Ab initio calculation of the anharmonic force and dipole fields of nitrogen trifluoride

19 July 1996 ,:r

,

J

CHEMICAL PHYSICS LETTERS

?; . : F ' . /

ELSEVIER

Chemical Physics Letters 257 (1996) 23-30

Ab initio calculation of the anharmonic force and dipole fields of nitrogen trifluoride Riccardo Tarroni a, *, Paolo Palmieri a, Maria Luisa Senent a,1, Andrew Willetts b a Dipartimento di Chimica Fisica ed lnorganica, Viale Risorgimento 4, 40136 Bologna. Italy b University Chemical Laboratory, Lensfield Road, CB2 IEW Cambridge, UK

Received 1 March 1996; in final form 8 May 1996

Abstract

The anharmonic force and electric dipole fields of nitrogen trifluoride were obtained from ab initio computations using the second-order Moller-Plesset (MP2) level of theory for the harmonic part of the force field and dipole first derivatives and Hartree-Fock self-consistent field (HF-SCF) for higher order derivatives. Following a previously proposed procedure, the theoretical computations are further improved by fitting a small number of scaling parameters to a selected set of experimental observables.

1. Introduction Nitrogen trifluoride, NF3, is a stable molecule used for the fluorination of organic materials and for plasma etching processes in the semiconductor industry [1]. Most spectroscopic studies date back to more than 20 years ago [2-16] but recent studies [17-19] using modern experimental and computational techniques, have renewed the interest in this molecule. The first infrared (IR) studies at medium resolution [7,8] were mainly focused on the identification of fundamental bands. Popplewell et al. [2] and Allan et al. [6] analyzed the partially resolved fundamentals and some combination bands for the ~4NF3 and

* Corresponding author. I Present address: Departamento de Fisica y Quimica Tebricas, I. Estructura de la Materia, Serrano 123, 28006 Madrid, Spain.

15NF3 species, respectively, providing band origins and spectroscopic parameters; in addition, overtone, combination and difference bands have been identified and assigned. The unusual structure of the v 3, v4 bands and their overtones and combinations have been the subject of a series of papers [3-5,11] appearing in the early seventies. The complete IR spectrum in liquid Ar solution was reported by Jeannotte and Overend [20]. In two recent papers [18,19] H~She et al. applied modem spectroscopic techniques such as Fourier transform and sub-doppler laser saturation to the study of the v j fundamental, determining with high accuracy the quadrupole hyperfine structure and other spectroscopic constants. Microwave (MW) techniques have been used to evaluate the r 0 structure and centrifugal distortion constants [14-16] The equilibrium structure was determined by Morino and co-workers [12,13] by extensive measurements of the ground state and

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R. Tarroni et aL/ Chemical Physics Letters 257 (1996) 23-30

1)1, ]Y2, 1)3, 1'4, 21)4 satellities for both 14N and 15N isotopic species and a tentative cubic force field derived from the rotational-vibrational interaction constants and the /-type doubling constants. About twenty years later Cazzoli et al. [17] measured, with greatly improved accuracy, the ground state vibrational constants of both isotopes and determined sextic centrifugal distortion constants f o r 14NF3. Starting from 1958 [21], the evaluation of the quadratic force field for this molecule closely follows the improvements in the experimental molecular parameters [6,13,22-24] but, as clearly shown by Allan et al. [6], two solutions are compatible with the experimental data. Sawodny and Pulay [25] settled this ambiguity by means of ab initio computations of the harmonic force field at the experimental geometry, using the self-consistent field (SCF) level of theory, though the intrinsic limitation of the method and the small basis set dimension led to serious overestimation of some diagonal force constants. More recently the calculation of the harmonic force field has been improved by Mack et al. [26] using a better 631G * basis and introducing electron correlation by means of second order Moller-Plesset (MP2) perturbation theory. To our knowledge, no effort has been made up to now to extend the calculation to higher energy derivatives in order to obtain the cubic and quartic force fields. As for intensities, we were able to find in the literature only two experimental papers [9,27], the former dealing with fundamentals and the latter with overtone and conbination bands. Figeys et al. [28] evaluated the dipole first derivatives using SCF and small basis sets. Their analysis was limited to fundamentals and the results were only in rough agree-

