UNSTABLE LINEARTRIATOMIC RIOLECULES
4257
Force Constants and Thermodynamic Properties of the Unstable
Linear Triatomic Molecules HCP, DCP, and FCN by H. F. Shurvell Department of Chemistry, Queen’s University, Kingston, Ontario, Canada
(Received April 28, 1970)
Force constants and thermodynamic quantities have been calculated for the unstable linear triatomic molecules HCP, DCP, and FCN. For FCN the relationships between the CF and CN stretching force constants and the interaction constant of the valence force field have been studied.
Introduction We have recently studied’ the ultraviolet and infrared absorption spectra of the phosphorus analog of hydrocyanic acid, HCP, and the deuterated molecule, DCP. Cyanogen fluoride, FCN, has been studied by Dodd and Little,z and force constants have been calculated previously for this m o l e ~ u l e . ~ -No ~ previous force constant calculations have been made for HCP. The thermodynamic properties of FCN were predicted6 before the molecule was isolated, and the infrared2 and microwave spectra’ were recorded.
only the C D stretching and DCP bending fundamentals (vl and VJ were observed for DCP.’ The structure was determined from the microwave spectrum. l 2 For these molecules it is possible to calculate a unique set of force constants of the general valence force field (GVFF) and to predict the CP stretching frequency of DCP. The results are shown in Table I. The HCP Table I: Force Constants and Frequencies (in cm-1) for HCP and DCP constants, mdyn/A
--HCP---
Force
Calculations We have used the Wilson FG matrix method8 for the force constant calculations and an iterative procedure to refine an initial set of force constants. A modifiedg version of the Fortran program written by Schachtschneiderlo was used for these calculations. Thermodynamic properties were calculated using the methods described by Herzberg. ” All calculations were carried out on an IBM 360/50 computer. The internal coordinates used for linear XYZ molecules are the changes in the XY and XZ bond lengths A
and the change in the angle XYZ. The valence force constants are XY stretching (fx,), YZ stretching (fJ,
fCH
f cp fHCP
fCH,Cp 0
5.525 9.040 0.145” -0.3965
Obsd
Cdod
~1
3216.9 3216.8
v2
1276.2 1276.2 674.7 666.6
v3
-DCP--Obsd
Calod
2419.4 2419.3
., , 510
The H%P bending constant has been divided by
1214.1 517.4 (TCB.TCP).
bending force constant is determined by v3 only, and the best value for this force constant gives calculated values for v3 for HCP and DCP which are, respectively, 8.1 cm-l lorn and 7.4 cm-’ high. This may be due in part to the uncertainty in v3 of DCO1 or to the effects
A
XYZ bending
(fxyz), and an interaction constant between the two stretching modes (fxy,yz). The G matrices mere set up in the usual way8 using the bond lengths for HCP reported by Tyler12of 1.067 8 for C-H and 1.542 8 for C-P and for F C S reported by Sheridan, et of 1.260 8 for C-F and 1.165 8 for C-N.
(1) J. W. C. Johns, H. F. 47, 893 (1969).
Shurvell, and J. K. Tyler, Can. J . Phys.,
(2) R. E. Dodd and R. Little, Spectrochim. Acta, 16, 1083 (1960). (3) E. E. Aynsley and R. Little, ibid., 18, 667 (1962). (4) H. Siebert, “Anwendungen der Schwingungsspelctroslcie in der anorganischen Chemie,” Springer-Verlag, Berlin, 1966, p 47.
Results and Discussion
(5) E. J. Williams and J. A. Ladd, J . Mol. Structure, 2, 57 (1968). (6) M. W.Luft, J . Chem. Phys., 21, 1900 (1953). (7) J. Sheridan, J, K. Tyler, E. F. Aynsley, R. E. Dodd, and R . Little, Nature, 185, 96 (1960).
