empirical potential energy functions: Stretching vibrations of hydroisocyanic acid, phosphaethyne, isocyanoacetylene, and phosphabutadiyne

JOURNAL

OF MOLECULAR

SPECTROSCOPY

100,

l-23 ( 1983)

Vibrational Frequencies from Anharmonic ab Initio/Empirical Potential Energy Functions: Stretching Vibrations of Hydroisocyanic Acid, Phosphaethyne, Isocyanoacetylene, and Phosphabutadiyne PETER BOTSCHWINA’ AND PETER SEBALD Fachbereich

Chemie der Universitiit Kaiserslautern, D-6 750 Kaiserslaurern.

West German)

Anharmonic potential energy functions for the stretchingvibrationsof HNC, HCP, HCP+, HC2NC,and HC,P have been constructedfrom ab initio calculations and little experimental information. Stretching vibrational frequencies are calculated by a variational method employing an approximate vibrational Hamiltonian which neglects the anharmonic coupling between stretching and bending modes. Equilibrium geometries are estimated for HCzNC and HC,P and quartic and sextic centrifugal distortion constants have been calculated. I. INTRODUCTION

In the last three papers of this series (I-3) the stretching vibrational states of several linear molecules (hydrocyanic acid, acetylene, fluoroacetylene, chloroacetylene, cyanoacetylene, diacetylene, and cyanogen) have been investigated by means of variational calculations (“vibrational CI”) employing the so-called ab initio/empirical potential energy functions (PEFs). These PEFs were obtained from ab initio calculations (at the SCF or CEPA level of approximation) and corrected for the most important errors (geometry correction and modification of the quadratic force constants, primarily the diagonal ones) by making use of a few pieces of usually easily obtainable experimental information. In this paper we will extend the previous work to four further linear molecules, namely hydroisocyanic acid, phosphaethyne, isocyanoacetylene, and phosphabutadiyne. Hydroisocyanic acid, HNC, is the simplest compound with an isocyanic group and thus of general chemical interest. It has been frequently observed in interstellar clouds; in fact, it seems to have about the same abundancy as its more stable isomer HCN (4). Under laboratory conditions, it was first detected by infrared spectroscopy in an argon matrix (5). More recently, the v1 bands of H14N12Cand D14N”C were observed in the gas phase by Arrington and Ogryzlo (6) and microwave spectra of various isotopic modifications could be recorded by several groups (7-10). High resolution infrared spectral measurements on the HNC-HCN equilibrium system at temperatures between 600 and 1000°C have been made by Maki and Sams (I I). They could give very accurate values for vl of H14N12C and Di4Nt2C and several band origins of hot bands. The vibration-rotation infrared emission spectrum of HNC around 2.75 pm was obtained under high resolution by Winter and Jones (12) and Maricq et al. (1.3) ’ To whom correspondence should be addressed. 1

0022-2852183 $3.00 Copyright 0

1983 by Academic Press. Inc.

All rights of reproductmn in any form resewed

2

BOTSCHWINA

AND

SEBALD

observed infrared chemoluminescence from HNC which was produced from the reaction between CN- and HI. The molecule phosphaethyne, HCP, was first prepared by Gier (14) in 196 1. It was investigated by microwave (15, 16), electronic (I 7), infrared (14, 17-19), NMR (20), and photoelectron (21) spectroscopy. The experimental information on the molecular vibrations of phosphaethyne is still scarce; in particular, only a little is known about the vibrational states of D’*CP. Some spectroscopic information on the two lowest electronic states of H’*CP’ and D’*CP+ is also available through the recent work of Ring et al. (22). We have therefore also constructed ab initio/empirical PEFs for the Z’II and k*Z states of the phosphaethyne cation. Isocyanoacetylene, HC2NC, has not yet been observed but attempts to produce it by dehydrogenation of vinylisocyanide have been undertaken (4, 23). HCJP and DC3P were recently detected by microwave spectroscopy as pyrolysis products of a 2: 1 mixture of I-chlorobut-2-yne and phosphorus trichloride (24). Analysis of these experiments yielded the rotational constants, quartic centrifugal distortion constants, the l-type doubling constants, several rotation-vibration coupling constants, as well as the dipole moments in the ground vibrational states. The purpose of the present work consists of an attempt to achieve a more detailed knowledge of spectroscopic properties of the aforesaid molecules, especially of the latter two pentatomics about which only very little is experimentally known. II. METHOD

OF CALCULATION

The computational method employed in the present work is described in detail in the three Feceding publications of this series (I-3) and therefore only a few remarks about it will be given here. Stretching vibrational term energies and the corresponding vibrational wavefunctions are calculated by diagonalization of an approximate vibrational Hamiltonian in a sufficiently large basis set of harmonic oscillator product functions. This Hamiltonian includes only stretching coordinates and the corresponding linear momenta and thus neglects the interaction between stretching and bending coordinates which is anharmonic in nature for the case of linear molecules. The construction of an “ab initio/empirical” potential energy function proceeds in the following way: (a) A reference geometry is chosen. This is either the experimental equilibrium geometry, if available, or an estimated equilibrium geometry obtained from SCF calculations plus corrections (see, e.g., Ref. (1) for some examples). (b) Around the reference geometry a sufficiently large number of potential surface points is calculated by means of ab initio methods (SCF/gradient or CI, depending on the size of the molecule and the importance of electron correlation effects) and an analytical fit in the form of a restricted power series of bond stretching coordinates is made to these points. (c) Two types of empirical corrections are applied to the analytical ab initio potential energy functions: first, the linear terms in the expansion are set to zero which corresponds to shifting the potential energy minimum into the reference geometry andbecause of anharmonicity-involves also a slight deformation of the calculated potential energy surface. Second, the quadratic PEF terms-usually only the diagonal

AB INITIO/EMPIRICAL POTENTIALS

3

ones-are modified in such a way that the experimental fundamental frequencies of the most abundant isotope of a given molecule are reproduced in the vibrational CI calculations. By applying the second correction the calculated diagonal quadratic terms are usually lowered by 5 to 20% when obtained from single-determinant SCF calculations or by about 2% when the PEF is calculated by a method which accounts for the most important electron correlation effects. In the present applications to HNC, HCP, H&NC, and HC3P, rather reliable experimental equilibrium geometries are available for the first two molecules. Those of the latter two are estimated on the basis of SCF/gradient calculations with moderately large basis sets, including 64 contracted Gaussian-type orbitals (CGTOs) in the case of isocyanoacetylene and 75 CGTOs for phosphabutadiyne. The influence of electron correlation effects is investigated for hydroisocyanic acid and phosphaethyne by means of Meyer’s (25) coupled electron pair approximation (CEPA) within the formalism of the theory of self-consistent electron pairs (SCEP) (26). Briefly, electron correlation effects arising from single and double substitutions with respect to the reference wavefunction (in this case a closed-shell Hartree-Fock determinant) are completely accounted for while the effect of the most important higher substitutions, the socalled unlinked clusters, is approximately taken care of at practically no extra cost. Only the 25 valence electron pairs constructed from canonical molecular orbitals are correlated and version 1 of CEPA (25, 26) is used throughout. III. HYDROISOCYANIC ACID

