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Infra-red spectrum, structure, force constants, mean amplitudes of vibration, thermodynamic functions and molecular polarizability of NSCl
Spectrochimica Act,a, 1967, Vol. 23A, pp. 2689 to 2689. Pergamon Press Ltd. Printed in Northern Ireland
Infra-red spectrum, structure, force constants, mean amplitudes of vibration, thermodynamic functions and molecular polarizability oi NSO1 A. Mi~LLER, G. NAGARAJAN*, O. GLEMSER, S. F. CYV~t and J. WEGENER Anorganisch-Chemisches Institut der Universit~it GSttingen (Received 9 February 1967) infra-red spectrum of NSC1 was studied from 300 to 4000 cm-1. The two fundamentals ul and v2 were directly observed and the third one ua was calculated from the overtone and combination bands. It was confirmed that NSC1 has the structure NSC1 with Cs-symmetry and not SNC1. Force constants, mean amplitudes of vibration, molar thermodynamic functions and molecular polarizability were computed and the results briefly discussed. Abstract--The
INTRODUCTIOlg NSC1, a gaseous greenish yellow compound was first prepared b y GLEMSER and RICHERT [lJ b y the action of chlorine on gaseous N SF and later b y GLEMSER and PERL [2] b y heating N3S3C13. Nevertheless, a complete vibrational analysis has so far not been made. I t seemed to be worthwhile to st udy the infra-red absorption spectrum of NSC], assign the fundamentals, and compute the force constants, mean amplitudes of vibration, molar t he r m odyna m i c functions, and molecular polarizability because this compound is v e r y interesting from t he nature of bonding and the structural point of view. EXPERIMENTAL PROCEDURE Gaseous NSC1 was prepared b y heating N3S3C13to ll0°C under high vacuum. The infra-red spectrum was studied with a Leitz spectrophotometer from 4000 to 300 cm -1. The sample was contained in a 10-cm glass cell with NaCI-, KBr-, and CsBr-windows at room temperature. Because of the rapid polymerization of NSC1 to NaS3C13, the spectrum was scanned v e r y quickly after the preparation of NSC1. Small amounts o f HNSO and SO 2 were found in the observed spectrum probably due to the following reaction of NSC1 with water vapour: NSC1 ~ H~O --~ HNSO ~ HC1 HNSO ~- H20 --~ N H a + SO~ INFRA-RED ABSORPTIO~ SPECTRUM According to the WALsH rule [3], NSC1 should be non-linear. A non-linear asymmetrical NSC1 molecule possessing the s y m m e t r y point group C, gives rise, according to the relevant s y m m e t r y considerations and selection rules, to three vibrational degrees of freedom constituting three fundamental frequencies, namely, * Department of Chemistry, University of Maryland, College Park, U.S.A. t Institute of Theoretical Chemistry, Technical University of Norway, Trondheim, Norway. [1] 0 . G L E M S ~ a n d H . RICKERT, Z. Anorg. Allgem. Chem. 3 0 7 , 3 1 3 ( 1 9 6 1 ) . [2] 0. GLEMSERand H. PERL, Natu~nvissenschaften. 48, 620 (1961); O. GLZMSERand M. FILD, Sulphur 1Vitrogen Compounds in Halogens Vol. 1, Academic Press (in press). [3] A. D. W~SH, J. Chem. See. 2260 (1953). 2683
2684
A. ]~OIJ~R, G. NAGA_RAJAN, O. GLEMSER, S. F, CYVI~ a n d J . W~.O~NER
V1 the frequency corresponding to the NS stretching vibration, v2 to the SC1 stretching vibration and u8 to the NSCI bending vibration. The normal modes of oscillation for a molecule of the present study has already been given b y W u [4]. All the vibrations are allowed in both the infra-red absorption and R a m a n spectra. The assignment of the observed fundamental frequencies is given in Table 1. The fundamental frequency • 3 has been determined from overtones and combination bands. The P - / ~ separation of vl is 15 cm -1 and of v2 is 16 cm-L F O R C E CONSTANTS AND I~EAN AMPLITUDES O1~ VIBRATION
The force constants and mean amplitudes of vibration have been calculated b y solving the secular equations [5, 6]. detIGF--~E[ =0 and detl~-G - ~ - A E [ = 0 In the case of a non-linear asymmetrical triatomic molecule with C s symmetry point Table 1. O b s e r v e d f u n d a m e n t a l frequencies of I~SC1 S y m m e t r y species
l~umber
Description of m o d e
Frequency (cm -1)
A' A" A"
~'1 v2 ~a
N S stretching SC1 stretching NSC1 bending
1325 414 273*
* O b t a i n e d f r o m t h e o b s e r v e d c o m b i n a t i o n b a n d v~ + v3 = 687 cm -1 a n d t h e o v e r t o n e 545 c m -1.
