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A study of nitrosyl fluoride
Volume 129, number 2
CHEMICAL PHYSICS LETTERS
22 August 1986
A STUDY OF NITROSYL FLUORIDE Ian L. ALBERTS, Nicholas C. HANDY and Paolo PALMIERI ’ University Chemical Laboraioty,
Lensfield Road, Cambridge CB2 IE W, UK
Received 5 March 1986; in final form 5 June 1986
A CI gradient study of the ground-state potential surface of the FNO molecule is presented. The geometries, the relative stabilities of the two isomers, FNO and FON, and the activation barrier of the isomerization reaction have been evaluated. The spectroscopic vibration-rotation interaction constants of FNO have been computed and compared with experiment.
1. Introduction
The ground-state equilibrium geometries of nitrosyl and thiazyl fluorides and chlorides correspond to one of two chemical structures: XNY (I); XYN (II) (X = Cl, F ; Y = 0, S). I is the stable form for nitrosyl compounds [ 1,2] in the gaseous phase, and II is the stable geometry for the corresponding thiazyl derivatives [3, 41. Evidence for the existence of the second isomeric form has been reported for NOF in matrix isolation experiments [5,6] but a recent high-resolution spectral study in the region of the v2 and v3 fundamentals of FNO failed to prove the existence of FON in the gaseous phase [7]. Two previous theoretical studies [8,9] on the FNO molecule indicate a potential minimum for FON, but there are large differences in the two computed equilibrium geometries. To discuss the binding energies, the relative stabilities of the two species and the rate of the isomerization reaction, we have extended the analysis of the ground-state potential surface of this molecule, looking at dissociation, FNO, NOF equilibrium geometries and the FNO f+ FON transition state, using accurate ab initio CI techniques [ 10,111. For one of the isomers (FNO) several spectroscopic studies have been reported in the infrared [7] and farinfrared [ 121 regions of the spectrum and these have ’ Permanent
address: Istituto di Chimica Fisica e Spettroscopia, ViaIe Risorgimento 4, 40136 Bologna, Italy.
176
provided the values of most vibration-rotation interaction constants. Since these properties are an important source of information for the determination of the harmonic and the lowest anharmonic components of the molecular force field [ 131, vibration-rotation interaction constants have been evaluated for the two isomers, using the computed quadratic and cubic force fields. In these studies we have used our ab initio CI gradient program, which ensures an efficient procedure for the location of stationary points on a potential energy surface at the correlated wavefunction level of accuracy.
2. The FNO ground-state potential energy surface Computations have been carried out with Dunning’s [ 14,151 (9s5pld) Gaussian basis contracted to [4s2pld] for all atoms. Configuration interaction has been performed [ 161 with the inclusion of all single and double (SD) excitations from the SCF reference state (excluding all excitations from the core orbitals and to the highest three virtual orbitals). Four stationary points on the surface have been investigated corresponding to structures I, II, III and IV, which are detailed in table 1. These are the most interesting parts of the molecular potential-energy surface. Structures I-III have a closed-shell reference configuration, while structure IV, which corresponds to FNO dissociated into ground state NO(211) and F(2P),
Volume 129, number 2
CHEMICALPHYSICS LETTERS
22 August 1986
Table 1 Energies (E, hartree); energy differences (AE, kJ mol-‘) and molecular geometries for structures I-IV computed by (a) SCF and (b) SD CL The CI limit (c) isestimated by adding Davidson’s correction [ 171 to the SD CI energies. The experimental equilibrium structure (d) of FNO is from ref. [ 121. Distances are in A and angles in deg a)
FNO
RN0
RNF/ROF
L FNO/L FON
E
AE
(I)
(a) (b) I:
1.136 1.151 1.131
1.382 1.448 1.517
110.3 109.9 109.9
-0.679730 -0.146951 -0.201520
0.0 0.0 0.0
(II)
(a) (b) (c)
1.050 1.088
1.979 1.971
93.4 86.8
-0.586467 -0.060866 -0.118490
244.9 226.0 218.0
FON
(III)
(a) (b) (c)
1.058 1.102
1.855 1.777
109.3 113.2
-0.588140 -0.070887 -0.132511
240.5 199.7 181.2
F+NO
(IV)
(a) (b) (c)
1.130 1.158
-0.663767 -0.079601 -0.123181
41.9 176.8 205.7
FNO+
FON
a) The internal coordinates are RNO, RNF, L FNO for I and RNO, ROF, L FON for II and III. In IV the NF distance was set to 24 A and L FNO to 110.3’. The SCF energies are shiited by 228 and the CI energies by 229 hartree.
