 See, for example, T. M. 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