HCP and DCP. These are relatively unstable molecules prepared by passing phosphine or PD3 through a carbon arc.13 The compounds are stable at liquid nitrogen temperatures but have a lifetime of only a few hours at room temperature. The three fundamental vibration frequencies of HCP were observed in the infrared spectrum.’ However,
(8) E. B. Wilson, Jr., J. C. Decius, and P. C. Cross, “Molecular Vibrations,” McGraw-Hill, New York, N. Y., 1955. (9) W. V. F. Brooks, private communication. (10) J. H. Schachtschneider, Technical Report No. 57-65, Shell Development Co., 1965. (11) G. Herzberg, “Infrared and Raman Spectra,” Van Nostrand, Princeton, N. J., 1945. (12) J. K. Tyler, J . Chem. Phys., 40, 1170 (1964). (13) T. E. Gier, J . Amer. Chem. Soc., 83, 1769 (1961).
The Journal of Physical Chemistry, Vol. 74, N o . 24, 1970
H. F. SHURVELL
4255
Table 11: Heat Content H", Free Energy Go,Entropy So, and Heat Capacity C", in Calories per Degree per Mole, for the Ideal Gaseous State of HCP and DCP a t 1 atm Pressure for Several Temperatures T
100 200 273.16 298.16 300 400 500 600 800 1000 1500 2000 a
EO0
6.95 7.11 7.38 7.50 7.51 7.98 8.44 8.85 9.54 10.09 11.08 11.75
6.96 7.15 7.36 7.44 7.45 7.76 8.06 8.33 8.83 9.25 10.04 10.58
36.07 40.94 43.19 43.84 43.89 46.11 47.94 49.51 52.16 54.35 58.64 61.92
is the energy per mole of the perfect gas a t T
=
36.48 41.35 43.60 44 25 44.30 46.48 48-25 49.74 52.21 54.22 58.13 61.10 I
A
The magnitudes of the CP stretching and HCP bending constants are about one-half of the CN stretching and HCN bending constants of HCITJs while the CH stretching constant is similar to the corresponding constant of HCN. The interaction is larger for HCP than for HCIT but has the same sign. The CP single bond stretching constant in molecules such as (CH&P is about 3.0 rndyn/&l4 so that in HCP the CP bond order probably approaches 3. Thermodynanzic Properties. Using the three fundamentals of HCP and DCP together with the rotational constants from the microwave work of Tyler,12the thermodynamic properties-heat content, free energy, entropy, and heat capacity-have been calculated for 12 temperatures from 100 to 2000°K for the ideal gaseous state at 1 atm pressure. The rigid-rotor harmonic OScillator approximation was used. The results of the calculations are given in Table 11. F C N . Cyanogen fluoride is an unstable molecule prepared by high-temperature pyrolysis of cyanuric fluoride (FCN)3under reduced pressure'b or by fluorination of cyanogens2 Orville-Thomas16 predicted CN and C F stretching constants for FCN of 17.5 and 5.07 mdyn/& respectively, prior t o the preparation of the compound, and Lufts calculated thermodynamic functions from the theoretical frequencies and structure extrapolated from other XCN molecules. Other force constant calculations for FCK have been reported in four previous papers.2-6 The results are summarized in Table 111. We have used these sets of force constants t o calculate the stretching frequencies of FCK, and in the two cases The Journal of Phusical Chemistrg, Vole74, NO.24, 1070
43.44 48.49 50.97 51.69 51.75 54.24 56.30 58.07 61.03 63.47 68.18 71.68
7.02 7.69 8.21 8.38 8.39 8.98 9.49 9.94 10.66 11.19 11.97 12.33
6.97 7.71 8.58 8.87 8.89 9.87 10.61 11 17 11.98 12.56 13.49 13.99 I
0°K.
of anharmonicity, which have been ignored in the present calculation. The CH and CP stretching constants, together with the interaction constant, have been varied to produce a fit between observed and calculated frequencies.