ment with experiment. Simplified models have been used by Overend and co-workers [27] to evaluate the intensities of combination and overtones, but again to our knowledge, no attempt has been made to predict these using fully ab initio methods. In this Letter we report improved ab initio anharmonic force and dipole fields of NF 3, obtained from a sensible blending of two levels of theory, i.e. second-order Moller-Plesset perturbation theory (MP2) for the geometry, harmonic force constants and dipole first derivatives and Hartree-Fock selfconsistent field (HF-SCF) for higher force and dipole derivatives, since this approach has provided a good description of the molecular force field for mediumsized molecules [29-32]. The theoretical computations are further improved by slightly modifying the geometry and force fields in order to reproduce, in a least-squares sense, a selected set of experimental observables, using a limited number of empirical scale factors as adjustable parameters [31,32]. Our methods and programs have recently been modified for symmetric top molecules [32] and this study is intended to provide an additional test for our approach.

2. C o m p u t a t i o n a l m e t h o d s 2.1. A b initio calculations

The equilibrium geometry, harmonic force field and dipole first derivatives were evaluated using MP2 with a basis set of triple ~ + polarization quality: the 5s4p set of Dunning [33] was augmented by adding two sets of d functions on nitrogen and

Table 1 Symmetrycoordinate definitions for NF3 in terms of redundant internal coordinates [35]. NF3 is numbered taking nitrogen as atom number 1. ra0 is the a-b stretching and Crabc the abc bending coordinates Symmetry coordinate

s I (a z) s2 (al) S3a(e) S3b(e) s~ (e) s,~ (e)

Intemal coordinates r12

3- 1/2

r13

r14

3-1/2

@314 3 - x/2

(2/3) I/z

-6

1/2

2-i/2

@214

~213

3- 1/2 3 - ~/2

3 - ~/2

-6-I/2 - 2 - i/2

(2/3) I/2

-6-1/2

-6-t/2

- 2 - i/2

- 2 - i/2

25

R. Tarroni et a l . / Chemical Physics Letters 257 (1996) 2 3 - 3 0

fluorine, with exponents 1.35, 0.45 and 2.0, 0.667, respectively. Higher derivatives (up to 4 for energy and 3 for electric dipole) were calculated at the SCF level with a smaller basis of double-~ quality including a set of d functions with exponents 0.8 for nitrogen and 1.2 for fluorine. In order to compare the performance of MP2 with respect to SCF for intensities, SCF dipole moment first derivatives were also evaluated using the smaller basis set. The derivatives were always evaluated at the MP2 equilibrium geometry. All computations were performed using CADPAC v5.2 [34].

2.2. Least-squares scaling of the force field Nitrogen trifiuoride is a symmetric top molecule, thus the most compact description of the anharmonic force field is achieved using symmetry coordinates. In Table I we report their definition in terms of redundant internal coordinates, following the convention of Duncan and Mills [35]. All the results reported in this Letter are expressed in term of these coordinates, or converted to them when data are taken from the literature [13]. The ab initio force field has been fitted following the procedure described in detail in Ref. [31], thus here we shall outline only the main steps. First we have selected from the literature (see Table 2) a consistent ensemble of experimental data for both ~4N and ~SN isotopomers. Next we have assigned to each quantity an error (cr or or%), which is related to the accuracy of the experimental measuremenrt and of our description based on perturbation theory. Finally, from the errors we obtained the weights w~ = 1/~r~ for the least-squares treatment. These errors have been defined as follows: rotational constants: Gr = 0.05 MHz; quartic rotational distortion constants: ~r% = 10%; /-type splitting constants: cr = 0.1 MHz; fundamentals and combination bands: cr = 0.5 cm - j . In the final step, a scaling scheme is applied to the ab initio anharmonic force field in order to reproduce, in a least-squares sense, the selected set of experimental observables. Thus, for each order n of derivatives, a set of scaling factors s ~n) is independently applied to the theoretical force field F ~')''h and optimized:

F(}' ,s = sl2)s~2)F~),th,

Fi(j~)'s = e(3)e(3)e(3)~'(3),th °i

Ff~)i s=

Jj

Jk * ijk

'

S~4)S)4)S~4)SI4)F(j4.k)ith.

(1)

Similarly, the theoretical geometry Rt;u is improved by adding a correction term 8R i adjusted in the same fitting procedure: R~ = Rt,h + 8R i.

(2)

From the geometry and the scaled force field, spectroscopic parameters are calculated using standard perturbation theory [36]. The number of fitting parameters is minimized using identical scaling factors for equivalent internal coordinates. The fitting procedure was set up using a customized version of the SPECTRO program [37].