has an open-shell reference configuration. To evaluate the energy gradient, closed-shell CPHF equations have been solved for I-III and the general open-shell singlet CPHF equation in case IV. At each structure (I-IV), the coefficient of the dominant configuration was ap proximately 0.95, indicating that a single reference CI SD was satisfactory for this study. Structure I corresponds to a stable PNO molecule. Previous theoretical studies [8,9] by the SCF method have failed to provide a satisfactory value for the molecular binding energy. In fact, the NF bond energy is estimated to be 176.8 kJ mol-l with SD CI (the Davidson correction predicts 205.7 kJ mol-l), compared with an SCF value of only 41.9 kJ mol-l and an experimental value of 232 kJ mol-l [9 1. Compared with the experimental equilibrium structure, the main discrepancy is in the NF bond length, with 50% of the SCF error recovered by SD CI. The remaining discrepancy is believed to be mainly due to basis set limitations. Structure III corresponds to a loosely bound complex. The OF bond energy is computed to be negative with SCF and SD CI, but with the Davidson correction this changes to t24.5 kJ mol-l, suggesting that important contributions to the bond energy come from higher-order excitations.
As suggested by the IR spectra in N2 and Ar matrices at low temperatures (8-20 K), the NOF molecule is formed when NO or methyl nitrite reacts with fluorine atoms generated photochemically [5,18] or by microwave discharge [6]. Therefore, we have calculated ab initio harmonic frequencies of FNO and NOF at the CI level with the following results: FNO 1954.7, 872.6,615.4 cm-l;FON 2256.2,598.6,414.9 cm-l. The corresponding experimental harmonic frequencies of FNO are 1877,776,523 cm-l [19,20]. The v2 and v3 fundamentals of FON in solid matrices [5,18] have been assigned at 735 and 493 cm-l, respectively, but v1 is unassigned [6]. We predict a large increase in this frequency compared to FNO and a large variation of the corresponding bond length (see table 1). Unlike the related HCN-HNC system [21], the large value computed for the FNO-NOF isomerization energy indicates that the high-energy species is an unlikely candidate for direct experimental observations in equilibrium conditions in the gas phase. To discuss this point further the energy values in table 1, and the related force constants, are easily converted to rate constants. By neglecting the contribution of tunnelling to the isomerization reaction and using a classical approximation to the density of states for the reactant 177
Volume 129, number 2
CHEMICAL PHYSICS LETTERS
Table 2 Computed rate constants (s-l) for the FNO + FON and FON + FNO isomerization reactions as a function of temperature
22 August 1986
Table 3 Centrifugal contributions metric top
to the rotational energy of an asym-
7’ (K)
FNO + FON
FON -, FNO
Operator
Coefficient
100 500 1000
0 0 2 x 10-2
2 x 10-s 2 x 10’ 2 x 108
2
- AJ
j2j2
[22,23], values for the two rate constants can be obtained and are reported in table 2. The dissociation reaction of FON was not investigated. Theoretically, structure III proved to be the most elusive of the species investigated. Due to the very low values of some of the curvature of the potential energy surface, 14 CI gradient evaluations were required to locate the corresponding minimum of the surface. Using a quasi-Newton procedure based on the MurtaghSargent algorithm [24]. For this molecule and for similar loosely bound complexes, different optimization strategies, such as the one proposed by Comeau [25], where all energies and gradients progressively evaluated in the course of the optimization process are used to obtain a global representation of the surface in the region of interest, are likely to be more effective than optimization procedures exploiting only the local prop erties at each point of the surface. This is especially important for CI gradient studies, which require considerable computational resources. Structure II corresponds to a saddle point on the potential surface and it is considered to be the activated complex for the FON + FNO isomerization reaction. The activation barrier is estimated to be 26.3 kJ mol-1 ; addition of the Davidson correction giving an estimate of 36.8 kJ mol-l.