The reference geometry for hydroisocyanic acid is taken to be the experimental equilibrium geometry of Creswell and Robiette (27): r,(NH) = 0.9940 A and R,(NC) zz 1.1689 A. Two ab initio/empirical PEFs have been calculated for this molecule. The first one, denoted by PEF A, is obtained from SCF/gradient calculations with a small basis set of 34 contracted GTOs (C: 7s, 3p, ld=z//N: 8s, 3p, ld=z//H: 3s; only the three innermost s functions of C and N are contracted). These calculations yield equilibrium bond lengths of r, = 0.9805 A and R, = 1.16 15 A, the NH and NC bond lengths thus resulting in values too small by 0.0135 A and 0.0074 A, respectively. The latter difference will be applied to correct the calculated R3,(NC) of isocyanoacetylene (see Section V). PEF B is obtained from SCEP-CEPA-1 calculations with the same basis set of 56 contracted GTOs as used previously for HCN (I): 9s, 5p, 1d for C; lOs, Sp, ld for N, and 4s, lp for H; the three innermost s functions and two p functions of C and N are contracted. As before (l-3), the potential energy functions are given as polynomial expansions in the bond stretching coordinates Ar = r - r, (exp.) and m = R - R, (exp.), the expansion coefficients (“force constants”) being given in Table I. “Diagonal” terms in Ar and AR are considered up to eighth and sixth degree, respectively. Off-diagonal terms are neglected after the quartic ones in PEF A and, since the quartics turned out’to be quite small, after the cubic ones in PEF B. There is rather close agreement between the PEF terms of PEF A and PEF B. The diagonal cubic terms are very similar to our previous ones (28) which were used as constraints in the experimental quartic force field of Creswell and Robiette (27). The force constants f,,, and frrrr, calculated from the empirical analytical potential energy function of Murrell et al.

7.928

17.043

-0.354

f rr

fRR

f rR

-2.2

-1.5

f rrRR

f rRRR

623

-0.5

654

f rrrR

fRRRR

0.18

0.51

-115

-50.9

-0.341

17.012

7.845

1.1689

0.9940

289

0.10

BcBd)

CEPA-l/empirical

PEF

316

f rRR

f rrrr

0.36

-117

f rrR

fRRR

-54.6

1.1689

f rrr

0.9940

r,W)

R,(WC)

SCF/empirical

terms

AbId)

PEF

PEF

620

254

-114

-52.9

-0.29

17.14

8.010

1.1689

0.9940

exp.

CRe)

13

-12

-27

649

180

3.16

5.14

-116

-43.7

-0.230

17.025

7.825

exp.

MCHf)

177

202

123

862

361

1.51

-0.47

-116

-50.9

-0.347

17.590

7.960

1.1719

DSi)

-0.20

18.1

7.94

1.168

0.995

-2

-3

-15

661

299

-0.04

0.4

-117

0

-2

-4

633

310

-0.32

0.02

-115

-52.0

-0.218

17.93

8.208

1.1722

0.9943

(correlated)

TBHHh)

-52.6

initio

0.9979

ab

HKD9)

Potential Energy Functions (Stretching Coordinates Only) for Hydroisocyanic Acid”

TABLE I

597

281

0.18

0.51

-111

-49.7

-0.340

17.099

7.933

1.176

0.998

CEPA-1')

of

the

E IS

=

27

31.

32.

work

e)Ret.

h) Ref.

i)Ref.

j) This

for

30.

coupled

to

cluster

obvious

doubles"

correction

calculations

(involving

y1

single

orbitals

(5)

r been

=

=

-3416,

9845,

colcuiated.

the geometry

11 and

substitutions)

clusters. single

hove

fR(5)

f (6) r-

table

equilibrium

-1842,

ref.

=

-3573,

in the

equilibrium

from

(CEPA-I)

substitutions)

(no

unlinked

f

=

given fR(5)

experimental

also

(H14N1'C)

-0.3070

the

are

the experimental

for

for

value around

pseudonatural

+ simple

involving

calculations

are

expanded

PEFs

and

Ct

=

-1643,

terms

the

quo-

in aJ F(-"

differential

constants")

partial

fr(5)

in the

("force

Besides

Included

5.48.105.

(~1-50)

=

56 CGTDs.

gas-phase

0.".

f(8) r

of

5. Both

-0.2828

one!

set

notation:

GTOs.

throuqhout.

the experimental

of

used

34 contracted

are

involved

coefficients

coordinates

polynomial

5.30-105.

an

of

a basis

=

in

set

-9.09.104

calculations

CI-SD

ref.

by fit

from

=

energies

fr(7)

with

f!8)

m),

stretching

summations

of

a basis terms

and

with

higher

doubles"

g) Ref.

(H14N'*C)

number

calculations

19385.

obtained

cluster

29

~3

are

"Approximated

"Coupled

f)Ref.

value

values

=

the

I" fi (1 8, = 1O-1o

Unrestricted

-9.13.104

iorreiotlon

fH(6)

di Underlined

(27).

=

on SCEP-CEPR-1

valanie

matrix

energy.

following

fr(7)

the

Jeonftry

12910,

based

16448,

lnVOlVe5

f(6) = I-

')PEF

f(6) R

It

on SCF

given

n denotes

are

calculations

where

lengths

potential

b) PEF A is based

tlent

J),

bond

(1 aJ = 10-l'