3. Results and discussion

3.1. Spectroscopic parameters In Table 2 we show the results of this scaling scheme together with the corresponding spectroscopic parameters obtained from the unscaled force field. In the same table we also report the predictions for some still unobserved properties. The scaling factors are listed in Table 3: all of them are close to one, thus confirming the good description of the molecular force field achieved for this molecule by our ab initio approach. Finally, in Table 4 we report both the unscaled and the scaled force field up to the quartic terms, and we compare the results with some available literature data [12]. The only strong resonance observed in this molecule is a Coriolis resonance between v~ and v 3, as demonstrated by the large values of oL~ and a~, of opposite sign, which are nicely reproduced by our computations. A weak Fermi resonance between vj and 2v ° has been claimed by Allan et al. [6] on the basis of the observed isotopic shifts of these frequencies, but this was not confirmed by MW measurements (see Note added in proof in Ref. [6]). From our theoretical computation we predict the Fermi resonance parameters as W = 7.8 cm -1 and W = 8.0 cm -~ for the ~4N and ~SN isotopomers, respectively, in close agreement with the experimental value of 7.0 cm-~ re-

26

R. Tarroni et a l . / Chemical Physics Letters 257 (1996) 2 3 - 3 0

Table 2 Comparison of experimental (a) spectroscopic parameters with those calculated from the (b) and (c) force fields in Table 4. Isotopes: (1) ~4NF3 (2) ~SNF3. Rotational and vibrorotational interaction constants in MHz, quartic centrifugal distortion constants in kHz, sextic centrifugal distortion constants in Hz, fundamental frequencies in c m - ~. Experimental data marked with × have been included in the fitting Fit

× × × × × × x × × × × ×

Parameter

Isotope

Ref.

N-F /FNF

-

[12] [12]

Be B~ Ce Ce Bo B~ B~2 B~3 B~4 B2 v, Bo B~ B~ 2 B~3 B~4 B2 v,

1 2 1 2 1 1 1 1 1 1 2 2 2 2 2 2

[ 12] [ 12] [12] [12] [ 12] [ 12] [ 12] [12] [ 12] [ 12] [ 12] [ 12] [ 12] [12] [ 12] [ 12]

10761.91 10710.63 5880. 5880. 10681.02 10724.47 10642.38 10602.22 10676.54 10671.90 10629.44 10667.85 10589.30 10553.77 10624.80 10620.12

10649.85 10597.39 5837.57 5837.57 10561.23 10598.03 10522.23 10478.54 10556.39 10551.55 10510.35 10545.46 10469.56 10431.08 10505.40 10500.46

10755.30 10703.82 5879.31 5879.31 10678.67 10723.04 10642.68 10601.38 10675.15 10671.62 10628.60 10699.82 10591.05 10555.20 10624.92 10621.25

B O/-vl

1 1 1 1 1

[ 12] [12] [ 12] [ 12] [12]

- 43.45 38.65 78.81 4.48 9.12 - - 38.41 40.14 75.67 4.64 9.32 17.79 27 15.9

- 36.80 38.99 82.69 4.84 9.68 -- 35.11 40.78 79.26 4.94 9.89 19.29 12.12 25.70 16.32 19.20 11.84 25.05 16.46 - 129.61 47.13 - 122.91 46.53

- 44.37 35.99 77.29 3.53 7.05 -- 41.23 37.55 73.40 3.67 7.35 17.63 10.20 21.72 16.50 17.55 9.95 21.10 16.70 - 122.19 51.88 - 114.54 51.04

B O~v2 B

(~v3 Otv4 B

a~, B O~vl

2

[12]

c~Bv2 O~B v~ w O~v,, a~, ac ~t (xcv2 ac

2 2 2 2 1 1 1 1 2 2 2 2 1 1 2 2

[12] [12] [ 12] [12] [ 19]

a~, (~vl aC v3 O~cv4

× × ×

q~3 q~, q~

×

qv 4

× ×

Ds Dj r Dr DJ Djx Dr

× ×

Hj Hjj r Hrr ~ Hr

1 1 1 2 2 2 1 1 1 l

[11] [3]

[6] [13] [13] [13] [ 13] [17] [ 17] [ 17] [17] [17] [ 17] [17]

a

b 1.3648 122.22

21 - 121.38 51.41 - 115.32 50.72 0.01461 - 0.02277 0.01432 - 0.02221 0.01953 - 0.09847 0.1490 -

c 1.3747 101.87

0.01417 - 0.02199 0.00970 0.01389 - 0.02146 0.00945 0.01632 - 0.08893 0.12947 - 0.05659