interaction constants of F’NO
Centrifugal forces manifest themselves in high-resolution spectroscopy. Their main effect is to shift the rotational molecular levels from the rigid-rotor expressions by terms which depend upon the fourth and the sixth power of rotational angular-momentum operators. For an asymmetric top [26,27] the additional terms are given in table 3. The coefficients A, 6, H, h, are referred to as quartic (A, 6) and sextic (H, h) cen178
J2j_2
-AK -263
IJ,“,J! I+
-6K
.P
molecule
3. Rotation-vibration
-AJK
:?z'z
HJ HJK HKJ HK
j4j2
2hJ hJK hK
trifugal distortion constants. Other manifestations of vibration-rotation interaction are the change of the rotational constants with the vibrational state, i.e. cr; = BO(n, = 0) - P(n,
= 1)
(rJ=(I,b,c)
Table 4 Quadratic and cubic force constants for FNO and FON evaluated by (a) SCF and (b) Cl gradient methods. The units are al Amn where n is the number of stretching coordinates appear ing in the definition of the force constants. Index 1, 2 are for stretching and 3 for the bending coordinates FNO
kll klz kn b-2 km k33 km hz km km km km km kin km
NOF
(a)
09
OJ)
20.133 2.994 0.665 4.209 0.581 2.694 -141.374 -30.406 -4.830 -1.135 -10.794 -3.448 -1.579 -4.995 -3.356
17.407 2.460 0.553 3.024 0.360 2.265 -127.375 -17.534 -4.172 -3.608 -6.627 -2.624 -0.797 -4.632 -2.258
22.567 0.926 -0.033 1.883 0.215 0.805 - -156.228 -7.408 -0.621 -2.777 -4.849 0.232 0.536 -2.256 -0.650
Volume 129, number 2
CHEMICAL PHYSICS LETTERS
and the inertial defect
22 August 1986
6A100 = A loo - Aooo*
Aooo = ZC - (1, + I.),
By using perturbation theory all these properties can be expressed in terms of force constants, atomic masses and equilibrium values of the internal coordinates. In particular, quartic centrifugal distortion con-
which, for a triatomic molecule, differs from zero due to vibrational motion. The inertial defects also change with the vibrational state, i.e.
Table 5 Spectroscopic constants for FNO. EqayiIibrium rotational constants (MHz), harmonic frequencies (cm-‘), quartic (kHz) and sextic ; mertiaI defects and inertial defect differences (amu A2) and Q vibration-rotation mterac(Hz) centrifugal distortion constants tion constants (MHz) computed by (a) SCF and (b) CI gradient techniques. The values in column (c) have been computed at the experimental geometry with the computed force field. Experhnental values (d) are from ref. [ 121
(4
(b)
w
(4
102195.19 13355.36 11811.75
95724.67
12501.24 11057.22
94961.77 11897.16 10572.59
94961.77 11897.16 10572.59
2101.5 726.8
872.6 1954.7 615.4
873.6 1953.8 610.9
775.5 1876.8 522.9
“JK AK 6J 6K
14.0 -30.7 3300 2.1 77.5
16.2 -33.8 3260 2.4 85.0
14.4 -41.5 3110 2.0 76.7
19.6 -35.3 3928 2.7 107.7
HJ HJK HKJ HK hJ hJK hK
0.0
-0.3 -26.3 365.0 0.0 -0.2 32.3
0.0 0.3 -32.8 388.0 0.0 -0.1 40.3
0.0 0.3 -29.9 366.0 0.0 -0.1 35.7
0.0 1.6 -52.9 628.0 0.0 0.4 61.9
Ae Be Ce
919.7
Wl w2 w3
*J
*ooo
0.0931 -0.0120 0.0635 0.1347
6AlOO 6*0x0 ~*OOI
359.4
393.2
19.4
-0.7
-4.5
- 14.4
-1.8
-9.0
-248.0
-327.8
73.7 73.3 -438.3
b
a) Cubic force constant
k123
0.1162 -0.0111 0.1185 0.1319
292.2
-139.6
a3
0.1040 -0.0121 0.0916 0.1285
262.3
15.3
a’:
0.1045 -0.0119 0.0860 0.1349
0.5 -226.3 49.7 56.6 -505.7
50.0 56.7 -561.8
30.1 45.5 -620.0
94.1
102.3
95.9
89.0
105.0
105.9
97.2
91.1
from ref. [ 131.
179
Volume 129. number 2
CHEMICAL PHYSICS LETTERS
&ants and inertial defects are related to the harmonic components of the force field [26,27], while the sextic constants and the o vibration-rotation constants have contributions from the cubic components. To evaluate the quadratic and the cubic force field, six geometries around each stationary point were considered and the force constants evaluated by quadratic polynomial interpolation of the computed gradients (table 4). Compared to the values quoted in ref. [13], our results allow a more consistent comparison of the SCF and the CI force fields, since the CI energies of the two isomers have been properly optimized. As shown by comparison with the experimental values in table 5, due to the systematic error of the SCF description, harmonic frequencies are overestimated and bond lengths underestimated. In the present case, the error is significant for the NF bond length. The overall agreement is satisfactory for most of the remaining constants even at the SCF level. Most notably, the signs and the relative magnitude of the 01constants are correctly predicted, with the exception of the two vibration-rotation constants with the smallest absolute value (of, ai). CI improves the agreement with experiment for all the constants. The improvement is significant for the a2 constant and we relate it to a more significant change of the corresponding normal mode. Values in column (c), which were obtained using the theoretical force field and the experimental geometry show, by comparison, how the error in the geometry prediction propagates to the spectroscopic parameters. The effect is larger for cut, oa2, cua 3 which correspond to the largest rotational constants. Indirectly, the values in column (c) indicate that CI gives a reasonably close approximation to the quadratic and cubic force field of this molecule.