2v 8 =
group, the number of symmetry co-ordinates is the same as the number of internal co-ordinates i.e., $1 = Arol, $ 2 = Aro2, $3 - A ~ The following G, F, and ~- matrix* elements are obtained for this type of molecule: Gll = ~1 -I- ~[g0'
G12 = 021 = COS ~t~0,
G22 -----/*~ + / Z o ,
G13 :
G2a = Gas =
G31 =
--POl sin ~Po,
--Pos s i n a/,o,
G33 = po12/.zl -{- p022/~2 -]-- (Do12 -]- P022 -- 2Po1P02 cos o¢)jUo, -~11 = f l '
£~12 = ~21' = fer,
"~13 = £~31 = rOJrotCt,
Z l l ~-~ ($12 > ---- OCrox, Z12 ---- Z21 = (~1~_~2> = flCrolroa, Z13 = Z31 = ---- O're,, Z23 = Z32 ---- ($2S3) ---- (rroa=,
Z33 ---: ($32) = (7=.
where r01, re2, and a correspond to 0--1 bond, 0--2 bond and 1--0---2 at the equilibrium configuration of the 1 - - 0 - - 2 molecular model representing the NSC1 molecule, p = I / r , and /z1, Po, and /~z are the reciprocM masses of the atoms 1, O, and 2, respectively. * I n t h e case of t h e ~- m a t r i x S 3 = (rolro2)ll2Ac¢ was used. [4] T. Y. W ~ , Vibrational Spectra and Structure of Polyatomic Molecules. N a t i o n a l U n i v e r s i t y o f Poking (1939). [5] E. B. W ~ s o N , J . C. D E c i u s and P. C, CRoss, Molecular Vibrations. McGraw-Hill (1955). [6] S. J . C r v r ~ , Spectroch~m. Acta 15, 828 (1959).
Infra-red spectrum of NSCI
2685
T h e values o f s t r u c t u r a l p a r a m e t e r s for NSC1 h a v e n e i t h e r e x p e r i m e n t a l l y n o r t h e o r e t i c a l l y b e e n d e t e r m i n e d . H e n c e , t h e values r~s ---- 1.45 A, rsc I ---- 2.00 A a n d NSC1 = 116 ° h a v e b e e n a s s u m e d here for NSC1 f r o m r e l a t e d m o l e c u l a r s y s t e m s h a v i n g similar chemical bonds. T h e force c o n s t a n t s h a v e b e e n calculated b y t h e leasts q u a r e m e t h o d [7-9] w h e r e b y all n(n ~ 1)/2 = 6 force c o n s t a n t s could a p p r o x i m a t e l y be calculated, a n d f u r t h e r m o r e w i t h t h e a s s u m p t i o n o f a diagonal F m a t r i x . T h e calculated n u m e r i c a l values o f t h e force c o n s t a n t s o f NSC1 are g i v e n in T a b l e 2 a l o n g w i t h those o f N S F , for c o m p a r i s o n [10]. Table 2. Force constants of NSC1 and NSF in mdyn/A Constant fNS fSX f~ fNs/sx
fNs/, fSXl~
NSC1 (a, c)
(a, b)
NSF [8, 9]
10.03 1.67 0.22 (d) (d) (d)
10.02 1.64 0.25 ----
10.721 2.884 0.410 0.008 0.014 0"023
(a, b) 10.71 2.89 0.41 ----
(a) This work. (b) Calculated with a diagonal F-matrix (this approximation is better for NSF than for I~SCL). (e) Calculated with the method of FADI~-I [7]. (d) The calculated force constants are too small to be considered as significant. T h e secular e q u a t i o n s giving t h e n o r m a l frequencies in t e r m s o f t h e m e a n - s q u a r e a m p l i t u d e s o f v i b r a t i o n were c o n s t r u c t e d w i t h help o f t h e v i b r a t i o n a l frequencies a n d m o l e c u l a r s t r u c t u r a l d a t a a t r o o m t e m p e r a t u r e . T h e off-diagonal e l e m e n t s were for t h e s a k e of convenience neglected a n d t h e e q u a t i o n s solved. T h e o b t a i n e d values o f t h e m e a n a m p l i t u d e s o f v i b r a t i o n a t r o o m t e m p e r a t u r e for NSC1 are uN s = vNS ~1/2 = 0.0392 A,
Usc1 = vsc ~,1121 =
0"0539
A,
and U~cI = a~c21 :
0"0847 A
T h e values r e p o r t e d here are g r e a t e r t h a n those o f N S F g i v e n elsewhere [11]. Since electron diffraction studies h a v e n o t b e e n u n d e r t a k e n so far, n o c o m p a r i s o n could be m a d e here b e t w e e n t h e e x p e r i m e n t a l a n d t h e o r e t i c a l results. H o w e v e r , t h e values of t h e p r e s e n t s t u d y w o u l d b e v e r y useful in t h e f u t u r e for t h e i n t e r p r e t a tion o f electron diffraction studies.
[7] A. FADINI, Z. Angew. Math. Mech. 44, 506 (1964). SAWODN'Y,_2k.FADrI~I and K. B~T,r.~IN,Spectroehim. Aeta ~1, 995 (1965). [9] H. SI~BERT, Anwendungen der Schwingungsspe~roskopie in der anorganischen Chemie. Springer (1966). [10] The help of A. FADI~ in calculating the force constants is gratefully acknowledged. [11] G. I~TAGARAJA_~,I~dl:an dr. Pure AppL Phys. 4, 244 (1966). [8] W.
