- Email: [email protected]
Heats of formation for ClFn (n=1–3)
23 June 2000
Chemical Physics Letters 323 Ž2000. 498–505 www.elsevier.nlrlocatercplett
Heats of formation for ClFn žn s 1–3/ Alessandra Ricca) Eloret Corporation NASA Ames Research Center Mail Stop 230-3 Moffett Field, CA 94035, USA Received 2 February 2000; in final form 11 April 2000
Abstract Accurate heats of formation have been computed for ClFn Ž n s 1–3.. The accuracy of the results is strongly dependent on the basis set quality and it is crucial to add at least one tight d function to Cl. The atomization energies are corrected for scalar relativistic, core-valence, spin–orbit, thermal effects, and zero-point energy. Our heats of formations are in very good agreement with the experimental values reported by Gurvich therefore suggesting that the JANAF values are slightly underestimated. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Chemical vapor deposition ŽCVD. processes require a periodic cleaning of the chamber to remove the material that deposits on the walls. To minimize the damage to the equipment the cleaning reagent must be able to react without the need of ion bombardment. ClF3 is now widely used to clean in situ semiconductor process tools w1x. It reacts readily at room temperature and decomposes to generate fluorine atoms and ClFx fragments. The reactions of ClF3 are usually spontaneous and can be violent. To improve the handling and safety, it is important to know the thermodynamic properties of ClF3 and its fragments. While the heats of formation of ClF and ClF3 are known from experiment very few data are available for ClF2 which is weakly bound. Theory is particularly well-suited to provide the data for molecules difficult to study experimentally. In the present paper we report accurate heats of formation for ClF3 , ClF2 , and ClF, computed using the coupled )
Fax: q1-650-604-0350; e-mail: [email protected]
cluster singles and doubles approach w2x, including a perturbational estimate of the triple excitations w3x, CCSDŽT., in conjunction with extrapolation to the complete basis set ŽCBS. limit.
2. Methods Geometries are first optimized using density functional theory ŽDFT., in conjunction with the hybrid w4x B3LYP w5x approach. We use both the 6-31GU and the 6-311 q GŽ2df. basis sets w6x. For comparison we also optimize the geometries at the CCSDŽT. level using the augmented-correlation-consistent polarized valence ŽAVNZ. sets developed by Dunning and co-workers w7–10x, namely the triple-zeta ŽAVTZ., quadruple-zeta ŽAVQZ., and quintuple-zeta ŽAV5Z. sets. For open-shell molecules, energetics are computed using the restricted coupled cluster singles and doubles approach w2,11x, including the effect of connected triples determined using perturbation theory w3,12x, RCCSDŽT.. In these CCSDŽT. calculations only the valence electrons are correlated
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 5 6 2 - 5
A. Ricca r Chemical Physics Letters 323 (2000) 498–505
Žthe Cl 3s and 3p and the F 2s and 2p.. The harmonic frequencies are computed at the B3LYPr6-31GU level of theory and the zero-point energy is computed as one half the sum of the harmonic frequencies, which are not scaled. To study the effect of additional tight d functions on chlorine, we add one and two tight d functions to the AVNZ basis sets to yield the AVNZq 1d and the AVNZq 2d basis sets, respectively. The tight d functions are even-tempered with a b value of 3.0. Core-valence ŽCV. calculations are performed by including the F 1s and the Cl 2s and 2p electrons in the correlation treatment. The F and Cl basis sets used in these CV calculations are derived from the AVTZ valence basis sets. The F basis set is derived by contracting the first five s primitives to one function. The rest of the s functions and all the p functions are uncontracted. The Cl basis set is derived by contracting the first eight s primitives to two functions and the first four p primitives to one function. Three even-tempered tight d functions and two even-tempered tight f functions are added to both F and Cl. A b value of 2.5 is used for the d functions and a value of 3.0 is used for the f functions. The a values are the tightest existing exponents. The core-valence results are not corrected for basis set superposition error ŽBSSE.. To improve the accuracy of the results, several extrapolation techniques are used. We use the twopoint Ž ny3 . scheme described by Helgaker et al. w13x. We also use the two-point Ž ny4 ., three-point Ž ny4 q ny6 ., and variable a Ž nya . schemes described by Martin w14x. The scalar relativistic effect is computed at the modified coupled pair functional w15x ŽMCPF. level of theory using the AVTZ basis set as the difference between the results using the nonrelativistic and the Douglas Kroll ŽDK. approaches w16x. In the DK calculations, the same primitive basis sets are used and contracted in the same manner as in the nonrelativistic calculations, but the contraction coefficients are taken from DK atomic calculations. The atomic spin–orbit contribution to the atomization energy is taken from experiment w17x and we use the difference between the lowest J component and the weighted average energy. The heat capacity, entropy, and temperature dependence of the heat of formation are computed for
499
300 to 4000 K using a rigid rotorrharmonic oscillator approximation. We include the effect of electronic excitation for the atoms using the data from Moore w17x. These results are fit in two temperature ranges, 300–1000 K and 1000–4000 K using the Chemkin w18x fitting program and following their constrained three step procedure. The B3LYP calculations are performed using Gaussian98 w19x, the RCCSDŽT. are performed using Molpro w20x, and the MCPF calculations are performed using Molecule– Sweden w21x. The DK integrals are computed using a modified version of the program written by Hess w16x.