Acknowledgement PP would like to acknowledge financial support from CNR (Rome) and Professor A.D. Buckingham for hospitality in Cambridge. All members of the Department of Theoretical Chemistry of Cambridge are acknowledged for helpful discussions during the course of this work and in particular Drs. R.D. Amos and J.E. Rice for many elucidations about the use of their programs. 180
22 August 1986
References [l] R.L. Cook, J. Chem. Phys. 42 (1965) 2927. [ 21 G. CazzoIi, C. Degli Esposti, P. Pahnieri and S. Simeone, J. Mol. Spectry. 97 (1983) 165. [ 3 ] W.H. Kirchhoff and E.B. Wilson Jr., J. Am. Chem. Sot. 85 (1963) 1726. [4] S. Mizumoto, J. Izumi, T. Beppu and E. Hirota, BuII. Chem. Sot. Japan 45 (1972) 786. [5 ] R.R. Smardzewski and W.B. Fox. J. Chem. Phvs. -. 60 (1974) 2104. 161M.E. Jacox, J. Phys. Chem. 87 (1983) 4940. 171 S.C. Foster and J.W.C. Johns, J. Mol. Spectry. 103 (1984) 176. 181 J. Peslak Jr., D.S. Klett and C.W. David, J. Am. Chem. sot. 93 (1971) 5001. PI L.J. Lawlor, K. Vasudevan and F. Crein, J. Am. Chem. Sot. 100 (1978) 8062. [lOI J.E. Rice, R.D. Amos, N.C. Handy, T.J. Lee and H.F. Schaefer III, J. Chem. Phys. (1986), to be published. 1111 R.D. Amos, CADPAC, the Cambridge Analytic Derivative Package, publication CCl/84/4, SERC, Daresbury, Warrington WA4 4AD, UK. 1121 G. Cazzoli, C. Degli Esposti, P.G. Favero and P. PaImieri, Nuovo Cimento 3 (1984) 627. [I31 G.L. Bendazzoli, G. Cazzoli, C. DegIi Esposti, G. Fano, F. Ortolani and P. Palmieri, J. Chem. Phys. (1986), to be published. [ 141 T.H. Dunning Jr., J. Chem. Phys. 53 (1970) 2823. [IS] T.H. Dunning Jr., J. Chem. Phys. 55 (1971) 3958. [la] J. PaIdus, J. Chem. Phys. 61 (1972) 5321; I. Shavitt, Intern. J. Quantum Chem. Sll(l977) 131; S12 (1978) 5; B.R. Brooks and H.F. Schaefer III, J. Chem. Phys. 70 (1979) 5092. [ 171 E.R. Davidson, in: The world of quantum chemistry, eds. R. Daudel and B. PuImam~ (ReideI, Dordrecht, 1974). [ 181 R.R. Smardzewski arid W.B. Fox, J. Chem. Sot. Commun. (1974) 241. [19] L.H. Jones, L.B. Asprey and R.R. Ryan, J. Chem. Phys. 47 (1967) 3371. 1201 R.R. Ryan and L.H. Jones, J. Chem. Phys. 50 (1969) 1492. [21] A.G. Maki and R.L. Sams, J. Chem. Phys. 75 (1981) 4178. [22] W.H. Miller, J. Am. Chem. Sot. 101 (1979) 6810. (231 S.M. ColweIl, Mol. Phys 51 (1984) 1217. [24] B.A. Murtagh and W.H. Sargent, Comput. J. 13 (1970) 185. [=I D.C. Comeau, R.J. Zeiimer and I. Shavitt, in: Geometrical derivatives of energy surfaces and molecular properties, eds. P. Jorgensen and J. Simons (Reidel, Dordrecht, 1986). WI I.M. Mills, in: Molecular spectroscopy: modern research, eds. K.N. Rao and C.W. Mathews (Academic Press, New York, 1972). v71 M.R. AIiev and J.K. Watson, J. Mol. Spectry. 6 1 (1974) 29.