a)Equilibrium

6

BOTSCHWINA AND SEBALD

(29), appear to be too small; they differ from the PEF B values by -14 and -38%, respectively. Table I also includes three published quartic force fields obtained from correlated ab initio wavefunctions. Agreement between our CEPA-1 potential and these force fields is in general reasonably good. A somewhat larger difference occurs between our CEPA- 1 value for frR and the values reported by Taylor et al. (32) and Dykstra and Secrest (32), while it agrees perfectly with the one given by Hennig et al. (30). Since our frR value is numerically stable and obtained from somewhat more flexible wavefunctions than those of Refs. (31) and (32) we believe it to be the more reliable one. The corresponding SCF value (basis B) amounts to -0.27 aJ A-* so that electron correlation contributes -0.07 aJ A-* to this force constant. Similar to those obtained for other linear triatomic molecules, the quartic coupling terms of Hennig et al. (30) are far too large and also f ,rT and fRRRRseem to be significantly overestimated; this is probably due to an inappropriate fitting procedure. Calculated and experimental frequencies for stretching vibrations of six different isotopes of hydroisocyanic acid are given in Table II. Similar to what was observed previously for hydrocyanic acid (I), the present treatment underestimates v3of D14N’*C (by 7 cm-‘) and overestimates vl of D14N1*C (by 11.7 cm-’ for PEF A and 8.0 cm-’ for PEF B). The isotopic shifts on v3arising from “C and “N substitution are calculated with an accuracy of better than 0.5 cm- ‘. By comparison with the previous results for hydrocyanic acid (I) we believe that our vI values for H”N’*C and H14N13C are accurate to better than 1 cm-‘. No experimental values are available so far for transitions to higher excited stretching vibrational states so that the calculated values stand as predictions. Differences between the values obtained from PEF A and PEF B are always smaller than 30 cm-‘; the results from PEF B are preferred since they are based on better wavefunctions. Due to the neglect of stretch-bend interaction and adjustment of fir and fRR to vI and v3 of H14N’*C, the frequencies of higher excited stretching vibrations of H isotopes of hydroisocyanic acid will probably systematically result too low. IV. PHOSPHAETHYNE

Similar to hydrocyanic acid (1) and hydroisocyanic acid (preceding section), two different basis sets are employed in the potential surface calculations for phosphaethyne, HCP. The first one (basis A), which is used for SCF/gradient calculations, consists of 45 contracted GTOs and is described as follows: the carbon basis set is 7s, 3p, I& contracted to [5, 3, l] and is the same as for HCN and HNC in PEF A; a basis set of 11s, 7p, I& in contraction [8,6, l] is used for phosphorus and three s functions are centered at the hydrogen nucleus. Exponents of s and p functions for C and P are taken from Roos and Siegbahn (33), the three outermost s and two p functions of phosphorus being replaced by four and three, respectively, in order to improve the description of the valence electrons (especially the lone pair at phosphorus). The exponents of the dzz functions amount to 0.6 and 0.5 for C and P, respectively. The second basis set (basis B) with which SCF and SCEP calculations have been performed comprises 58 contracted GTOs. It consists of Huzinaga’s (349 8s, 4p set for carbon (plus one d set with exponent 0.6, three innermost s and two p functions contracted9 and a phosphorus basis set of 12s, 8p, ld in contraction [9, 6, I]. The

B

9164.3

9634.0

9930.8

10518.8

9149.1

9624.9

9922.3

10493.7

2Vl+U3

v1+3v

(5) at-e marked

a) Experimental

3Vl

5U3

4w3

with

A A

11, Values

for

given

8185.3

9491.6

8470.6

7404.2

7627.8

6595.5

5522.8

5746.8

12) are

8181.6

9481.0

8463.2

7401.0

7621.5

6592.9

5524.3

5743.7

4703.7

10482.4

10457.0

further

isotopes

in parentheses

9548.3 9808.9

9539.8

9116.4

9101.3

9800.9

7887.7

7602.4

7134.1

5947.1

5632.9

‘3640.4

(361Ot) 3986.0

A

5896.9 7156.4 7576.2 7822.9 9119.4

5894.8 7146.1 7571.4 7818.2 9104.5

are

available

I

B, upon

PEF

10515.4

10490.1

column

9730.9

9722.3

9503.5

5625.4

5623.3

9495.3

%f3

T---~--

1986.2 f19A6.5+1 3651.6

2012.6

3805.0

6

3951.0

3651.7

1986.2

2014.4

PEF

H14N13C

3825.2

PEF

under

2003.8 f2003.6+)

2030.5

3792.8

B

7883.3

7597.4

7123.7

5945.1

5630.8

3985.4

4704.8

3640.5

‘2795.i

(2787.1) 3848.5

2003.8

2032.3

PEF

H15N12C

3813.0

PEF

2798.8

1932.9 r1940+1

1961.5

2875.0

B

3847.5

1932.9

1963.9

PEF

D14N12C

2889.3

PEF

a + siy.

(5,

7986.4

values

7663.7

7658.5

7981.6

v1+2v

2Y

3"3

3

7158.5

7148.2

3

5669.9

6022.0

6019.7

"1+"3

5667.7

2V3

(Z

3652.7

4035.7

3652.7

2

2029.2

2029.2 __-

2056.8

3805.8

PEF

v3

3826.0

A

H14N1%

2058.6

(%NH)

PEF

w3 (-NC)

w1

origin

band A

8109.9

9416.3

8407.5

7343.8

7567.7

6545.3

5473.2

5701.8

4666.3

3818.5

2770.6

1917.9

1945.6

2850.0

B

The

B

spectra

8165.7

9187.5

8355.1

7357.2

7474.8

6516.3

5511.1

5631.2

4661.2

3770.9

2789.9

1893.8

1921.1

2870.0

values

to matrix

8161.6

9292.1

8348.4

7354.1

7469.1

6514.0

5512.4

5628.5

4662.4

3770.0

2793.5

1893.9

1923.4

2884.3

PEF

D14N13C PEF A

underlined

referring request.

those

8105.9

9406.6

8400.6

7340.7

7562.0

6542.9

5474.5

5699.0

4667.5

3817.7

2774.2

1917.9

1947.8

PEF

D15N12C

2864.2

PEF

Harmonic and Anharmonic Stretching Vibrational Frequencies (in cm-‘) for Isotopes of Hydroisocyanic Acid”