A
43.04 48.04 50.57 51.34 51.39 54.09 56.38 58.36 61.69 64.43 69.72 73.68
Table 111: Previous Stretching and Interaction Constants (mdyn/& for FCN Reference 16' fCF
fCN j C F , CN
8.07 17.5 0.45
-Reference2
9 . 2 9.3b 16.3 17.6b 0.0 l . 3 b
Reference Reference 3 4
Referenoe
8.70b 7.95 19.2 17.44b 0.45b'c 1.66
8.41 17.92 0.83
5
These sets are a Force constants predicted theoretically. incorrect (see text). c This value has been incorrectly quoted as 0.70 mdyn/A by Williams and Ladd.6
Table IV: Stretching and Interaction Force Constants (in mdyn/& for FCN fCF, C N
0.00 0.25 0.45 0.50 0.75 0.83 1.00 1.30 1.50 1.66 1.75
fCF
9.18 8.90 8.71 8.67 8.47 8.41 8.30 8.12 8.02 7.95 7.91
fCN
16.31 16.82 17.20 17.30 17.74 17.88 18.16 18.64 18.94 19.18 19.31
noted in the table we could not reproduce the experimental frequencies. The bending constant is dete:mined uniquely as 0.379 mdyn 8 or 0.258 mdynlh, from the bending fundamental. However, the two (14) H. Siebert, 2. Anorg. Allg. Chem., 273, 161 (1953). (15) F. S. Fawcett and R. D. Lipscomb, J. Amer. Chem. floc., 86, 2576 (1964). (16) W. J. Orville-Thomas, J . Chem. Phys., 20, 920 (1952).
UNSTABLE LINEARTRIATOMIC MOLECULES
4259
Table Y : Heat Content H', Free Energy Go, Entropy So, and Heat Capacity C," in Calories per Degree per Mole for the Ideal Gaseous State of Cyanogen Fluoride a t 1 atm Pressure for Several Temperatures T --(,qo
- po)/T5----,
T,OK
This work
Ref 6
100 200 273.16 298.16 300 400 500 600 800 1000 1500 2000
6.99 7.49 7.97 8.12 8.14 8.71 9.21 9.63 10.32 10.86 11.81 12.41
...
... ... 8.28 8.29 8.88 9.36 9.77 10.45 10.97
...
...
--(a"
- W"O)/T--~
This work
Ref 6
37.43 42.40 44.81 45.51 45.56 47.98 49.98 51 70 54.57 56.93 61.53 65.01
... ...
I
..I
45.69 45.74 48 21 50.24 51.99 54.89 57.68 I
...
...
------so
This work 44.42 49.89 52.77 53.64 53.70 56.70 59.19 61.33 64.89 67.79 73.34 77.43
------cPa-----
Ref 6
This work
... ...
7.21 8.78 9.72 9.98 10.00 10.84 11.48 11.98 12.75 13.28 14.03 14.37
...
53 * 97 54.03 57.09 59.60 61.76 65.34 68.65
... ...
Ref G
...
... . I .
10.18 10.20 11.01 11.59 12.08 12.80 13.32
... ...
Boo is the energy per mole of the perfect gas at T = 0°K.
stretching constants and the interaction cannot be determined from the stretching frequencies alone. Williams and Ladd5have calculated sets of force constants for the cyanogen halides. In the case of ClCN and BrCN they were able to make use of centrifugal distortion constants to fix the value of the interaction constants for these molecules. However, they were unable to apply this method t o FCK because the centrifugal distortion constant was insensitive to the force constants. They estimated ~ C and F ~ C F , C Nby assuming a value of 17.92 rndyn/A for ~ C N . We have investigated how the values of the CF and CN stretching constants vary with the value of the interaction constant. These calculations have been carried out using the W-ilson FG matrix method, which lends itself to a perturbation calculation in which f c F and fCN are adjusted to give an exact fit between ob-
served and calculated frequencies for a series of values of the interaction constant. I n fact the interaction can take on a large number of reasonable values and still give reasonable values for the CN and CF stretching constants. We have calculated the stretching constants, when the interaction wts given a series of values in the range 0.0 to 1.75mdyn/A. The results of these calculations are shown in Table IV. In Table IV we have included sets of stretching constants determined by fixing the interaction at 0.45,0.83, 1.3, and 1.66. The second and last of these agree with previous calculation^,^^^ whereas the first and third sets are not in agreement with previous ~ o r k . ~ , ~ Thermodynamic properties have been calculated for FCN using the frequencies and the rotational constant from the work of Dodd and Little.2 The results are given in Table V together with the estimated values of Luft.6 It is seen that the agreement is close.
The J O U Tof ~Physical Chemistry, Vol. 74, hTo.g43 1.970