CHEMICAL PHYSICS LETTERS
22 August 1986
A STUDY OF NITROSYL FLUORIDE Ian L. ALBERTS, Nicholas C. HANDY and Paolo PALMIERI ’ University Chemical Laboraioty,
Lensfield Road, Cambridge CB2 IE W, UK
Received 5 March 1986; in final form 5 June 1986
A CI gradient study of the ground-state potential surface of the FNO molecule is presented. The geometries, the relative stabilities of the two isomers, FNO and FON, and the activation barrier of the isomerization reaction have been evaluated. The spectroscopic vibration-rotation interaction constants of FNO have been computed and compared with experiment.
1. Introduction
The ground-state equilibrium geometries of nitrosyl and thiazyl fluorides and chlorides correspond to one of two chemical structures: XNY (I); XYN (II) (X = Cl, F ; Y = 0, S). I is the stable form for nitrosyl compounds [ 1,2] in the gaseous phase, and II is the stable geometry for the corresponding thiazyl derivatives [3, 41. Evidence for the existence of the second isomeric form has been reported for NOF in matrix isolation experiments [5,6] but a recent high-resolution spectral study in the region of the v2 and v3 fundamentals of FNO failed to prove the existence of FON in the gaseous phase [7]. Two previous theoretical studies [8,9] on the FNO molecule indicate a potential minimum for FON, but there are large differences in the two computed equilibrium geometries. To discuss the binding energies, the relative stabilities of the two species and the rate of the isomerization reaction, we have extended the analysis of the ground-state potential surface of this molecule, looking at dissociation, FNO, NOF equilibrium geometries and the FNO f+ FON transition state, using accurate ab initio CI techniques [ 10,111. For one of the isomers (FNO) several spectroscopic studies have been reported in the infrared [7] and farinfrared [ 121 regions of the spectrum and these have ’ Permanent
address: Istituto di Chimica Fisica e Spettroscopia, ViaIe Risorgimento 4, 40136 Bologna, Italy.
176
provided the values of most vibration-rotation interaction constants. Since these properties are an important source of information for the determination of the harmonic and the lowest anharmonic components of the molecular force field [ 131, vibration-rotation interaction constants have been evaluated for the two isomers, using the computed quadratic and cubic force fields. In these studies we have used our ab initio CI gradient program, which ensures an efficient procedure for the location of stationary points on a potential energy surface at the correlated wavefunction level of accuracy.
2. The FNO ground-state potential energy surface Computations have been carried out with Dunning’s [ 14,151 (9s5pld) Gaussian basis contracted to [4s2pld] for all atoms. Configuration interaction has been performed [ 161 with the inclusion of all single and double (SD) excitations from the SCF reference state (excluding all excitations from the core orbitals and to the highest three virtual orbitals). Four stationary points on the surface have been investigated corresponding to structures I, II, III and IV, which are detailed in table 1. These are the most interesting parts of the molecular potential-energy surface. Structures I-III have a closed-shell reference configuration, while structure IV, which corresponds to FNO dissociated into ground state NO(211) and F(2P),
Volume 129, number 2
CHEMICALPHYSICS LETTERS
22 August 1986
Table 1 Energies (E, hartree); energy differences (AE, kJ mol-‘) and molecular geometries for structures I-IV computed by (a) SCF and (b) SD CL The CI limit (c) isestimated by adding Davidson’s correction [ 171 to the SD CI energies. The experimental equilibrium structure (d) of FNO is from ref. [ 121. Distances are in A and angles in deg a)
FNO
RN0
RNF/ROF
L FNO/L FON
E
AE
(I)
(a) (b) I:
1.136 1.151 1.131
1.382 1.448 1.517
110.3 109.9 109.9
-0.679730 -0.146951 -0.201520
0.0 0.0 0.0
(II)
(a) (b) (c)
1.050 1.088
1.979 1.971
93.4 86.8
-0.586467 -0.060866 -0.118490
244.9 226.0 218.0
FON
(III)
(a) (b) (c)
1.058 1.102
1.855 1.777
109.3 113.2
-0.588140 -0.070887 -0.132511
240.5 199.7 181.2
F+NO
(IV)
(a) (b) (c)
1.130 1.158
-0.663767 -0.079601 -0.123181
41.9 176.8 205.7
FNO+
FON
a) The internal coordinates are RNO, RNF, L FNO for I and RNO, ROF, L FON for II and III. In IV the NF distance was set to 24 A and L FNO to 110.3’. The SCF energies are shiited by 228 and the CI energies by 229 hartree.