TABLE II

8

BOTSCHWINA AND SEBALD

latter is derived from Huzinaga’s (34) 1 Is, 7p set by replacing the outermost two s and p functions by three (s exponents: 0.4, 0.19, and 0.09; p exponents: 0.5, 0.208, and 0.087). The d exponent for phosphorus is taken to be 0.5 and a basis set of four s functions contracted to three and one p set is used for hydrogen (s exponents: 16.03, 2.416, 0.545, and 0.148; p exponent: 0.6). Ab initio and ab initio/empirical PEFs for phosphaethyne are given in Table III; the latter are obtained by making use of the experimental equilibrium geometry reported by Strey and Mills (35) and the frequencies v1 and u3 of H’*CP as given by Garneau and Cabana (28). The latter is probably somewhat perturbed by anharmonic interaction with (0 2’ 0), but a thorough analysis is still missing. Included are also the experimental force field of Strey and Mills (35), which is based on the relatively few experimental data available at that time and had to incorporate several constraints, the very recent force constants of Murrell et al. (29), and the ab initio SCF force field of Botschwina et al. (36). The quadratic force constants published by Shurvell (37) are not given since they were calculated from the observed anharmonic vibrational frequencies of H’*CP and D’*CP within the formalism of the harmonic approximation and are thus not very accurate. The SCF calculations with the smaller basis set A yield equilibrium bond lengths which are relatively close to the experimental values (35, 19) as is frequently observed for SCF calculations involving moderately large basis sets. For basis B, only the CEPA1 results are quoted in Table III (SCF and SCEP-VAR results are available upon request); in this case, the limited basis set overestimates the bond lengths by 0.0 130.01 5 A for r, and by 0.014 A for R,, but the force constants compare quite favorably with the more reliable ab initio/empirical ones. There are only small differences between the two ab initio/empirical PEFs, PEF A (SCF, basis A + corrections) and PEF B (CEPA- 1, basis B -t corrections). Agreement between the calculated PEFs and the experimental quartic force field of Strey and Mills (35) is reasonably good. The most significant difference occurs for frR for which a value of -0.18 aJ A-* (basis B, CEPA-1) is predicted. The value of Strey and Mills of -0.06 aJ A-* and that of Murrell et al. (29) of -0.035 aJ A-* are both almost certainly inaccurate. In particular we have to note that the vibrational frequencies employed by Strey and Mills in their fit were not corrected for Fermi resonances which are probably quite substantial for v1 of D’*CP (strong anharmonic interaction with 2~~). As found previously for HCN and HCCH (I), the effect of the electron correlation on frR is very small (+O.Ol aJ A-*). Our calculations yield slightly smaller diagonal CH stretching force constants for HCP than for HCN which is in line with the slight increase in r,. This small but significant trend is not reflected in the force fields of Strey and Mills (35). Stretching vibrational frequencies for H’*CP and Hi3CP as calculated from PEFs A and B are given in Table IV and compared with the available experimental values. From the calculated values, we have calculated the anharmonicity constant Xi, by means of the following formulas: (a)

XI, = 1/2*[(2u,) - 2-v,]

(b)

X,, = l/2 - [(3Vi) + Yl - 2 - (2u,)].

The resulting values range between -67 and -73 cm-‘, while Strey and Mills (35)

AB INITIO/EMPIRICAL

9

POTENTIALS

obtained a significant larger value of -84.7 cm-’ from their force field by means of traditional second-order perturbation theory. Actually, our X1, values are almost certainly still too large since our vibrational model tends to underestimate (2~~) and (3~~) resulting in too large XII values (see, e.g., Ref. (I) for corresponding results for HCN). TABLE III Potential Energy Functions (Stretching Coordinates Only) for Phosphaethyne PEF

SMb)

MCHC)

BPP*)

termsa'

exp.

exp.

SCF

re(CH)

1.0692

1.0692

1.0614

1.082

1.0692

1.0692

R,(CP)

1.5398

1.5398

1.5441

1.554

1.5398

1.5398

t-2

6.250

6.396

6.947

6.031

6.108

6.0564

6.250

this work SCF,

A

R2

9.100

9.lOB

10.809

10.844

rR

-0.060

-0.035

-0.224

-0.221

r3

-40.0

R3

-45.2

CEPA-1,

B

PEF A

9.309

PEF Be)

9.227

-0.18

-0.219

9.2119 -0.19

-36.3

-35.5

-39.7

-33.6

-38.2

-35.7

-30.1

-53.6

-52.4

-50.7

-53.3

-53.8

r2R

1.8

0.34

0.22

0.22

rR2

3.6

-0.40

-0.05

-0.06

r4

190.5

143.7

179

201

160

194

171

R4

226.5

80.9

217

211

205

215

217

r3R

-6.8

-1

-1

,2R2

-7.8

-2

-2

-30.7

-1

-1

rR3 r5

-958

-794

-921

-864

R5

-930

-818

-948

-869

r6

4867

5167

4574

5793

4102

3558

4158

3558

r’

-38857

-47212

-36311

50611

r8

338189

265455

326474

265455

R6

a) In

this

is used Values b)Ref. e)At

35

table

and

in the following

to denote

the

PEF

terms.

ones,

an

obvious

As an example,

rR2

shorthand stands

notation

for

(a3V/dr3R2)e.

in aJ E(-". ')Ref.

29

the experimental

one

is given

and

-0.2769

in ref. a.".

d)Ref.

36

equilibrium

geometry

19) valence

(CEPA-1)

are

of

correlation

obtained.

ref.

35

energies

(a slightly of -0.2490

different (CI-SD)

10

BOTSCHWINA AND SEBALD TABLE IV Calculated and Experimental Stretching Vibrational Frequencies (in cm-‘) for H’%P and H’%P” H13CP PEF B

H%P PEF A

PEF B

PEF A

(-CH)

3368.1

3352.2

3354.6

3338.9

03 (-CP)

1295.8

1295.6

1264.0

1263.7

Band origin

w1

"3

-1278.3

1278.3

1247.3

1247.3

2u 3

2541.4

2541.1

2480.3

2480.0

v1

3216.9 --

3216.9

3204.2

3204.3 (3204.6)

3V 3

3789.1

3788.4

3698.6

3697.8

"lty3

4489.2

4490.7

4446.0

4447.4

4v 3

5021.1

5019.9

4902.1

4900.7

v1+2v3

5746.0

5748.8

5673.1

5675.7

5v 3

6237.3

6235.6

6090.5

6088.4

Zv1

6287.9

6299.6

6263.2

6274.8

v1+3v3

6987.1

6991.2

6885.3

6889.1

6V3

7437.6

7436.8

7263.7

7262.4

2v1+v3

7553.5

7568.3

7498.6

7513.3

v1+4v3

8212.4

8217.9

8082.5

8087.5

7u3

8624.0

8634.4

8423.5

8432.2

2v1c2v3

8802.9

8821.6

8719.1

8737.0

3Y

9219.6

9246.2

9183.0

9209.8

a)Experimental value for u1 of H13CP (18) is given in parentheses. The underlined calculated values are equal to the experimental ones (18) since the latter have been used in order to fit frr and fRR.

Calculated and experimental stretching vibrational frequencies for D’*CP and D13CP are listed in Table V. Both PEFs underestimate u3 of D’*CP, PEF A by 9.0 cm-’ and PEF B by 8.4 cm-‘. Similar deviations between calculated and experimental values were also obtained for D’*C14N (1); they are probably due to the neglect of anharmonic stretch-bend interaction. Both ab initio/empirical potential energy functions yield a strong Fermi resonance between vl and 2v3 of D’*CP which has not yet been reported in the experimental literature. Using the SCEP-CEPA-1 dipole moment function of basis B, rather similar integrated infrared intensities of 98 and 90 cm*/mole are obtained for both components of the Fermi diad (38). The band origins are calculated at 24 17/2453 cm-’ by PEF A and at 24 15/2452 cm-’ by PEF B. In their analysis of the vibration-rotation spectrum of D’*CP, Johns et al. (I 7) did not take the Fermi

AB INITIOIEMPIRICAL

11

POTENTIALS

TABLE V Calculated and Experimental Stretching Vibrational Frequencies (in cm-‘) for D12CP and D’?P” Band