1.3656 102.31

0.01432 - 0.02246 0.00999 0.01405 - 0.02193 0.00974 0.01897 - 0.09867 0.14167 - 0.06158

R. Tarroni et al. / Chemical Physics Letters 257 (1996) 23-30

27

Table 2 (continued) Fit

Parameter

Isotope

Ref.

b

nj

-

HjjK

-

HKKJ

-

g~

-

oJ I

-

oJ 2

oJ 1

-

oJ 2

-

~3 co 4

-

to 3 oJ 4

X

]Yl

X

~2 v3

X

v4

X

2v I 2v 2

[2] [2] [2] [2] [21

2~

X

v I +v

X

vI

X

V I +V 4

X

V2 + v 3

X

v 2 + V1

X

,4 + ,4

X

v I

X

v 2

X

v 3

X

1' 4

1031.9 647.2 908.4 492.6 2058.2 1809 984.0 1675 1930 1523 1548 1137.3 1399 1008.9 644.8 886.3 492.0 -

[2] [21 [2] [2] [2] [2] [2] [2] [6] [6] [6] [6]

X 2

+v~

2v I 2v2

-

v I +v

981.9

[6]

2~4° 2

-

v t + v ~

-

v I +v~ v 2 + v3I

-

v 2 + v~

-

-

,4 + ,'I

c 0.01566 - 0.08548 0.12449 - 0.05440

-

X

X

a

0.01831 - 0.09521 0.13669 - 0.05941

1042.8 659.3 905.0 500.6 1018.5 656.8 883.8 500.0

1058.0 659.6 937.2 497.8 1034.7 656.2 915.5 497.0

1018.6 645.9 866.7 491.0 2030.0 1290.2 1704.0 977.2 1660.3 1872.6 1507.4 1505.2 1134.8 1350.7 977.0 643.9 847.1 490.6 1987.3 1286.1 1666.2 974.4 1636.7 1831.7 1487.6 1483.9 1132.4 1330.9

1038.5 649.1 906.8 490.0 2071.2 1297.1 1789.2 976.2 1683.8 1936.0 1525.8 1550.0 1137.3 1390.7 1016.1 646.0 886.5 489.4 2026.9 1291.1 1749.7 974.6 1658.4 1893.5 1503.3 1526.9 1133.7 1369.9

Table 3 (a) Shifts (/~, deg) o f the equilibrium internal coordinates and scaling factors for quadratic (b), cubic (c) and quartic (d) terms o f the potential (1) Internal coordinate

a

b

c

d

N-F Z.FNF

- 0.0091 0.0075

1.0404 0.9771

0.9954 1.0212

1.0033 1.0253

R. Tarroni et aL / Chemical Physics Letters 257 (1996) 23-30

28 Table 4

(a) E x p e r i m e n t a l [12], ( b ) theoretical u n s c a l e d a n d ( c ) s c a l e d f o r c e field f o r N F 3, e x p r e s s e d in t e r m s o f the s y m m e t r y c o o r d i n a t e s d e f i n e d in T a b l e 1. F o r c e c o n s t a n t s in a J ~ , - " w h e r e n is the n u m b e r o f s t r e t c h i n g c o o r d i n a t e s e n t e r i n g in the d e f i n i t i o n o f the f o r c e c o n s t a n t . O m i t t e d t e r m s are z e r o a