3. Results and discussion The computed and experimental geometries of ClFn Ž n s 1–3. are reported in Table 1 and the harmonic frequencies are reported in Table 2. For all the systems, the systematic improvement of the basis set from AVTZ to AV5Zq 1d has the effect of reducing the Cl–F bond length. The geometries are practically converged for the AV5Z basis set. ClF has a 1 Sq ground state with an experimental Cl–F ˚ w22x. The geometries combond length of 1.628 A puted at the B3LYPr6-311q GŽ2df. and at the CCSDŽT.rAVTZ levels of theory are very similar to each other, but differ from the experimental geometry. It is necessary to use at least the AV5Z basis set in conjunction with the CCSDŽT. approach to obtain close agreement with experiment. ClF2 in its 2A 1 ground state has a bent structure with C2 Õ symmetry. The two Cl–F bonds are longer than the Cl–F bond in ClF indicating a weaker bonding. Experimentally the F–Cl–F angle is known to be 140 " 19 w23x. The geometry of ClF2 is sensitive to the theoretical treatment used and, as for ClF, a basis set of at least AV5Z quality and the CCSDŽT. approach must be used. ClF3 has a 1A 1 ground state with C2 Õ symmetry. The geometry has a T shape with one short axial Cl–F bond and two long equatorial Cl–F bonds. The axial bond is similar to the Cl–F bond in ClF whereas the two equatorial bonds are very close to the ones in ClF2 . We do not include tight d functions to the AV5Z basis set to optimize the ClF3 geometry as they have little effect on the geometry of ClF and ClF2 . Two experimental geometries have been re-
A. Ricca r Chemical Physics Letters 323 (2000) 498–505
500
Table 1 Geometries of ClFn Ž n s 1–3. optimized at the B3LYPr6-311q GŽ2df., CCSDŽT.rAVTZ, CCSDŽT.rAVQZ, CCSDŽT.rAV5Z, and CCSDŽT.rAV5Zq 1d levels of theory. The experimental values are given for comparison. The calculated r e values are compared with the experimental r e ones. The units are in angstroms and in degrees r ŽCl–F.
/ŽF–Cl–F.
ClF 1 Sq ClF2 2A 1 ClF3 1A 1
Ž C`Õ . Ž C2 Õ . Ž C2 Õ .
B3LYPr6-311q GŽ2df. 1.648 1.740 1.624 Fax 1.730 Feq
153.96 87.91 Fax ClFeq 175.81 FeqClFeq
ClF 1 Sq ClF2 2A 1 ClF3 1A 1
Ž C`Õ . Ž C2 Õ . Ž C2 Õ .
CCSDŽT.rAVTZ 1.646 1.726 1.613 Fax 1.717 Feq
152.04 86.98 Fax ClFeq 173.96 FeqClFeq
ClF 1 Sq ClF2 2A 1 ClF3 1A 1
Ž C`Õ . Ž C2 Õ . Ž C2 Õ .
CCSDŽT.rAVQZ 1.637 1.715 1.603 Fax 1.706 Feq
152.42 87.05 Fax ClFeq 174.10 FeqClFeq
ClF 1 Sq Ž C`Õ . ClF2 2A 1 Ž C2 Õ . ClF3 1A 1 Ž C2 Õ .