has an open-shell reference configuration. To evaluate the energy gradient, closed-shell CPHF equations have been solved for I-III and the general open-shell singlet CPHF equation in case IV. At each structure (I-IV), the coefficient of the dominant configuration was ap proximately 0.95, indicating that a single reference CI SD was satisfactory for this study. Structure I corresponds to a stable PNO molecule. Previous theoretical studies [8,9] by the SCF method have failed to provide a satisfactory value for the molecular binding energy. In fact, the NF bond energy is estimated to be 176.8 kJ mol-l with SD CI (the Davidson correction predicts 205.7 kJ mol-l), compared with an SCF value of only 41.9 kJ mol-l and an experimental value of 232 kJ mol-l [9 1. Compared with the experimental equilibrium structure, the main discrepancy is in the NF bond length, with 50% of the SCF error recovered by SD CI. The remaining discrepancy is believed to be mainly due to basis set limitations. Structure III corresponds to a loosely bound complex. The OF bond energy is computed to be negative with SCF and SD CI, but with the Davidson correction this changes to t24.5 kJ mol-l, suggesting that important contributions to the bond energy come from higher-order excitations.
As suggested by the IR spectra in N2 and Ar matrices at low temperatures (8-20 K), the NOF molecule is formed when NO or methyl nitrite reacts with fluorine atoms generated photochemically [5,18] or by microwave discharge [6]. Therefore, we have calculated ab initio harmonic frequencies of FNO and NOF at the CI level with the following results: FNO 1954.7, 872.6,615.4 cm-l;FON 2256.2,598.6,414.9 cm-l. The corresponding experimental harmonic frequencies of FNO are 1877,776,523 cm-l [19,20]. The v2 and v3 fundamentals of FON in solid matrices [5,18] have been assigned at 735 and 493 cm-l, respectively, but v1 is unassigned [6]. We predict a large increase in this frequency compared to FNO and a large variation of the corresponding bond length (see table 1). Unlike the related HCN-HNC system [21], the large value computed for the FNO-NOF isomerization energy indicates that the high-energy species is an unlikely candidate for direct experimental observations in equilibrium conditions in the gas phase. To discuss this point further the energy values in table 1, and the related force constants, are easily converted to rate constants. By neglecting the contribution of tunnelling to the isomerization reaction and using a classical approximation to the density of states for the reactant 177
Volume 129, number 2
CHEMICAL PHYSICS LETTERS
Table 2 Computed rate constants (s-l) for the FNO + FON and FON + FNO isomerization reactions as a function of temperature
22 August 1986
Table 3 Centrifugal contributions metric top
to the rotational energy of an asym-
7’ (K)
FNO + FON
FON -, FNO
Operator
Coefficient
100 500 1000
0 0 2 x 10-2
2 x 10-s 2 x 10’ 2 x 108
2
- AJ
j2j2
[22,23], values for the two rate constants can be obtained and are reported in table 2. The dissociation reaction of FON was not investigated. Theoretically, structure III proved to be the most elusive of the species investigated. Due to the very low values of some of the curvature of the potential energy surface, 14 CI gradient evaluations were required to locate the corresponding minimum of the surface. Using a quasi-Newton procedure based on the MurtaghSargent algorithm [24]. For this molecule and for similar loosely bound complexes, different optimization strategies, such as the one proposed by Comeau [25], where all energies and gradients progressively evaluated in the course of the optimization process are used to obtain a global representation of the surface in the region of interest, are likely to be more effective than optimization procedures exploiting only the local prop erties at each point of the surface. This is especially important for CI gradient studies, which require considerable computational resources. Structure II corresponds to a saddle point on the potential surface and it is considered to be the activated complex for the FON + FNO isomerization reaction. The activation barrier is estimated to be 26.3 kJ mol-1 ; addition of the Davidson correction giving an estimate of 36.8 kJ mol-l.