D12CP

origin PEF

PEF

A

B

&P PEF B'

PEF A

PEF

B

PEF

B'

Ol

2519.5

2506.6

2507.4

2497.5

2484.7

2485.4

"3

1239.3

1239.6

1247.5

1214.3

1214.6

1222.4

"3

1222.4

1223.0

1231.4

1198.3

1198.8

1207.1

2417.4

2414.8

2422.7

2377.4

2376.6

2389.7

2452.5

2451.9

2462.3

2423.7

2421.2

2425.9

(q/213)

(.qfJ3/3J3)

(2~1/~~+2~~/4v~)

(2vlfL3/U1+3”3/5V3)

(3~,1/2v1+2v3/,~1+4v3/6u3)

a)The

underlined

since

it has

been

value used

v3 of in the

D1*CP fit

3607.7

3605.7

3625.8

3544.6

3543.4

3566.2

3671.8

3672.7

3688.8

3620.0

3619.5

3632.2

4776.5

4773.2

4787 .a

4697.5

4695.6

4725.4

4803.1

4802.7

4823.0

4751.7

4750.1

4757.5

4883.1

4886.5

4908.7

4811.6

4813.6

4832.3

5939.9

5936.7

5970.4

5837.8

5835.3

5875.9

5995.7

5997.2

6020.8

5919.8

5919.9

5938.9

6087.2

6093.5

6121.7

5996.9

6001.9

6026.2

7075.7

7076.8

7088.3

6965.2

6962.2

7010.9

7093.8

7095.3

7137.0

7016.6

7021.0

7029.9

7177.9

7182.3

7213.8

7079.4

7082.6

7111.1

7283.1

7293.6

7327.9

7174.8

7183.6

7213.6

(PEF 6')

is identical

to determine

frr and

with

the experimental

fRR of PEF

value

(19)

Be.

resonance into account and derived a band origin of 24 19 cm-’ which lies close to the calculated values for the lower component of the Fermi diad. The strength of the Fermi resonance is, however, almost certainly overestimated by the present calculations since both PEFs underestimate v3 and thus probably also 2~. A rather similar situation was previously found for D’*C12CF (I), where a strong Fermi resonance exists between 2u3 and v2. Here, u3 was underestimated by 5.6 cm-’ and the lower component of the Fermi diad 2v3/u2 was calculated to be too low by 16.6 cm-‘. This showed up also in the calculated infrared intensities of the Fermi diads 2u3/u2 and 3u3/u2 + v3 (39) when compared with the observed spectra (40). To get improved predictions for DCP, the force constants frr and fRR have been also determined in a new fit to the experimental values for uI of H12CP and v3 of Dr2CP, with all other PEF parameters held fixed at the PEF B values, resulting in jr, = 6.0559 al Ab2 and fRR = 9.3372 aJ Ae2. The stretching vibrational frequencies for D12CP and D13CP obtained from this modified PEF (termed PEF B’) are also given in Table V. For the first Fermi diad v,/2v3, the integrated infrared intensities (in cm2/mole) are now calculated to be 136 and 5 1, respectively, demonstrating that the Fermi resonance is now ,less pronounced.

12

BOTSCHWINA

AND SEBALD

The electron impact excited emission spectra of HCP+ and DCP+ (k*C+ - f*II) have been recently reported by Ring et al. (22). From these experiments, the ground state vibrational frequencies v3 were obtained to be 1150 + 10 cm-’ for HCP+ and to 1110 + 10 cm-’ for DCP+. In the present work, the two electronic states of the phosphaethyne cation, J?*II and 2*X’, are studied by means of Koopmans’ approximation, which requires no additional calculations with respect to those already performed for the neutral molecule, and by the open-shell restricted Hartree-Fock selfconsistent field (RHF-SCF) method. In both cases, the smaller basis A is employed. The following equilibrium geometries are calculated (first numbers: Koopmans’ approximation; second numbers: open-shell RHF-SCF): (a)

j211: r, = 1.065 and 1.072 8,

R, = 1.620 and 1.609 A

(b)

A”*Z+:r, = 1.078 and 1.072 A

R, = 1.528 and 1.520 A.

Compared with the neutral molecule, the CP equilibrium bond length is thus considerably lengthened in the ground state of the ion due to ejection of an electron out of a binding K orbital while the CH equilibrium bond length is only slightly increased. In the k*Z’ state, the CH equilibrium bond length is also only slightly elongated (by about 0.01 A) and the CP bond length is calculated to be shortened by 0.02 A with respect to the neutral. Since the SCF calculations with basis A yielded only relatively small errors for r, and R, of the neutral molecule (Ar, = -0.008 A and hR, = 0.004 A from Table III) and the effect of the electron correlation on the changes in the equilibrium bond lengths occurring upon ionization can hardly be accurately estimated without explicit calculations, we apply no further corrections to the calculated equilibrium geometries of the two electronic states of the ion and expand the potential energy functions around these geometries. The parameters of the PEFs obtained in this way are given in Table VI. Due to the small changes in r, occurring upon ionization, no excitation of the CH (CD) stretching modes could be observed in emission or in the photoelectron spectra (41). We have therefore represented the CH potentials of the two states of the ion only by polynomials of the sixth degree. Quartic and higher coupling terms are neglected since they are believed to be small and of little influence on the vibrational frequencies. To improve the calculated PEFs, the force constant fRR of the ,%?state is determined by fit to the experimental value for u3 of H’*CP+ (22) and, since an experimental value is not available for u,, f,r is estimated by transferring a scaling factor from neutral HCP: f,(HCP+, estim.) = fJHCP+, talc.) - C with the scaling factor C being defined as f,JHCP, fit) 6.108 ’ = f,(HCP, talc.) = 6.947 = o*87g2’ The values from basis A are employed and f,(HCP, talc.) is the calculated quadratic CH stretching force constant at the calculated equilibrium geometry. Quite the same procedure is also applied to estimate frr of the A*2’ state. The remaining diagonal

AB INITIO/EMPIRICALPOTENTIALS

13

TABLE VI Potential Energy Functions (Stretching Coordinates Only) for the Lowest Two Electronic States of Phosphaethyne Catin+ PEF

ii %+

'j;% KT, corr.

terms

RHF-SCF,

KT, corr.

corr.

RHF-SCF,

re (CH)

1.065

1.072

1.078

1.072

Re

1.620

1.609

1.528

1.520

r2

6.040

5.729

5.355

5.671

R2

7.460

7.542

9.934

(CP)

-0.25

rR

10.29 -0.34

-0.41

-0.22

r3

-39.4

-38.0

-37.4

-38.1

R3

-40.1

-42.6

-55.0

-57.0

r2R

0.2

-0.1

0.0

rR2

0.2

-0.1

-0.1

200

r4

194

190

194

R4

156

107

222

223

r5

-919

-907

-891

-924

R5

-633

-1333

-951

-993

r6

4494

4319

3718

4441

5826

4410

421C

3279

Rb

a)

corr.

