COMMUNICATIONS TO THE EDITOR
2483
On a Comparison of Isotope Shifts in the Vibrational Spectrum of Gas-Phase and Matrix-Isolated Hydrogen Cyanide’ Publication costs assisted by Argonne National Laboratory, U.S. Atomic Energy Commission
Sir: Recently, Pacansky and Calder2 (PC) compared calculations of the bond-length ratio, ?CN/THC, obtained from application of the Teller-Redlich product rule to the v2 bending frequency of gas-phase and matrixisolated HCN isotopes. The deviations of the matrix values from the accepted value of 1.082 obtained from rotational fine-structure data,3 even when corrections were applied for anharmonicity, and the scatter in the ratios that they calculated from the matrix data as compared with those calculated from the “gas-phase data” led PC to conclude that “the discrepancies most likely result from the failure of the linear xyz vibrational model to describe the vibrations of the matrixisolated molecule adequately.’’ Because of the serious implication that molecular geometries, particularly of molecules containing light atoms, may be incorrectly deduced from isotope shifts of matrix-isolated molecules, we decided to reinvestigate the apparent discrepancies. The present study shows that no anomalies exist between the matrix and gas-phase data when the uncertainities in the measurements and the sensitivity of the bond-length ratio to these uncertainties are properly taken into account. Application of the Teller-Redlich product rule to v2 of two isotopes of HCN, H’C’N’ and H”C”N”, yields w2‘ 1 RE= w2“ mc’
[(
where x is the ratio of TCN t o r H c , the wz’s are zero-order bending frequencies, and the m’s are the atomic masses of the various constituent elements of the HCN isotopes. Equation 1 may easily be inverted t o obtain x as a function of R based on the observed fundamentals, vz, or the zero-order frequencies, 02, which are corrected for anharmonicity. For the six isotopes discussed by PC, 15 values of x may be calculated from the various combinations of values of v Z e 4 The bending frequencies for the gas-phase and matrix-isolated molecules, together with the rotational and anharmonic correction terms and the PC “gasphase data,” are presented in Table I. The anharmonic correction factors [= -(3xZz ‘/2(x12 x23) xzt)] have been taken from Nakagaw-a and M ~ r i n o . These ~ are subject to some error because of improper use of vz for G(O,l,O,l)- G(O,O,O,O) in the case of H1W4N. However, since their values for H12C14Nand D’zC14N do not differ significantly from those computed by Suzuki, et u Z . , ~ we have used the values of Nakagawa and Morino for all isotopes. A comparison of the 15
+
+
+
ratios of isotopic frequencies using the gas-phase, matrix-isolation, and PC “gas-phase’’ data, both corrected and uncorrected for anharmonic effects, is presented in Table 11, together with the theoretical values computed from eq 1. Values of r c N / r H c computed from these frequency ratios are shown in Table 111. The dependence of the bond-length ratio on the frequency ratio, bx/bR, has also been calculated and is shown in column viii of Table 111. For isotopic pairs in which both molecules contain hydrogen atoms or both contain deuterium atoms, the calculated bond-length ratio is seen to be 10 to 25 times more sensitive to changes in the frequency ratio than for isotopic pairs containing each a hydrogen and a deuterium atom. Although the precision of the frequency data is better than *0.05 cm-’, the uncertainties in the anharmonic corrections are calculated as h0.54 cm-’ for the H-containing isotopes and =t0.74 cm-I for the D-containing isotopes.5 The uncertainty in rCN/rHC, A s [ = ( b x / b R ) A R ] , for a probable error of * 0 . 