2686
A. ]~?)LLER, G. NAGXRAJ~, O. GLEMSER, S. F. CYVIN and J. WEGENER
SOME REM_AI~XS ON THE STRUCTURE (cf. [9]) On principle it is possible that NSC1 has the structure N
/s
A
\ and not
/2\--
IN
ell
B
but the very high value of force constant fNS = 10"02 mdyn/A and the bond order N•s = 2.3 calculated according to SIEBERT [9, 12], show that only the t y p e B structure with the valence bond structures e s
\~
~_. I
IN
-
-
II
III
is possible. The reason for it is that in the case of the structure SNC1 no expansion of the valence'shell of the nitrogen is possible to give a bond order NNS > 2. In the cases of N S F and N S F a molecules (with strong d~-p~ bonds between S and N atoms), there is also a bond order greater than 2 according to the investigations of SIEBERT [9]. THERMODYNAMIC FUNCTIONS The statistical thermodynamic functions such as enthalpy function, free enthalpy function, entropy, and heat capacity were computed for this molecule for the temperature range 200-2000°K. The same fundamental frequencies and molecular structural data used for the calculations of force constants and mean amplitudes of vibration were used for these computations. A rigid rotator, harmonic oscillator model was assumed and all the quantities were computed for the thermodynamic standard gaseous state of unit fugacity (one atmosphere) b y using the standard formulae and the tables of functions for the harmonic oscillator contributions given b y PITZER [13]. The contributions due to centrifugal distortion, isotopic mixing, interaction between vibration and rotation, nuclear spins etc. were neglected in the computations since they are negligibly small. Assumed in the calculations were a symmetry number of l, singiet ground electronic state, and chemical atomic weights. The computed values of all the four thermodynamic quantities in calories per degree, mole for the NSC1 molecule are given in Table 3. The values presented here would be very useful in future for the interpretation of the experimental values of entropies and heat capacities for the ideal gaseous state. [12] H. SI:EBERT, Z. Anorg. Allgem. Chem. 273, 170 (1953). [13] K. S. PITZER,Quantum Chemistry. Prentice-Hall (1953).
Infra-red spectrum of I~SC1
2687
MOLECULAR POLARIZABILITY In order to test how far the polarizability could be a useful criterion in testing the accuracy of wave functions chosen, various potential models have been developed by many investigators and polarizabilities calculated for many ions, atoms and simple diatomic molecules. However, the potential models so far developed were partially successful in the cases of few atoms of the periodic table and simple diatomic molecules but not successful in the cases of even simple polyatomic Table 3. Enthalpy function, free enthalpy function, entropy and heat capacity of NSC1 for the ideal gaseous state at a pressure of one atmosphere. (All the quantities are in cal./dog, mole) T (°K) 200 273.16 298.16 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
(H o -- Ho°)/T
8.908 9.399 9-546 9.556 10.060 10.456 10.795 11.062 11.302 11.508 11.681 11.837 11.965 12.087 12.192 12.288 12-371 12.452 12.515 12.583 12.636
--(F o -- Ho°)/T
50.433 53.284 54.112 54.169 56.998 59.275 61.228 62.880 64.390 65.730 66.960 68.072 69.111 70.085 70.968 71.827 72.599 73.381 74.074 74-761 75.369
,So 59-341 62-683 63.658 63-725 67-058 69-731 72.023 73.942 75.692 77.236 78.641 79.909 81.076 82-172 83.160 84.115 84.970 85.833 86-590 87-344 88-005
Cp° 10.420 11.069 11.243 11"255 11.833 12.270 12.607 12.862 13"055 13"203 13"316 13.409 13.478 13"536 13"584 " 13.623 13.656 13.684 13"706 13"726 13.743
molecules. Of the various potential models developed, the first use of a deltafunction potential model was made by RUDENBERG and his associates [14, 15]. Later, FROST [16] applied a delta-function model of chemical binding to the calculation of energies of various systems with introduction of a branching condition and further improvements were made by LII't'II~COTT [17] with a semi-empirical potential model. By such semi-empirical delta-function techniques LIPPI~COTT and DAYHOFF [18] predicted vibrational frequencies, anharmonicities, bond dissociation energies, and equilibrium internuclear distances in many diatomic molecules and also bond properties of polyatomic molecules. Recently, this semi-empirical model was applied by LIPPI~COTT and his associates [19-21] to the calculations of bond and molecular polarizabilities of various diatomic and polyatomic molecules. Their [14] [15] [16] [17] [18] [19] [20] [21]
K. K. A. E. E. E. E. G. 7
RUDENBERG and R. G. PARR, J. Chem. Phys. 19, 1268 (1951). RUDENBERG and C. W. SC~RR, J. Chem. Phys. 21, 1565 (1953). A. FROST, Or. Chem. Phys. 22, 1613 (1954); 23, 985 (1955); 25, 1150, 1154 (1956). R. LIPPr~COTT, J. Chem. Phys. 23, 603 (1955); 26, 1678 (1957). R. LIPPI~COTT and M. O. DAYHOFF, Spectrochim. Acta 16, 807 (1960). R. LIPPI~COTT and J. M. S T U T ~ , J. Phys. Chem. 68, 2926 (1964). R. LIPPI~COTT, G. NA~ARAJA~ and J. M. STUT~r2~, J. Phys. Chem. 70, 78 (1966). NAG~AJA~, Indian J. Pure Appl. Phys. 4, 97 (1966).