CCSDŽT.rAV5Z 1.630 1.706 1.595 Fax 1.698 Feq
152.84 87.12 Fax ClFeq 174.24 FeqClFeq
CCSDŽT.rAV5Zq 1d 1.629 1.705
152.97
ClF 1 Sq Ž C`Õ . ClF2 2A 1 Ž C2 Õ .
Experiment 1.628 a
ClF 1 Sq Ž C`Õ . ClF2 2A 1 Ž C2 Õ . ClF3 1A 1 Ž C2 Õ .
a b c d
Ref. Ref. Ref. Ref.
1.598 1.698
c
1.584 1.703
d
c
d
140 " 19 b 87.5 c Fax ClFeq
Fax Feq Fax Feq
87.0
d
Fax ClFeq
w22x. w23x. w24x. w25x.
ported for ClF3 w24,25x. Both have a T shape with C 2 Õ symmetry. The Cl–Feq bond lengths agree to
˚ whereas the Cl–Fax bond lengths within 0.005 A ˚ Overall the two experimenagree to within 0.014 A.
Table 2 The computed harmonic frequencies, in cmy1 ClF ClF2 ClF3
785 245Ža 1 . 305Ža 1 .
543Žb 2 . 314Žb1 .
552Ža 1 . 402Žb 2 .
542Ža 1 .
739Ža 1 .
755Žb 2 .
A. Ricca r Chemical Physics Letters 323 (2000) 498–505 Table 3 Total Cl d populations of ClFn Ž ns1–3. computed at the B3LYP level of theory by a Mulliken population analysis. The geometries are optimized at the B3LYPr6-311qGŽ2df. level of theory
ClF ClF2 ClF3
AVTZ
AVTZq1d
AVTZq2d
0.07 0.16 0.28
0.08 0.19 0.35
0.08 0.19 0.35
tal geometries are very similar. Our best results at the CCSDŽT.rAV5Z level of theory agree somewhat better with the experimental geometry of Smith w24x. In Table 3 we report the total Cl d populations of ClFn Ž n s 1–3. obtained at the B3LYP level of theory by a Mulliken population analysis. To show the influence of the tight d orbitals on the d population we report the Cl d populations as a function of the AVTZ, AVTZq 1d, and AVTZq 2d basis sets. Adding one tight d function on Cl has a large effect particularly on the Cl d population of ClF3 , whereas the addition of a second tight d has essentially no effect on the Cl d populations of ClFn Ž n s 1–3.. We suspect that the addition of one tight d function on Cl will also affect the energetics.
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The computed and extrapolated atomization energies are reported in Tables 4 and 5. In Table 4 we report the atomization energies at the AVTZ, AVQZ, and AV5Z levels with and without additional tight d functions. For ClF3 the addition of tight d functions to the AV5Z basis set makes the calculations prohibitively large and we could not perform them. The AVNZq 1d and the AVNZq 2d results are extrapolated using the TZ,QZ ny4 scheme. To obtain the CBS values we correct the TZ,QZ ny4 results by the average difference between the ny4 q ny6 and the ny4 results for ClF and ClF2 . The results for ClF and ClF2 show that for the AVNZq 1d basis set the ny4 q ny6 values differ from the ny4 ones by y0.26 kcalrmol while for the AVNZq 2d basis set they differ by y0.40 kcalrmol. We use these two corrections to obtain our final ClF3 AVNZq 1d and AVNZq 2d CBS values. The addition of one tight d has the largest effect on the atomization energy and this effect increases going from ClF to ClF3 as the systems becomes increasingly more hypervalent. Adding a second tight d function modifies only slightly the CBS value. We have previously shown w26x that by comparing the results of various extrapolations it is possible to pick the most reliable basis set. The three-point
Table 4 Atomization energies Žin kcalrmol. computed at the CCSDŽT. level of theory and without including zero-point energies. The geometries used are optimized at the CCSDŽT.rAVNZ ŽNZ s TZ, QZ, and 5Z. levels of theory. The CBS values are obtained using the three-point Martin Ž ny4 q ny6 . extrapolated values unless noted otherwise Basis set
TZ
AVNZ AVNZq 1d AVNZq 2d
ClF 58.44 59.21 59.44
60.97 61.58 61.67
62.16 62.21 62.22
63.36 62.65 62.57
AVNZ AVNZq 1d AVNZq 2d
ClF2 70.70 72.57 73.08
74.66 76.10 76.30
76.76 77.12 77.14
79.00 77.88 77.71
AVNZ AVNZq 1d AVNZq 2d
ClF3 115.86 119.62 120.62
122.80 125.57 125.96
126.65
130.82 128.75 128.65
a b
QZ
5Z
Obtained using the two-point Martin Ž ny4 . value corrected by y0.26 kcalrmol. Obtained using the two-point Martin Ž ny4 . value corrected by y0.40 kcalrmol.