3 cm-l in the w i s is given in the last column of Table 111. The following conclusions may be drawn from examination of Tables I to 111. (1) Very good agreement among values of rCN/YHC computed from gas-phase and matrix-isolation data exists when the nine isotopic combinations which are least sensitive to uncertainties in the vibrational frequencies are used. (2) The excellent consistency of values of rCN/rHC computed from the PC “gas-phase data” results from the fact that these values are not based on experimental gasphase frequencies but rather on calculated frequencies fit to only three vz isotopic frequencies and their overtones, as well as combination and difference bands involving those fundamentals, and an assumed value of TCN/THC = 1.082 introduced through values of B, in the calculations of Nakagawa and i\ilorino.6 ( 3 ) A conservative estimate of the uncertainties in the zeroorder frequencies of h 0 . 3 cm-’ more than accounts for any discrepancies between the true value of rCN/THC and those values based on the bending frequencies of matrix-isolated HCN isotopes, This work demonstrates the necessity of calculating the uncertainties in the geometric factors deduced from isotope shifts and the importance of choosing (1) Work performed under the auspices of the U. S. Atomic Energy Commission. (2) J. Pacansky and G. V. Calder, J . Phys. Chem., 76, 454 (1972). (3) D. H. Rank, G. Skorinko, D. P. Eastman, and T. A. Wiggins,
J . Opt. 80c. Amer., 50, 421 (1960). (4) Care must be taken to correct the observed band centers, Y O , [c G(vi,vz,va,l) - #(v~’,v~’,v~’J’)] by adding the term Bv(12 1 ’ 2 ) to
-
obtain the value of the fundamental frequency. Some confusion exists in the literature because the values of YO reported by Rank, et al.,a already incorporate the B , correction term. This has led to errors in the values of YO for the bending frequencies of the six isotopes which were computed by Nakagawa and Morinob and used by P C as “gas-phase data.” (5) T. Nakagawa and Y. Morino, Bull. Chem. SOC.Jap., 42, 2212 (1969). (6) I. Suzuki, M. A. Pariseau, and J. Overend, J . Chem. Phys., 44, 3561 (1966).
The Journal of Physical Chemistry, Vol. 76, No. 17, 1973
COMMUNICATIONS TO THE EDITOR
2484
Table I : Bending Vibrational Frequencies (cm-l) of Gas-Phase and Matrix-Isolated HCN Isotopes
-
Gas phase
c
Anharmonicd correction
01’0B”b
0000
v2c
--PC 01’00000
wz
-
”gas phase”owa
YZ
---PC
matrix--
0110-
00~0’
wa
711.98f 1.48 713.46 13.26zt 0.54 726.72 711.98 712.35 727.10 720.96 734.22 708.948 1.45 707.39 12.94 720.33 707.39 706.34 720.71 714.94 727.88 1.44 712.41 13.16 725.57 711.41 726.01 719.74 732.90 569.04h 1.21 570.25 9.34 0.74 579.59 569.04 569.30 579.85 576.02 585.36 1.19 562.58 9.04 571.59 561.60 571.82 568.01 577.05 1.18 569.0 9.25 578.25 568.06 578.49 574.44 583.69 Calculated using rCN = 1.15313A and rCH = 0.61593A (ref 3). c Where no actual gas-phase data a Obtained by P C from ref 5. exist, values of vz were obtained by adjusting values calculated in ref 5 for discrepancies between observed and calculated v2 values for HW14N, H1SC14N, and D12C14N. d Obtained from ref 5. Although these values may be slightly in error for reasons cited in text, the values for H 1 0 4 N , and DW14N are in close agreement with those computed in ref 6. e Because rotational motion except about the internuclear axis is constrained in the matrix, no correction for B, is necessary; Le., YZ = C(O,1,0,1)- G(O,O,O,O). f Obtained from ref 3 and W. W.Brim, J. M. Hoffman, H. H. Nielsen, and K. N. Rao, J. Opt. SOC.Amer., 50, 1208 (1960). p Obtained from ref 3. Obtained from A. G. Maki, E. K. Plyler, and R. Thibault, J. Opt. SOC.Amer., 54, 869 (1964). H12C14N H13C14N H12CW D12C14h’ D18C14N DlZC16N
~
~~
~
Table I1 : Observed, Calculaked, and Theoretical Values of HCN Isotopic Bending Frequency Ratios ,---
-d/P2JP-
-W2‘”*“-
PC Gas
0.79927 0.78848 0.79752 0.80613 0.79825 0.80437 0.80045 0.78964 0.79870 0.99149 0.99853 1.0071 0.98650 0.99781 1.0115
Matrix
0.79896 0.78785 0.79677 0.80569 0.79449 0.80348 0.80032 0.78919 0.79812 0.99165 0.99831 1,0067 0.98609 0.99726 1.0113
-.