2688
A. ]~VITJLLER,G. NAGARAJAI~, O. GLEMSER, S. F. CYvIN and J. WEGENER
calculated values are in good agreement with the available experimental ones. The same method has been adopted here for the I~SC1 molecule and hence one m a y refer to the earlier studies [19-21] for the detailed theoretical considerations and calculations. The delta-function strengths A in atomic units, atomic polarizabilities ~ in 10-35 cm 3 and c values in atomic units adopted from the earlier method [19] for such computations are given as follows: .4 n = 0.927, A s = 0.688, Acl = 0.753, ~ = 7.43, a s = 18.2, ~Cl = 13.88, c~ = 4.146, cs = 4.128, and c c l = 4.88. The same internuclear distances used for the calculations of force constants, mean amplitudes of vibration and thermodynamic functions were used for such calculation. The following values of electronegativities X~ = 3.0, X s = 2.5, and Xcl = 3.0 were adopted from PA~JLING [22] for the calculation of the polarity correction. The molecular polarizability is mainly composed of a bond parallel component and a bond perpendicular component. The bond parallel component is obtained from bond as well as nonbond region electrons wlfile the bond perpendicular component is derived from atomic polarizabilities and electronegativities of the concerned atoms involved in the bonding. The contribution to the bond parallel component by the bond region electrons is calculated using a linear combination of atomic delta-function wave functions representing the two nuclei involved in the bonding and analytically expressed as ~llb = 4nA12(1/ao)((x~)) 2 where n is the bond order, A1,. the root meansquare delta-function strength of the two nuclei involved, a 0 the radius of the first Bohr orbit or atomic hydrogen and (x2) the mean-square position of a bonding electron i.e., (x2) = (R2/4) ~- (½c~) where R is the internuclear distance at the equilibrium configuration. When the structure is adopted nearly as
IN
cAI
with approximate NS-bond order of 3, the obtained values of bond parallel components a]lb for the N = S and S--C1 bonds are 50-291 × 10-25 cm 3 and 55.24 × 10 -25 cm 3, respectively. No polarity correction has been introduced for the N=-~S bond. Since the S--C1 bond is of the heteronuclear type, a polarity correction has been introduced to*determine the percent covalent character; accordingly, the expression for the bond parallel component by introducing the polarity correction is given as ~l[~ ~ ~llb~ where a = exp [--(¼)(X 1 -- X2)2]. Here X refers to the electronegativity on the PAUr,I~G scale [22]. Hence, the obtained value of the parallel component for the S--C1 bond after introducing the polarity correction is given as 51.893 × 10 -35 cm 3. The nonbond region electron contribution to the bond parallel component ~ll- is calculated from the fraction of the electrons in the valence shell of each atom not involved in bonding and its atomic polarizability and an analytical expression of it is given as Z~ll. = Z f ~ j where f~. is the fraction of electrons in the valence shell of the j - t h atom not involved in bonding and ~ the atomic polarizability of the j - t h atom obtainable from the delta-function strength Aj. The contribution by the non-bond region electrons to the bond parallel [22] L. I~AULING, The Nature of the Che~r~ica[ Bond. Cornell University Press (1960).
Infra-red spectrum of NSC1
2689
c o m p o n e n t s of t h e e n t i r e NSC1 m o l e c u l a r s y s t e m is given as ~](Xlln ~-- (~)~N -~- (½)0CS -~- (~-)~C1 --~ 20"936 × 10 -25 em a I n a diatomic molecule t h e p e r p e n d i c u l a r c o m p o n e n t is assumed to be t h e sum of the two a t o m i c polarizabilities i.e., ~± = 2~x for a non-polar molecule A 2 a n d ~.± = 2 ( X A ~ x ~ - X B ~ B ) / ( X A 2 + XB 2) for a n A - B molecule. On e x t e n d i n g this principle to a p o l y a t o m i c molecule, t h e sum of t h e perpendicular c o m p o n e n t s of all the bonds is given as Z2~± ----nd/(ZXi2¢t~)/(ZXi 2) where nd! is the n u m b e r of residual a t o m i c polarizability degrees of freedom a n d it is five in t h e case o f NSC1. T h e calculated value of t h e sum of all the p e r p e n d i c u l a r c o m p o n e n t s of NSC1 is given as 62.999 × 10 -2a cm a. H e n c e the average or m e a n molecular polarizability is given as ~M = (½)(Z~llp ~- Z~lin ~- Z2~±) = (½)(102.184 ~- 20.936 ~- 62-999) × 10 -~a cm a = 62.04 × 10 -2~ cm a. N e i t h e r t h e refractive i n d e x n o r t h e m o l a r refraction o f NSC1 is available t o derive t h e molecular polarizability a n d to m a k e a comparison here.