b

c

Fll

6.14

5.986

6.480

FI2

0.84

0.868

0.883

F22

2.41

2.614

2.495

F33

3.39

3.369

3.647

F34

- 0.45

- 0.463

- 0.471

1.67

1.773

1.693

F~ Fll I

-- 33.5

-- 2 6 . 7 8 6

-- 2 6 . 4 1 5

F j 12

- 5.3

- 3.820

-- 3.865

Fi22

-- 1.4

-- 3 . 8 8 6

-- 4.033

- 19.584

- 19.312

FI33

-30.4

FI34

2.3

2.199

2.225

FI44

- 4.0

-- 3 . 6 9 9

-- 3 . 8 4 0

F222

- 3.2

0.415

0.442

F223

- 0.2

0.000

0.000

F224

- 0.2

0.000

0.000

F233

-- 3.2

- 0.745

- 0.754

F234

0.6

1.895

1.967

Fz44

- 2.7

- 3.192

- 3.400

- 11.614

- 11.453

F334

0.2

- 0.403

- 0.408

F344

0.2

1.317

1.367

F444

- 1.5

- 1.749

- 1.862

Fit I 1

-

97.450

98.754

Fll

J2

-

10.699

11.080

FIX22

-

7.560

8.001

Fx 133

-

73.675

74.661

Fi134

-

-- 7 . 2 6 5

- 7.523

F I 144

--

8.498

8.993

FI222

-

5.401

5.841

FI233

-

0.461

0.478

FI234

-

- 4.120

- 4.360

FI244

-

7.235

F1333

-

FI334

-

2.394

2.479

FI344

-

- 3.182

- 3.367

F333

-20.0

43.953

7.824 44.541

4.458

4.821

17.727

19.590

FI444

--

F2222

-

F2233

-

1.873

1.983

F2234

-

- 3.624

- 3.919

/72244

-

7.045

7.786

F2333

-

-- 2.690

- 2.786

F2334

-

2.722

2.880

F2344

-

- 2.296

- 2.482

F2444

-

4.530

5.006

F3333

-

67.775

68.681

F3334

-

1.224 2.533

-- 1.268 2.680

-- 5.033

- 5.443

11.721

12.953

F33 ~ F3444

F4444

-

-

29

R. Tarroni et a l . / Chemical Physics Letters 257 (1996l 2 3 - 3 0

Table 5 Experimental [9,27] and calculated intensities (km/mol) for NF 3 14NF3 experimental

vi v2 v3 v4 2v i 2v 2

29.61 1.54 398 1.36 0 0.02 ~l }

2v 3

iSNF3 calculated

calculated

SCF

MP2

SCF

MP2

44.67 2.42 458.05 2.76 0.02 0.02 0.32

34.18 1.41 423.19 3.26 0.02 0.01 0.23

35.21 2.68 438.76 2.40 0.02 0.02 0.29

26.99 1.59 405.50 2.89 0.02 0.01 0.21

4.06 2.38

3.81 1.87

3.81 11.01

3.57 8.71

5.07 ~l )

2v 4

0.53 a 2.47

2.20

1.36

1.25

V I Jr 1)2

0

0.06

0.04

0.05

0.08

vI + vI + v2 + v2 +

4.33 0.48 0.46 1.06

5.84 0.53 0.83 1.15 0.16

5.54 0.50 0.77 1.07 0.12

5.54 0.47 0.69 0.87 0.13

5.26 0.44 0.63 0.81 0.10

0.25

0.21

0.20

0.16

v~ v~ v~ v4I At~

v~ + v~

) E

0.01

a The experimental value of the intensity is affected by a large error due to the partial overlap of the 2v 4 and v~ bands.

ported in Ref. [6]. Thus the resonance is sufficiently small to be safely accounted for by perturbation theory. 3.2. Intensities

The theoretical evaluation of IR intensities is known to be a difficult task, in particular for overtones and combination bands, since these quantities depend both on the electrical and the mechanical anharmonicity [38]. In Table 5 we compare the computed intensities for the fundamental, overtone and combination bands of 14NF3 with experimental values [9,27] and we also report the predicted intensities for ~5NF3. Both SCF and MP2 intensities compare well with experiment, not only for fundamentals (for which MP2 performs only slightly better than SCF) but also for overtones and combinations. The intensity patterns of the two isotopic species are similar, except for the two components of the 2 v 4 band: while for laNE3 the g and E components are

found to have similar intensity, for ~5NF3 the A~ is predicted to be ~ 10 stronger than the E component.

4. Conclusions

We present an ab initio anharmonic force field for NF 3, evaluated using MP2 for the harmonic part and SCF for higher order derivatives, with medium-sized bases of triple- and double-~ quality. Following a previously proposed approach, the field is further improved by a least-squares adjustment of scaling factors to fit a selected set of experimental observables. The anharmonic dipole field is also calculated and used to evaluate the intensities of fundamental, overtone and conbination bands. The frequencies and intensities compare well with the available experimental data, thus confirming the reliability of quantum chemistry methods to calculate spectroscopic parameters of medium-sized molecules.

30

R. Tarroni et al. / Chemical Physics Letters 257 (1996) 23-30

Acknowledgement Financial support from CNR, MURST and from the EEC under the 'Human Capital Mobility Program' (contract No. ERBCHRXCT93-0157) is gratefully acknowledged. MLS and AW acknowledge the award of EEC fellowships (ICARUS, contract N. CHGECT93-0048) to visit CINECA, the computer center of the University of Bologna, where this work has been completed.

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