CBS
a b
A. Ricca r Chemical Physics Letters 323 (2000) 498–505
502
Table 5 Extrapolated atomization energies Žin kcalrmol. ny3 QZ,5Z
ny4 TZ,QZ
ny4 QZ,5Z
ClF AVNZ ClF AVNZq 1d ClF AVNZq 2d
62.82 63.30 63.29
63.40 62.87 62.80
62.43 62.94 62.95
63.12 62.72 62.67
63.36 62.65 62.57
64.14 Ž2.334. 62.61 Ž4.743. 62.53 Ž5.058.
ClF2 AVNZ ClF2 AVNZq 1d ClF2 AVNZq 2d
77.56 78.68 78.65
78.96 78.19 78.02
76.95 78.14 78.16
78.47 77.95 77.82
79.00 77.88 77.71
81.57 Ž1.806. 77.83 Ž4.432. 77.65 Ž4.846.
ClF3 AVNZ ClF3 AVNZq 1d ClF3 AVNZq 2d
127.87 129.92 129.86
130.69
126.81 129.01 129.05
129.78
130.82
136.79 Ž1.603.
a
ny4 q ny6 TZ,QZ,5Z
a
ny3 TZ,QZ
Basis set
Variable a TZ,QZ,5Z
The a values are reported in parentheses.
Martin Ž ny4 q ny6 . values computed using the AVNZ basis set don’t agree well with the variable a ones and the a values are significantly smaller than 4.5. The disagreement between the ny4 q ny6 and the variable a extrapolated results increases going from ClF to ClF3 . By adding one tight d function the agreement between the ny4 q ny6 and the variable a extrapolations becomes very good for ClF and ClF2 and the a value increases significantly. Adding a second tight d function to Cl reduces slightly the extrapolated values. Clearly the AVNZ basis set is not adequate to describe the ClFn systems, particularly ClF2 and ClF3 which are hypervalent and a basis set of at least AVNZq 1d quality must to be used. For all the systems we use the AVNZq 2d extrapolated values as our AE CBS values. We assume that these extrapolated values are accurate to "1.0 kcalrmol based on the excellent agreement between
the ny4 q ny6 and the variable a extrapolation values. We correct the AE CBS values for scalar relativistic effects, spin–orbit effects, core-valence effects, zero-point energy, and thermal effects to obtain our best atomization energies at 0 K ŽAEŽ0.. and at 298 K ŽAEŽ298.. which are reported in Table 6. The core-valence and the scalar relativistic effects are negligible for ClF2 in agreement with the fact that the system is weakly bound. ClF and ClF3 have very similar core-valence and scalar relativistic effects as an indication that the bonding in ClF3 consists mainly of one Cl–F bond which is very similar in nature to the one in ClF. Our AEŽ0. and AEŽ298. values are used in conjunction with the D H f Ž0 K. and the D H f Ž298 K. values for Cl and F to obtain the heats of formation reported in Table 7. We assign an error bar of "1.0 kcalrmol to our computed heats of formation. Experimental values at 298 K are available for both ClF and ClF3 . The most recent
Table 6 Atomization energies Žin kcalrmol. computed at 0 K and 298 K and corrected for scalar relativistic effects, spin–orbit effects, core-valence effects, zero-point energy, and thermal effects AE CBS ClF ClF2 ClF3 a b
62.57 77.71 128.65
a
Rel
SO
CV
ZPE
Therm b
AEŽ0.
AEŽ298.
y0.17 q0.08 y0.19
y1.23 y1.61 y2.00
q0.09 0.00 q0.08
y1.12 y1.92 y4.37
q0.93 q1.69 q2.85
60.14 74.26 122.17
61.07 75.95 125.02
Taken from Table 4. Therm s w H Ž298. y H Ž0.x trans q w H Ž298. y H Ž0.x rot q w H Ž298. y H Ž0.x vib q w H Ž298. y H Ž0.xelec .