Infra-red spectrum, structure, force constants, mean amplitudes of vibration, thermodynamic functions and molecular polarizability oi NSO1 A. Mi~LLER, G. NAGARAJAN*, O. GLEMSER, S. F. CYV~t and J. WEGENER Anorganisch-Chemisches Institut der Universit~it GSttingen (Received 9 February 1967) infra-red spectrum of NSC1 was studied from 300 to 4000 cm-1. The two fundamentals ul and v2 were directly observed and the third one ua was calculated from the overtone and combination bands. It was confirmed that NSC1 has the structure NSC1 with Cs-symmetry and not SNC1. Force constants, mean amplitudes of vibration, molar thermodynamic functions and molecular polarizability were computed and the results briefly discussed. Abstract--The
INTRODUCTIOlg NSC1, a gaseous greenish yellow compound was first prepared b y GLEMSER and RICHERT [lJ b y the action of chlorine on gaseous N SF and later b y GLEMSER and PERL [2] b y heating N3S3C13. Nevertheless, a complete vibrational analysis has so far not been made. I t seemed to be worthwhile to st udy the infra-red absorption spectrum of NSC], assign the fundamentals, and compute the force constants, mean amplitudes of vibration, molar t he r m odyna m i c functions, and molecular polarizability because this compound is v e r y interesting from t he nature of bonding and the structural point of view. EXPERIMENTAL PROCEDURE Gaseous NSC1 was prepared b y heating N3S3C13to ll0°C under high vacuum. The infra-red spectrum was studied with a Leitz spectrophotometer from 4000 to 300 cm -1. The sample was contained in a 10-cm glass cell with NaCI-, KBr-, and CsBr-windows at room temperature. Because of the rapid polymerization of NSC1 to NaS3C13, the spectrum was scanned v e r y quickly after the preparation of NSC1. Small amounts o f HNSO and SO 2 were found in the observed spectrum probably due to the following reaction of NSC1 with water vapour: NSC1 ~ H~O --~ HNSO ~ HC1 HNSO ~- H20 --~ N H a + SO~ INFRA-RED ABSORPTIO~ SPECTRUM According to the WALsH rule [3], NSC1 should be non-linear. A non-linear asymmetrical NSC1 molecule possessing the s y m m e t r y point group C, gives rise, according to the relevant s y m m e t r y considerations and selection rules, to three vibrational degrees of freedom constituting three fundamental frequencies, namely, * Department of Chemistry, University of Maryland, College Park, U.S.A. t Institute of Theoretical Chemistry, Technical University of Norway, Trondheim, Norway. [1] 0 . G L E M S ~ a n d H . RICKERT, Z. Anorg. Allgem. Chem. 3 0 7 , 3 1 3 ( 1 9 6 1 ) . [2] 0. GLEMSERand H. PERL, Natu~nvissenschaften. 48, 620 (1961); O. GLZMSERand M. FILD, Sulphur 1Vitrogen Compounds in Halogens Vol. 1, Academic Press (in press). [3] A. D. W~SH, J. Chem. See. 2260 (1953). 2683
2684
A. ]~OIJ~R, G. NAGA_RAJAN, O. GLEMSER, S. F, CYVI~ a n d J . W~.O~NER
V1 the frequency corresponding to the NS stretching vibration, v2 to the SC1 stretching vibration and u8 to the NSCI bending vibration. The normal modes of oscillation for a molecule of the present study has already been given b y W u [4]. All the vibrations are allowed in both the infra-red absorption and R a m a n spectra. The assignment of the observed fundamental frequencies is given in Table 1. The fundamental frequency • 3 has been determined from overtones and combination bands. The P - / ~ separation of vl is 15 cm -1 and of v2 is 16 cm-L F O R C E CONSTANTS AND I~EAN AMPLITUDES O1~ VIBRATION
The force constants and mean amplitudes of vibration have been calculated b y solving the secular equations [5, 6]. detIGF--~E[ =0 and detl~-G - ~ - A E [ = 0 In the case of a non-linear asymmetrical triatomic molecule with C s symmetry point Table 1. O b s e r v e d f u n d a m e n t a l frequencies of I~SC1 S y m m e t r y species
l~umber
Description of m o d e
Frequency (cm -1)
A' A" A"
~'1 v2 ~a
N S stretching SC1 stretching NSC1 bending
1325 414 273*
* O b t a i n e d f r o m t h e o b s e r v e d c o m b i n a t i o n b a n d v~ + v3 = 687 cm -1 a n d t h e o v e r t o n e 545 c m -1.