0-l.

Bond

Lengths

obtained (RHF-SCF,

in "A, force

constants

by fit or scaling. corr.)

were

The

calculated

Underlined

in aJ A cubic both

coupling as 0.1

t&ms

aJ A

values

of the and

are

are

x state neglected

in the vibrations.

quadratic force constant fRR of the k state is obtained in a similar way by transferring scaling factors of 0.9069 (Koopmans’ approximation) and 0.8780 (RHF-SCF) from the 2 state to the k state. The use of such scaling factors is certainly not very accurate since the geometry dependence of the correlation energy may be different for different electronic states and we have also to expect errors at the Hartree-Fock level in view of the small basis set used. The differences between Koopmans’ approximation and RHF-SCF are not large enough that we can decide which approximation will work better in this particular case. On the whole, it is hoped that the chosen scaling procedure will compensate at least for a substantial part of the errors introduced by making Koopmans’ or the RHF-SCF approximation within a rather small basis set. The stretching vibrational frequencies calculated for the 2 and k states of H”CP+ and D”CP+ with the potential energy functions of Table VI are listed in Table VII. The H/D shift on u3 of the 2 state, which is calculated to be 46 cm-’ (KT, corr.) and 48 cm-’ (RHF-SCF, corr.), is probably overestimated by a similar amount as for neutral phosphaethyne where it amounted to 9 cm-’ (PEF A, see Table V). The errors in the other vibrational frequencies are hard to estimate: u3 of the k state is

3

3

origin

ii %

2288

ValUeS

(22)

are

given

4460

4225

4322

4525

3384

3082

3413

3178

(2285-2300)

in parentheses.

5126

4257

3878

2958

2614

1315

-1150

1150

2279

1335

1172

(1ZlO)

x %+ cow.

1166

KT,

3172

corr.

3260

RHF-SCF,

H%P+

3347

KT, cow.

a) Experimental

4v

“l+v3

3v

“1

2u 3

v3

w3

Y

Band

TABLE VII

COW.

The

Underlined

5294

4405

3991

3071

2674

1344

1362

3256

RHF-SCF,

corr.

value

4344

3502

3275

2405

(2210-2215)

2195

(lllo+lo)

1104

1118

2496

KT,

fRR.

5037

been

to

3612

3504 4860

3433

employed

3794

3675 3247

4283

2354

2282

2540 2339

2475

1275

1244

1103 2185

1294

1265

1124

2454

RHF-SCF, cot-r.

2395

fix

7i %+ cow.

2433

KT,

D%P+

Lowest

cow.

TWO

RHF-SCF,

has

ii %

Calculated Stretching Vibrational Frequencies (in cm-‘) for the Electronic States of H’*CP’ and D”CP+”

AB INITIO/EMPIRICAL

POTENTIALS

15

probably accurate to 50 cm-‘, and the vI values may well be in error by 100 cm-‘. From the photoelectron spectrum, u3 of the k state was reported to be 1250 f 30 cm-’ (21); the corresponding value for the 2 state is smaller than the value from the emission spectrum (22) by 40 cm-‘. V. ISOCYANOACETYLENE

Using basis A of hydroisocyanic acid (64 contracted GTOs; see Section III) SCF calculations yield the following equilibrium geometry for isocyanoacetylene: r,(CH) = 1.053 A, R,,(C=C) = 1.189 A, R2,(C-N) = 1.319 A, and R,,(N=C) = 1.169 A. Previous geometry optimizations at the SCF level have been published by Wilson (42) and Haese and Woods (43) both using basis sets of double zeta quality, To our calculated bond lengths we apply corrections taken over from acetylene (Are and AR,,) and hydroisocyanic acid (AR3J while Rze remains uncorrected due to lack of suitable experimental information. The resulting estimated equilibrium bond lengths thus amount to r, = 1.060 A, R,, = 1.201 A, Rze = 1.3 19 A, and R3, = 1.176 A. While the estimated r,, RI,, and R3e should be accurate to about 0.003 A, the error in RZeis difficult to estimate and may have a value of up to about 0.01 A. From our estimated equilibrium structure we calculate equilibrium rotational constants of 4964 MHz for H’2C2’4N’2C and of 4594 MHz for D’2C214N’2Cwith possible errors of up to about 1%. By comparison of experimental Be and B. values for cyanoacetylene (44), the difference between Be and B. values for isocyanoacetylene isotopes is probably small-on the order of 0.1%. The PEF terms calculated at the estimated equilibrium geometry are given in Table VIII. Since some of the quadratic coupling terms turned out to be strongly basis-setdependent (l-3), we have calculated them also from the basis enlarged by d, functions. The terms fR,R2(C=C/C-N) and f,&C-N/N=(Z) are then enlarged by 0.11 and 0.18 aJ Ae2 to 0.58 and 0.42 aJ A-2, respectively. Both are positive and not very different from the values obtained for cyanoacetylene within the same basis set (0.39 and 0.38 aJ Am2, respectively), while 0.66 and 0.60 aJ Ae2 were obtained from a fit to experimental vibrational frequencies (see Table 5 of Ref. (1)). The coupling term is calculated to be negative in both molecules but larger in isocyanoacetylene f R,R3 by a factor of 1.5 (basis set with d, functions). The CH/C=C coupling term frR,is almost equally large (-0.117 vs -0.100 aJ A-2 from larger basis) in HC3N and HC2NC. The remaining two quadratic coupling terms f ,R2 and f rR3 are too small to be of significance within the accuracy of the present approach. The diagonal quadratic force constants are estimated by the simple scaling procedure employed previously for HCP+ (see Section IV). Scaling factors (ratio of fitted and calculated diagonal quadratic force constants for a reference molecule) for frr, f R,R,,and fR2R2with numerical values of 0.8925, 0.8135, and 0.8509 are taken over from cyanoacetylene and the scaling factor for fR3R3 (0.8553) is transferred from hydroisocyanic acid. The scaled diagonal quadratic force constants then amount to (in aJ Am2):frr = 6.462, fRIR, = 16.10, fRZR2= 8.236, and fRjR,= 15.86. Harmonic and anharmonic stretching vibrational frequencies for 10 different isotopes of isocyanoacetylene as calculated with a basis set of 365 harmonic oscillator product functions are listed in Table IX. The fundamental frequencies of H’2C’2C’4N’2C are predicted to occur (in cm-‘) at 3343, 2240, 2050, and 925. The

16

BOTSCHWINA AND SEBALD TABLE VIII Potential Energy Functions for Isocyanoacetylene and Phosphabutadiyne” PEF