interaction constants of F’NO
Centrifugal forces manifest themselves in high-resolution spectroscopy. Their main effect is to shift the rotational molecular levels from the rigid-rotor expressions by terms which depend upon the fourth and the sixth power of rotational angular-momentum operators. For an asymmetric top [26,27] the additional terms are given in table 3. The coefficients A, 6, H, h, are referred to as quartic (A, 6) and sextic (H, h) cen178
J2j_2
-AK -263
IJ,“,J! I+
-6K
.P
molecule
3. Rotation-vibration
-AJK
:?z'z
HJ HJK HKJ HK
j4j2
2hJ hJK hK
trifugal distortion constants. Other manifestations of vibration-rotation interaction are the change of the rotational constants with the vibrational state, i.e. cr; = BO(n, = 0) - P(n,
= 1)
(rJ=(I,b,c)
Table 4 Quadratic and cubic force constants for FNO and FON evaluated by (a) SCF and (b) Cl gradient methods. The units are al Amn where n is the number of stretching coordinates appear ing in the definition of the force constants. Index 1, 2 are for stretching and 3 for the bending coordinates FNO
kll klz kn b-2 km k33 km hz km km km km km kin km
NOF
(a)
09
OJ)
20.133 2.994 0.665 4.209 0.581 2.694 -141.374 -30.406 -4.830 -1.135 -10.794 -3.448 -1.579 -4.995 -3.356
17.407 2.460 0.553 3.024 0.360 2.265 -127.375 -17.534 -4.172 -3.608 -6.627 -2.624 -0.797 -4.632 -2.258
22.567 0.926 -0.033 1.883 0.215 0.805 - -156.228 -7.408 -0.621 -2.777 -4.849 0.232 0.536 -2.256 -0.650
Volume 129, number 2
CHEMICAL PHYSICS LETTERS
and the inertial defect
22 August 1986
6A100 = A loo - Aooo*
Aooo = ZC - (1, + I.),
By using perturbation theory all these properties can be expressed in terms of force constants, atomic masses and equilibrium values of the internal coordinates. In particular, quartic centrifugal distortion con-
which, for a triatomic molecule, differs from zero due to vibrational motion. The inertial defects also change with the vibrational state, i.e.
Table 5 Spectroscopic constants for FNO. EqayiIibrium rotational constants (MHz), harmonic frequencies (cm-‘), quartic (kHz) and sextic ; mertiaI defects and inertial defect differences (amu A2) and Q vibration-rotation mterac(Hz) centrifugal distortion constants tion constants (MHz) computed by (a) SCF and (b) CI gradient techniques. The values in column (c) have been computed at the experimental geometry with the computed force field. Experhnental values (d) are from ref. [ 121
(4
(b)
w
(4
102195.19 13355.36 11811.75
95724.67
12501.24 11057.22
94961.77 11897.16 10572.59
94961.77 11897.16 10572.59
2101.5 726.8
872.6 1954.7 615.4
873.6 1953.8 610.9
775.5 1876.8 522.9
“JK AK 6J 6K
14.0 -30.7 3300 2.1 77.5
16.2 -33.8 3260 2.4 85.0
14.4 -41.5 3110 2.0 76.7
19.6 -35.3 3928 2.7 107.7
HJ HJK HKJ HK hJ hJK hK
0.0
-0.3 -26.3 365.0 0.0 -0.2 32.3
0.0 0.3 -32.8 388.0 0.0 -0.1 40.3
0.0 0.3 -29.9 366.0 0.0 -0.1 35.7
0.0 1.6 -52.9 628.0 0.0 0.4 61.9
Ae Be Ce
919.7
Wl w2 w3
*J
*ooo
0.0931 -0.0120 0.0635 0.1347
6AlOO 6*0x0 ~*OOI
359.4
393.2
19.4
-0.7
-4.5
- 14.4
-1.8
-9.0
-248.0
-327.8
73.7 73.3 -438.3
b
a) Cubic force constant
k123
0.1162 -0.0111 0.1185 0.1319
292.2
-139.6
a3
0.1040 -0.0121 0.0916 0.1285
262.3
15.3
a’:
0.1045 -0.0119 0.0860 0.1349
0.5 -226.3 49.7 56.6 -505.7
50.0 56.7 -561.8
30.1 45.5 -620.0
94.1
102.3
95.9
89.0
105.0
105.9
97.2
91.1
from ref. [ 131.
179
Volume 129. number 2
CHEMICAL PHYSICS LETTERS
&ants and inertial defects are related to the harmonic components of the force field [26,27], while the sextic constants and the o vibration-rotation constants have contributions from the cubic components. To evaluate the quadratic and the cubic force field, six geometries around each stationary point were considered and the force constants evaluated by quadratic polynomial interpolation of the computed gradients (table 4). Compared to the values quoted in ref. [13], our results allow a more consistent comparison of the SCF and the CI force fields, since the CI energies of the two isomers have been properly optimized. As shown by comparison with the experimental values in table 5, due to the systematic error of the SCF description, harmonic frequencies are overestimated and bond lengths underestimated. In the present case, the error is significant for the NF bond length. The overall agreement is satisfactory for most of the remaining constants even at the SCF level. Most notably, the signs and the relative magnitude of the 01constants are correctly predicted, with the exception of the two vibration-rotation constants with the smallest absolute value (of, ai). CI improves the agreement with experiment for all the constants. The improvement is significant for the a2 constant and we relate it to a more significant change of the corresponding normal mode. Values in column (c), which were obtained using the theoretical force field and the experimental geometry show, by comparison, how the error in the geometry prediction propagates to the spectroscopic parameters. The effect is larger for cut, oa2, cua 3 which correspond to the largest rotational constants. Indirectly, the values in column (c) indicate that CI gives a reasonably close approximation to the quadratic and cubic force field of this molecule.