2v 8 =
group, the number of symmetry co-ordinates is the same as the number of internal co-ordinates i.e., $1 = Arol, $ 2 = Aro2, $3 - A ~ The following G, F, and ~- matrix* elements are obtained for this type of molecule: Gll = ~1 -I- ~[g0'
G12 = 021 = COS ~t~0,
G22 -----/*~ + / Z o ,
G13 :
G2a = Gas =
G31 =
--POl sin ~Po,
--Pos s i n a/,o,
G33 = po12/.zl -{- p022/~2 -]-- (Do12 -]- P022 -- 2Po1P02 cos o¢)jUo, -~11 = f l '
£~12 = ~21' = fer,
"~13 = £~31 = rOJrotCt,
Z l l ~-~ ($12 > ---- OCrox, Z12 ---- Z21 = (~1~_~2> = flCrolroa, Z13 = Z31 =
Z33 ---: ($32) = (7=.
where r01, re2, and a correspond to 0--1 bond, 0--2 bond and 1--0---2 at the equilibrium configuration of the 1 - - 0 - - 2 molecular model representing the NSC1 molecule, p = I / r , and /z1, Po, and /~z are the reciprocM masses of the atoms 1, O, and 2, respectively. * I n t h e case of t h e ~- m a t r i x S 3 = (rolro2)ll2Ac¢ was used. [4] T. Y. W ~ , Vibrational Spectra and Structure of Polyatomic Molecules. N a t i o n a l U n i v e r s i t y o f Poking (1939). [5] E. B. W ~ s o N , J . C. D E c i u s and P. C, CRoss, Molecular Vibrations. McGraw-Hill (1955). [6] S. J . C r v r ~ , Spectroch~m. Acta 15, 828 (1959).
Infra-red spectrum of NSCI
2685
T h e values o f s t r u c t u r a l p a r a m e t e r s for NSC1 h a v e n e i t h e r e x p e r i m e n t a l l y n o r t h e o r e t i c a l l y b e e n d e t e r m i n e d . H e n c e , t h e values r~s ---- 1.45 A, rsc I ---- 2.00 A a n d NSC1 = 116 ° h a v e b e e n a s s u m e d here for NSC1 f r o m r e l a t e d m o l e c u l a r s y s t e m s h a v i n g similar chemical bonds. T h e force c o n s t a n t s h a v e b e e n calculated b y t h e leasts q u a r e m e t h o d [7-9] w h e r e b y all n(n ~ 1)/2 = 6 force c o n s t a n t s could a p p r o x i m a t e l y be calculated, a n d f u r t h e r m o r e w i t h t h e a s s u m p t i o n o f a diagonal F m a t r i x . T h e calculated n u m e r i c a l values o f t h e force c o n s t a n t s o f NSC1 are g i v e n in T a b l e 2 a l o n g w i t h those o f N S F , for c o m p a r i s o n [10]. Table 2. Force constants of NSC1 and NSF in mdyn/A Constant fNS fSX f~ fNs/sx
fNs/, fSXl~
NSC1 (a, c)
(a, b)
NSF [8, 9]
10.03 1.67 0.22 (d) (d) (d)
10.02 1.64 0.25 ----
10.721 2.884 0.410 0.008 0.014 0"023
(a, b) 10.71 2.89 0.41 ----
(a) This work. (b) Calculated with a diagonal F-matrix (this approximation is better for NSF than for I~SCL). (e) Calculated with the method of FADI~-I [7]. (d) The calculated force constants are too small to be considered as significant. T h e secular e q u a t i o n s giving t h e n o r m a l frequencies in t e r m s o f t h e m e a n - s q u a r e a m p l i t u d e s o f v i b r a t i o n were c o n s t r u c t e d w i t h help o f t h e v i b r a t i o n a l frequencies a n d m o l e c u l a r s t r u c t u r a l d a t a a t r o o m t e m p e r a t u r e . T h e off-diagonal e l e m e n t s were for t h e s a k e of convenience neglected a n d t h e e q u a t i o n s solved. T h e o b t a i n e d values o f t h e m e a n a m p l i t u d e s o f v i b r a t i o n a t r o o m t e m p e r a t u r e for NSC1 are uN s = vNS ~1/2 = 0.0392 A,
Usc1 = vsc ~,1121 =
0"0539
A,
and U~cI = a~c21 :
0"0847 A
T h e values r e p o r t e d here are g r e a t e r t h a n those o f N S F g i v e n elsewhere [11]. Since electron diffraction studies h a v e n o t b e e n u n d e r t a k e n so far, n o c o m p a r i s o n could be m a d e here b e t w e e n t h e e x p e r i m e n t a l a n d t h e o r e t i c a l results. H o w e v e r , t h e values of t h e p r e s e n t s t u d y w o u l d b e v e r y useful in t h e f u t u r e for t h e i n t e r p r e t a tion o f electron diffraction studies.
[7] A. FADINI, Z. Angew. Math. Mech. 44, 506 (1964). SAWODN'Y,_2k.FADrI~I and K. B~T,r.~IN,Spectroehim. Aeta ~1, 995 (1965). [9] H. SI~BERT, Anwendungen der Schwingungsspe~roskopie in der anorganischen Chemie. Springer (1966). [10] The help of A. FADI~ in calculating the force constants is gratefully acknowledged. [11] G. I~TAGARAJA_~,I~dl:an dr. Pure AppL Phys. 4, 244 (1966). [8] W.