HC2NC

PEF

HC3P

HC3P

HC2NC

term

term

r*

6.428

6.462

8.236

R:

15.86

R5

8029

5263

R3

-111

6.812

R4

634

209

8.768

R:

-3624

-931

16245

3981

15.20

16.10

R*

R6 2

3

-51.5

'Rl

-0.100

-0.105

R;

rR2

-0.013

-0.011

r2R1

0.54

0.53

0.017

-0.006

r2R2

-0.01

-0.03

r2R3

-0.01

0.01

0.02

-0.02

-0.06

-0.02

0.01

-0.02

0.00

0.00

0.00

0.01

0.00

0.00

rR

3

R1R2

0.575

0.689

RlR3

-0.410

-0.323

R2R3

0.421

0.455

r3

-39.7

-39.5

r4

201

200

r5

-953

-950 5001

r6

4976

R3 1

-101

R4 1

539

489

R:

-2453

-2282

R6 1

9661

9425

a)Underlined values from

rR: R:R* 2 R1R3

- 1486

-1157

RlRZ RER3 R*R$

are obtained

by scaling

The off-diagonal including

dn

as described

quadratic

functions

PEF terms

at the

-0.18

0.27

-0.08

-0.26

-1.81

-1.85

1.18

RlR2R3

211

calculations

rRi

R1Ri

259

.

rR1R3

-97.5

-42.0

va&s

rR1R2

rR2R3

-51.8

in aJ A

rR* 1

nuclei

0.73

-0.20

-0.19

-2.45

-1.28

0.25

-0.04

in the text.

All

are obtained C, N, and

P.

first three values are rather close to the corresponding ones in cyanoacetylene and they are possibly hard to detect in a mixture of the two isomers. The band u4 with band origin calculated at 925 cm-’ lies 61 cm-’ higher than in cyanoacetylene and might thus be a better candidate for the search for isocyanoacetylene in the infrared although the integrated ir intensity of this band is calculated to be rather low (38). VI. PHOSPHABUTADIYNE

A basis set of 75 contracted GTOs, which is the same as that used to construct PEF A of phosphaethyne, is employed in most of the calculations performed for phosphabutadiyne, HC3P. From SCF calculations with this basis set, the following

AB INITIO/EMPIRICAL POTENTIALS

17

TABLE IX Harmonic and Anhannonic Stretching Vibrational Frequencies for HCzNC Isotopes” H12C214N12C

D1*C214N1*C

Hl*C

2

15pc

H13c12c14p,12c

H12c13c14N12c

'Y

3481

2700

3481

3464

3480

“2

2267

2209

2249

2256

2232

d3

2076

1998

2053

2062

2057

iL! 4

935

918

930

922

930

“4

925

908

920

912

920

* 34 v3

1842

1810

1832

1817

1832

2050

19 70

2027

2037

2033

u2

2240

2178

2222

2229

2205

3%

2751

2702

2740

2714

2736

“3+ ‘4

2973

2878

2946

2947

2951

J2h4

3163

3085

3141

3138

3124

“1

3343

2629

3343

3327

3341

“1

3481

3464

3464

3480

3464

4

2259

2224

2246

2219

2209

“‘3

2049

2040

2037

2035

2019

“!4

923

918

910

918

905

O4

913

908

900

908

896

*v4

1818

1808

1793

1808

1784

‘3

2023

2016

2012

2010

1995

‘2

2232

2196

2219

2192

2182

3Xd4

2715

2701

2675

2700

2664

J3+ ,d4

2934

2922

2910

2916

2889

“2+ “4

3142

3103

3116

3099

30 76

J1

3343

3325

3326

3341

3325

a)In mm’.

A basis

set of

365 harmonic

oscillator

product

functions

is employed

in the calculations.

equilibrium geometry is obtained: r,(CH) = 1.054 A, R,,(C=C) = 1.198 A, R2,.(CC) = 1.374 A, and R3,(CP) = 1.55 1 A. Assuming the same errors in the calculated

equilibrium bond lengths as for cyanoacetylene (1) and phosphaethyne (Section IV), the estimated equilibrium bond lengths are obtained to be r, = 1.06 1 A, R,, = 1.2 10 A, RZe = 1.372 A, and RJ, = 1.547 A. Compared with cyanoacetylene (I), we thus predict an increase of 0.007 A in R,, and a decrease of 0.009 A in Rze, while r, is almost equally large in both molecules. The CP equilibrium bond length R3e is calculated to be longer than in phosphaethyne by 0.007 A which is a bit more than the increase in the CN equilibrium bond length of 0.005 8, from HCN to HC,N (I). From the estimated equilibrium geometry for phosphabutadiyne we calculate equi-

18

BOTSCHWINA AND SEBALD

librium rotational constants Be of 2661 and 2492 MHz for H’*CjP and D’*C3P, respectively, which may be compared with the experimental B. values of 2656 and 2489 MHz (22). For comparison, a small difference of -1 MHz between Be and B. values was observed for both H’*CJ14N and D12C314N by Mallinson and de Zafra (44). The parameters of the ab initio/empirical potential energy function constructed for phosphabutadiyne are given in Table VIII. Analogously as for isocyanoacetylene, the off-diagonal quadratic terms are also calculated from the basis set enlarged by d, functions (83 CGTOs in total). All anharmonic terms are calculated (at the estimated equilibrium geometry) by the smaller basis, and the diagonal quadratic terms are obtained by multiplying the calculated values (at the calculated equilibrium) by scaling factors transferred from cyanoacetylene (for frr, fR,~, , and f~& and phosphaethyne (for fR&. The calculated quadratic force constants at calculated equilibrium amount to (in aJ A-*) 7.202, 18.680, 7.846, and 10.305 in the order of fr,, fRIR,, fRzR2, and f RjR, and are scaled by factors of 0.8925, 0.8135, 0.8682, and 0.8509, respectively, the resulting scaled values being given in Table VIII. While the diagonal PEF terms involving the Ar coordinate are practically indistinguishable in cyanoacetylene (1) and phosphabutadiyne, the slight differences between R,, and RZeare also reflected in the force constants. The off-diagonal quadratic terms are rather similar to those in cyanoacetylene and isocyanoacetylene, fRIRz and f R2R,again being positive and fairly large while fRIR, is negative and smaller. Using the potential energy function of Table VIII, stretching vibrational frequencies have been calculated for nine different isotopes of phosphabutadiyne (see Table X). According to the present calculations, the CH stretching frequency vI of H’*&P has practically the same value as in cyanoacetylene and isocyanoacetylene. More characteristic for H12C3P are the other stretching fundamentals with band origins (in cm-‘) calculated at 676(v4), 1528(~& and 2083(v2). Within the harmonic approximation we may obtain a picture of these vibrations by inspection of the 1 matrix which connects normal coordinates and mass-weighted Cartesian coordinates. This matrix is given in Table XI, where comparison is also made with H1*C3N and H12C2’4N’2C. As expected, the normal coordinate Q, is practically identical in all the three molecules. Q2 is qualitatively similar in cyanoacetylene and isocyanoacetylene, involving substantial movement of the terminal heavy atom in both molecules, while QZ of phosphabutadiyne differs significantly, the terminal phosphorus nucleus getting only a tiny amplitude. Q3 and Q4 also show relatively close resemblance in cyanoacetylene and isocyanoacetylene with substantial movement of all heavy nuclei. During normal vibrations 3 and 4 of HL2C3P, however, one carbon nucleus oscillates only with a very small amplitude. VII. CENTRIFUGAL