Acknowledgement PP would like to acknowledge financial support from CNR (Rome) and Professor A.D. Buckingham for hospitality in Cambridge. All members of the Department of Theoretical Chemistry of Cambridge are acknowledged for helpful discussions during the course of this work and in particular Drs. R.D. Amos and J.E. Rice for many elucidations about the use of their programs. 180
22 August 1986
References [l] R.L. Cook, J. Chem. Phys. 42 (1965) 2927. [ 21 G. CazzoIi, C. Degli Esposti, P. Pahnieri and S. Simeone, J. Mol. Spectry. 97 (1983) 165. [ 3 ] W.H. Kirchhoff and E.B. Wilson Jr., J. Am. Chem. Sot. 85 (1963) 1726. [4] S. Mizumoto, J. Izumi, T. Beppu and E. Hirota, BuII. Chem. Sot. Japan 45 (1972) 786. [5 ] R.R. Smardzewski and W.B. Fox. J. Chem. Phvs. -. 60 (1974) 2104. 161M.E. Jacox, J. Phys. Chem. 87 (1983) 4940. 171 S.C. Foster and J.W.C. Johns, J. Mol. Spectry. 103 (1984) 176. 181 J. Peslak Jr., D.S. Klett and C.W. David, J. Am. Chem. sot. 93 (1971) 5001. PI L.J. Lawlor, K. Vasudevan and F. Crein, J. Am. Chem. Sot. 100 (1978) 8062. [lOI J.E. Rice, R.D. Amos, N.C. Handy, T.J. Lee and H.F. Schaefer III, J. Chem. Phys. (1986), to be published. 1111 R.D. Amos, CADPAC, the Cambridge Analytic Derivative Package, publication CCl/84/4, SERC, Daresbury, Warrington WA4 4AD, UK. 1121 G. Cazzoli, C. Degli Esposti, P.G. Favero and P. PaImieri, Nuovo Cimento 3 (1984) 627. [I31 G.L. Bendazzoli, G. Cazzoli, C. DegIi Esposti, G. Fano, F. Ortolani and P. Palmieri, J. Chem. Phys. (1986), to be published. [ 141 T.H. Dunning Jr., J. Chem. Phys. 53 (1970) 2823. [IS] T.H. Dunning Jr., J. Chem. Phys. 55 (1971) 3958. [la] J. PaIdus, J. Chem. Phys. 61 (1972) 5321; I. Shavitt, Intern. J. Quantum Chem. Sll(l977) 131; S12 (1978) 5; B.R. Brooks and H.F. Schaefer III, J. Chem. Phys. 70 (1979) 5092. [ 171 E.R. Davidson, in: The world of quantum chemistry, eds. R. Daudel and B. PuImam~ (ReideI, Dordrecht, 1974). [ 181 R.R. Smardzewski arid W.B. Fox, J. Chem. Sot. Commun. (1974) 241. [19] L.H. Jones, L.B. Asprey and R.R. Ryan, J. Chem. Phys. 47 (1967) 3371. 1201 R.R. Ryan and L.H. Jones, J. Chem. Phys. 50 (1969) 1492. [21] A.G. Maki and R.L. Sams, J. Chem. Phys. 75 (1981) 4178. [22] W.H. Miller, J. Am. Chem. Sot. 101 (1979) 6810. (231 S.M. ColweIl, Mol. Phys 51 (1984) 1217. [24] B.A. Murtagh and W.H. Sargent, Comput. J. 13 (1970) 185. [=I D.C. Comeau, R.J. Zeiimer and I. Shavitt, in: Geometrical derivatives of energy surfaces and molecular properties, eds. P. Jorgensen and J. Simons (Reidel, Dordrecht, 1986). WI I.M. Mills, in: Molecular spectroscopy: modern research, eds. K.N. Rao and C.W. Mathews (Academic Press, New York, 1972). v71 M.R. AIiev and J.K. Watson, J. Mol. Spectry. 6 1 (1974) 29.