2686
A. ]~?)LLER, G. NAGXRAJ~, O. GLEMSER, S. F. CYVIN and J. WEGENER
SOME REM_AI~XS ON THE STRUCTURE (cf. [9]) On principle it is possible that NSC1 has the structure N
/s
A
\ and not
/2\--
IN
ell
B
but the very high value of force constant fNS = 10"02 mdyn/A and the bond order N•s = 2.3 calculated according to SIEBERT [9, 12], show that only the t y p e B structure with the valence bond structures e s
\~
~_. I
IN
-
-
II
III
is possible. The reason for it is that in the case of the structure SNC1 no expansion of the valence'shell of the nitrogen is possible to give a bond order NNS > 2. In the cases of N S F and N S F a molecules (with strong d~-p~ bonds between S and N atoms), there is also a bond order greater than 2 according to the investigations of SIEBERT [9]. THERMODYNAMIC FUNCTIONS The statistical thermodynamic functions such as enthalpy function, free enthalpy function, entropy, and heat capacity were computed for this molecule for the temperature range 200-2000°K. The same fundamental frequencies and molecular structural data used for the calculations of force constants and mean amplitudes of vibration were used for these computations. A rigid rotator, harmonic oscillator model was assumed and all the quantities were computed for the thermodynamic standard gaseous state of unit fugacity (one atmosphere) b y using the standard formulae and the tables of functions for the harmonic oscillator contributions given b y PITZER [13]. The contributions due to centrifugal distortion, isotopic mixing, interaction between vibration and rotation, nuclear spins etc. were neglected in the computations since they are negligibly small. Assumed in the calculations were a symmetry number of l, singiet ground electronic state, and chemical atomic weights. The computed values of all the four thermodynamic quantities in calories per degree, mole for the NSC1 molecule are given in Table 3. The values presented here would be very useful in future for the interpretation of the experimental values of entropies and heat capacities for the ideal gaseous state. [12] H. SI:EBERT, Z. Anorg. Allgem. Chem. 273, 170 (1953). [13] K. S. PITZER,Quantum Chemistry. Prentice-Hall (1953).
Infra-red spectrum of I~SC1
2687
MOLECULAR POLARIZABILITY In order to test how far the polarizability could be a useful criterion in testing the accuracy of wave functions chosen, various potential models have been developed by many investigators and polarizabilities calculated for many ions, atoms and simple diatomic molecules. However, the potential models so far developed were partially successful in the cases of few atoms of the periodic table and simple diatomic molecules but not successful in the cases of even simple polyatomic Table 3. Enthalpy function, free enthalpy function, entropy and heat capacity of NSC1 for the ideal gaseous state at a pressure of one atmosphere. (All the quantities are in cal./dog, mole) T (°K) 200 273.16 298.16 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000
(H o -- Ho°)/T
8.908 9.399 9-546 9.556 10.060 10.456 10.795 11.062 11.302 11.508 11.681 11.837 11.965 12.087 12.192 12.288 12-371 12.452 12.515 12.583 12.636
--(F o -- Ho°)/T
50.433 53.284 54.112 54.169 56.998 59.275 61.228 62.880 64.390 65.730 66.960 68.072 69.111 70.085 70.968 71.827 72.599 73.381 74.074 74-761 75.369
,So 59-341 62-683 63.658 63-725 67-058 69-731 72.023 73.942 75.692 77.236 78.641 79.909 81.076 82-172 83.160 84.115 84.970 85.833 86-590 87-344 88-005
Cp° 10.420 11.069 11.243 11"255 11.833 12.270 12.607 12.862 13"055 13"203 13"316 13.409 13.478 13"536 13"584 " 13.623 13.656 13.684 13"706 13"726 13.743
molecules. Of the various potential models developed, the first use of a deltafunction potential model was made by RUDENBERG and his associates [14, 15]. Later, FROST [16] applied a delta-function model of chemical binding to the calculation of energies of various systems with introduction of a branching condition and further improvements were made by LII't'II~COTT [17] with a semi-empirical potential model. By such semi-empirical delta-function techniques LIPPI~COTT and DAYHOFF [18] predicted vibrational frequencies, anharmonicities, bond dissociation energies, and equilibrium internuclear distances in many diatomic molecules and also bond properties of polyatomic molecules. Recently, this semi-empirical model was applied by LIPPI~COTT and his associates [19-21] to the calculations of bond and molecular polarizabilities of various diatomic and polyatomic molecules. Their [14] [15] [16] [17] [18] [19] [20] [21]
K. K. A. E. E. E. E. G. 7
RUDENBERG and R. G. PARR, J. Chem. Phys. 19, 1268 (1951). RUDENBERG and C. W. SC~RR, J. Chem. Phys. 21, 1565 (1953). A. FROST, Or. Chem. Phys. 22, 1613 (1954); 23, 985 (1955); 25, 1150, 1154 (1956). R. LIPPr~COTT, J. Chem. Phys. 23, 603 (1955); 26, 1678 (1957). R. LIPPI~COTT and M. O. DAYHOFF, Spectrochim. Acta 16, 807 (1960). R. LIPPI~COTT and J. M. S T U T ~ , J. Phys. Chem. 68, 2926 (1964). R. LIPPI~COTT, G. NA~ARAJA~ and J. M. STUT~r2~, J. Phys. Chem. 70, 78 (1966). NAG~AJA~, Indian J. Pure Appl. Phys. 4, 97 (1966).