DISTORTION

CONSTANTS

Equilibrium quartic and sextic centrifugal distortion constants-denoted by 0; and H;, respectively-are calculated by the standard formulae (45, 46) which have been derived by second- and fourth-order perturbation theory. The resulting values are given in Table XII where comparison is also made with experimental D’j values for isotopes of hydroisocyanic acid, phosphaethyne, and phosphabutadiyne. The ex-

4

4

a) A

basis

set

of 365

P

670

oscillator

3313

3032

2853

2720

product

3327

3043

2863

2699

2197 2663

2655

2037

2003

1528

1338

2189

2062

1993

1522

1331

667

677

2069

3468

H1*Cx3C1*CP

1549

P

674

2

1543

2097

3453

H13C12C

harmonic

2591

3328

Y

3

3016

3043

2”

2640

2838

2750

2877

2177

2650

2204

1975

2083

2691

1989

2020

1514

665

676

1528

673

683

1328

1535

1349

2011

1549

3

2119

13%

” +2v4 3

‘2+‘4

4v4

v3+v4

“2

3”

v3

2”

“3

w4

w3

w2

P

2670

3

3469

H=C

functions

3323

2951

2836

2742

2691

2161

2077

2020

1482

1350

676

683

1501

2115

3469

3311

3032

2839

2668

2633

2182

2014

1977

1522

1321

662

669

1543

2045

3452

H13C2**CP

is employed.

H12c 13 2 cp

3312

2941

2811

2712

2654

2146

2056

1993

1477

1331

667

674

I496

2093

3453

H13C12C13CP

3327

2951

2819

2694

2667

2152

2032

2003

1482

1338

670

677

1501

2065

3468

H12C13C

Calculated Harmonic and Anharmonic Stretching Vibrational Frequencies (in cm-‘) for Phosphabutadiyne Isotopes”

TABLE X

2

P 3

3311

2941

2796

2663

2633

2138

2009

1987

1477

1321

662

669

1496

2041

3452

H13C

P

-0.178 -0.572 -0.390 0.378 0.588

units

are

employed

(me

=

1;

1

CI.U.

of

length

-10

numerated 0.529177.10

are

m).

-0.187 -0.588 -0.362 0.395 0.577

0.197 0.396 -0.433 -0.543 0.567

nuclei

-0.176 -0,577 -0.455 0.032 0.654

94

0.269 0.527 -0.674 -0.292 0.334

0.208 0.367 -0.662 0.524 -0.332

=

0.118 0.310 -0.012 -0.880 0.341

Q3

0.111 0.182 -0.387 0.733 -0.518

-0.929 0.358 -0.094 0.002 0.004

accordingto the chemical formulae. Atomic

0.267 0.520 -0.781 0.221 -0.023

Q2

-0.929 0.357 -0.093 0.003 0.001

"12C 14 3 N

a)The ! matricesconnect the normal coordinateswith the mass-weightedCartesiancoordinates.The

-0.932 0.352 -0.085 0.001 0.001

Ql

H12C P 3

X1

1 Matrices for H’*CsP, H’2C3’4N, and H’2C214N1ZCa

TABLE

AB INITIO/EMPIRICAL POTENTIALS

21

TABLE XII Quartic and Sextic Centrifugal Distortion Constant.9 Molecule

DJ'(talc.)

HJ' (talc.)

101.2

53.4b)

64.3b)

70.0

43.9b)

fi9.zb)

95.5

47.0b'

93.Db)

97.3

49.7b)

85.9b)

90.2

43.6b)

62.7b)

67.5

41.4b)

59.6b)

62.8

38.4b)

58.Db)

61.9

36.0b)

21.0b)

21.2

-3.ob)

96.4b)

H1*CP

D; (exp.)

D'*CP

14.2b)

14.5

-O.sb)

H13CP

19.4b)

19.0+0.6

-2.7b)

H12C214N12C

0.594

-0.028

D12C214N12C

0.489

-0.019

H%

3P

0.175

0.195+0.008

-0.003

D1*C P 3

0.149

0.149tO.016

-0.002

a)Quartic centrifugal distortion constants are given in kHz, sextic ones in mtiz. The experimental Di values are taken from the following sources: 1) hydroisocyonic

tieid:

ref.

10

2) H**CP and Dl'CP: ref. 16 (millimeter wave data); H13CP: ref. 18 (IR data) 3) phosphabutadiyne:ref. 22 b)PEFs B of hydroisocyanic acid and phosphaethyne are employed.

perimental 0: values for various isotopes of HNC are larger than the present 05 values by 4 to 9% which is roughly twice as much as for HCN isotopes (I). The 0; values for H12CP and D12CP differ from the experimental 0s values, derived by fit to millimeter wave data (15, 16), by only 0.2 and 0.3 kHz, respectively. We would thus predict a Dy value of 19.6 kHz for H13CP which still lies within the error bars of the less precise infrared value of Garneau and Cabana (18). The D_?values calculated for isotopes of isocyanoacetylene are larger than the corresponding ones for cyanoacetylene by 14%. The Dj value calculated for H’*C3P is smaller than the experimental Dy (24) by 10% while the present 05 and experimental 0: for D12C3P agree within 3 digits. The latter has, however, a standard deviation of 0.0 16 kHz or 11%. We would iike to recommend Dy(D12C3P) = 0.16 f 0.0 1 kHz.

22

BOTSCHWINA AND SEBALD

The calculated sextic centrifugal distortion constants H; for isotopes of hydroisocyanic acid are slightly larger than those reported previously (I) for isotopes of hydrocyanic acid. The H; values for the other molecules are again very small due to almost complete cancellation of harmonic, coriolis and anharmonic contributions (see also Ref. (1)). ACKNOWLEDGMENTS Thanks are due to the Regionales Hochschulrechenzentrum Kaiserslautem for providing computation time. The use of the SCEP program written by Professor Reinach and Dr. Werner (University of Frankfurt) is gratefully acknowledged.

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AB INITIO/EMPIRICAL

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23

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