“Gas-phase”
Gas
Matrix
PC “Gas-phase”
0.79918 0.78837 0.79744 0.80599 0.79509 0.80423 0.80024 0.78942 0.79850 0.99156 0.99868 1.0072 0.98647 0.99782 1.0115
0.79754 0.78653 0,79870 0.80462 0,79351 0.80276 0.79881 0.78778 0.79696 0.99121 0.99842 1.0073 0.98620 0.99769 1.0117
0.79725 0.78594 0.79498 0.80420 0.79278 0.80190 0.79869 0.78735 0.79641 0.99136 0.99820 1,0069 0.98580 0.99715 1.0115
0.79748 0.78644 0.79561 0.80455 0,79341 0.80267 0.79868 0.78762 0.79681 0,99121 0.99850 1.0073 0.98615 0,99765 1.0117
From wa oak
From wz
Theoreticala
0.79748 0.78644 0.79561 0,80454 0.79340 0.80265 0.79867 0.78761 0.79679 0.99122 0.99851 1.0074 0.98616 0.99766 1.0117
Table I11 : Calculation of rCN/rHC from Isotope Shifts From Y Z HttC!,N ! I
H‘C‘N’
DW’W D13C14N D12C16N D”04N D13C14N D 1zCl6N D12C14N D13C14N Dl!JC16N H13C14N H12C16N H12Cl6N D13C14N D 12CW D ‘2C 16N
Hl2Cl4N H12C14N H12Cl4N H13C14N H13C14N HlaC14N
H”GW HW16N H12C16N HW14N H12C14N Hl3C14N D12C14N DW14N D13C14N
- rCN/rnC;
a x =
R =
WZ‘/W~’’.
gas
From va matrix
1.0819 1.0595 1.0820 1.0585 1.0819 1.0635 1.0818 1.0657 1.0819 1,0653 1.0818 1.0698 1.0818 1,0578 1.0819 1.0567 1.0818 1,0616 1.0804 1.1686 1.0029 1.0780 1.0823 1.3230 1.0818 1.0715 0.9735 1,0814 1.1993 1.0801. b Based on dzO.3cm-1 probable error in
of
1.0810 1.0804 1,0805 1,0809 1,0803 1.0805 1,0799 1.0792 1.0794 1.0796 1.0440 1,1087 1.0882 1.0917 1.0840
1,0549 1.0484 1.0520 1,0596 1.0838 1.0570 1.0559 1.0496 1.0530 1,1354 1.0898 1.1711 1.1390 1.1303 1.1480
the proper isotopic species t o minimize the uncertainties in the desired geometric factors since some combinations are much more sensitive than others to uncertainties in the measured frequencies. The Journal
gas
Physical Chemistry, Vol. 76, No. 17,1978
From wz matrix
1,0854 1.0906 1.0922 1.0869 1.0918 1.0933 1.0816 1.0863 1.0880 1.1099 0.9669 1.2470 1.0262 0,9474 1.1337
A(wN{
bx/bRa
- 17 - 19 - 18
- 16 - 18 - 17 - 17 - 18 - 18
189 429 -326 164 304 - 334
THO)
10.009 *o. 010 *0.010 ztO.008 f0.009
1.0.009 10.009 fO.O1O 10.010 *o. 11 10.25 zto. 19 zt0.12 zt0.22 h0.25
w’s.
CHEMICAL ENGINEERING DIVISION NAT1ONAL LABoRAToRY
ARGONNE, ILLINOIS 60439 RECEIVEDAPRIL 14,1972
S. D. GABELNICK