2688
A. ]~VITJLLER,G. NAGARAJAI~, O. GLEMSER, S. F. CYvIN and J. WEGENER
calculated values are in good agreement with the available experimental ones. The same method has been adopted here for the I~SC1 molecule and hence one m a y refer to the earlier studies [19-21] for the detailed theoretical considerations and calculations. The delta-function strengths A in atomic units, atomic polarizabilities ~ in 10-35 cm 3 and c values in atomic units adopted from the earlier method [19] for such computations are given as follows: .4 n = 0.927, A s = 0.688, Acl = 0.753, ~ = 7.43, a s = 18.2, ~Cl = 13.88, c~ = 4.146, cs = 4.128, and c c l = 4.88. The same internuclear distances used for the calculations of force constants, mean amplitudes of vibration and thermodynamic functions were used for such calculation. The following values of electronegativities X~ = 3.0, X s = 2.5, and Xcl = 3.0 were adopted from PA~JLING [22] for the calculation of the polarity correction. The molecular polarizability is mainly composed of a bond parallel component and a bond perpendicular component. The bond parallel component is obtained from bond as well as nonbond region electrons wlfile the bond perpendicular component is derived from atomic polarizabilities and electronegativities of the concerned atoms involved in the bonding. The contribution to the bond parallel component by the bond region electrons is calculated using a linear combination of atomic delta-function wave functions representing the two nuclei involved in the bonding and analytically expressed as ~llb = 4nA12(1/ao)((x~)) 2 where n is the bond order, A1,. the root meansquare delta-function strength of the two nuclei involved, a 0 the radius of the first Bohr orbit or atomic hydrogen and (x2) the mean-square position of a bonding electron i.e., (x2) = (R2/4) ~- (½c~) where R is the internuclear distance at the equilibrium configuration. When the structure is adopted nearly as
IN
cAI
with approximate NS-bond order of 3, the obtained values of bond parallel components a]lb for the N = S and S--C1 bonds are 50-291 × 10-25 cm 3 and 55.24 × 10 -25 cm 3, respectively. No polarity correction has been introduced for the N=-~S bond. Since the S--C1 bond is of the heteronuclear type, a polarity correction has been introduced to*determine the percent covalent character; accordingly, the expression for the bond parallel component by introducing the polarity correction is given as ~l[~ ~ ~llb~ where a = exp [--(¼)(X 1 -- X2)2]. Here X refers to the electronegativity on the PAUr,I~G scale [22]. Hence, the obtained value of the parallel component for the S--C1 bond after introducing the polarity correction is given as 51.893 × 10 -35 cm 3. The nonbond region electron contribution to the bond parallel component ~ll- is calculated from the fraction of the electrons in the valence shell of each atom not involved in bonding and its atomic polarizability and an analytical expression of it is given as Z~ll. = Z f ~ j where f~. is the fraction of electrons in the valence shell of the j - t h atom not involved in bonding and ~ the atomic polarizability of the j - t h atom obtainable from the delta-function strength Aj. The contribution by the non-bond region electrons to the bond parallel [22] L. I~AULING, The Nature of the Che~r~ica[ Bond. Cornell University Press (1960).
Infra-red spectrum of NSC1
2689
c o m p o n e n t s of t h e e n t i r e NSC1 m o l e c u l a r s y s t e m is given as ~](Xlln ~-- (~)~N -~- (½)0CS -~- (~-)~C1 --~ 20"936 × 10 -25 em a I n a diatomic molecule t h e p e r p e n d i c u l a r c o m p o n e n t is assumed to be t h e sum of the two a t o m i c polarizabilities i.e., ~± = 2~x for a non-polar molecule A 2 a n d ~.± = 2 ( X A ~ x ~ - X B ~ B ) / ( X A 2 + XB 2) for a n A - B molecule. On e x t e n d i n g this principle to a p o l y a t o m i c molecule, t h e sum of t h e perpendicular c o m p o n e n t s of all the bonds is given as Z2~± ----nd/(ZXi2¢t~)/(ZXi 2) where nd! is the n u m b e r of residual a t o m i c polarizability degrees of freedom a n d it is five in t h e case o f NSC1. T h e calculated value of t h e sum of all the p e r p e n d i c u l a r c o m p o n e n t s of NSC1 is given as 62.999 × 10 -2a cm a. H e n c e the average or m e a n molecular polarizability is given as ~M = (½)(Z~llp ~- Z~lin ~- Z2~±) = (½)(102.184 ~- 20.936 ~- 62-999) × 10 -~a cm a = 62.04 × 10 -2~ cm a. N e i t h e r t h e refractive i n d e x n o r t h e m o l a r refraction o f NSC1 is available t o derive t h e molecular polarizability a n d to m a k e a comparison here.