0K
298 K
Theory PW ClF ClF2 ClF3 Cl F a
a
y13.1 y8.7 y38.2 w18.47x w87.25x
Theory PW y13.1 y9.0 y39.1 w28.99x w18.97x
Experiment G2 y14.0
Feller b
y38.4 b ,y39.6 c
d
y13.2
JANAF w31x
Gurvich w27x
y12.0"0.1
y13.3"0.1
y38.0"0.7 28.99 18.97
y39.3"1.2
Present work. The values given in square brackets for Cl and F are taken from Gurvich w27x. Original G2 w28x. c G2 modified to include spin–orbit corrections w29x. d Feller and Peterson w30x. To obtain their AEŽ0. value we correct the experimental D 0 value of 60.4 kcalrmol by y0.13 kcalrmol, which is the average between the errors of the three CBS extrapolations used by the authors. The AEŽ0. is converted to AEŽ298. using our thermal correction. b
A. Ricca r Chemical Physics Letters 323 (2000) 498–505
Table 7 Heats of formation Žin kcalrmol.
503
504
A. Ricca r Chemical Physics Letters 323 (2000) 498–505
compilation is the one by Gurvich w27x. On the theoretical side, G2 values have been computed for ClF and ClF3 w28x. For ClF3 the original G2 values have been improved to include spin–orbit corrections w29x. Feller and Peterson w30x have performed accurate calculations to obtain the D 0 value for ClF. We have converted their D 0 value to a D 298 value using our thermal correction, and then computed their heat of formation at 298 K. Our result for ClF at 298 K is in very good agreement with the result of Feller and Peterson and with the experimental value of Gurvich. The G2 value is somewhat too negative. For ClF3 our heat of formation at 298 K is in good agreement with the modified G2 value and with the experimental value of Gurvich. Overall our results are in excellent agreement with the experimental values of Gurvich which suggests that the JANAF w31x values are slightly underestimated. We use our heats of formation at 298 K, the CCSDŽT.rAV5Z optimized geometries and the B3LYP vibrational frequencies to compute the heat capacity, entropy, and heat of formation from 300 to 4000 K. The parameters obtained from the resulting fits can be found on the web w32x. 4. Conclusions The atomization energies of ClFn Ž n s 1–3. are computed at the CCSDŽT. level of theory. The basis set quality strongly affects the results. It is essential to add at least one tight d function to Cl to obtain accurate properties. The atomization energies are extrapolated to the CBS limit and corrected for scalar relativistic, core-valence, spin–orbit, thermal effects, and for zero-point energy. We combine the atomization energies with the heats of formation of Cl and F to obtain the heats of formation of ClFn Ž n s 1–3.. Our heats of formation agree with previous calculated values and are very similar to the experimental values reported by Gurvich. This suggests that the JANAF values are slightly underestimated. Acknowledgements A.R. would like to acknowledge helpful discussions with Charlie Bauschlicher. A.R. was supported
by NASA Contracts No. NAS2-14031 and No. NAS2-99092 to ELORET.
References w1x C.J. Gugliemini, A.D. Johnson, Semiconductor Int. 22 Ž1999. 162. w2x R.J. Bartlett, Annu. Rev. Phys. Chem. 32 Ž1981. 359. w3x K. Raghavachari, G.W. Trucks, J.A. Pople, M. Head-Gordon, Chem. Phys. Lett. 157 Ž1989. 479. w4x A.D. Becke, J. Chem. Phys. 98 Ž1993. 5648. w5x P.J. Stephens, F.J. Devlin, C.F. Chabalowski, M.J. Frisch, J. Phys. Chem. 98 Ž1994. 11623. w6x M.J. Frisch, J.A. Pople, J.S. Binkley, J. Chem. Phys. 80 Ž1984. 3265, and references therein. w7x T.H. Dunning, J. Chem. Phys. 90 Ž1989. 1007. w8x R.A. Kendall, T.H. Dunning, R.J. Harrison, J. Chem. Phys. 96 Ž1992. 6796. w9x D.E. Woon, K.A. Peterson, T.H. Dunning, unpublished. w10x D.E. Woon, T.H. Dunning, J. Chem. Phys. 98 Ž1993. 1358. w11x P.J. Knowles, C. Hampel, H.-J. Werner, J. Chem. Phys. 99 Ž1993. 5219. w12x J.D. Watts, J. Gauss, R.J. Bartlett, J. Chem. Phys. 98 Ž1993. 8718. w13x T. Helgaker, W. Klopper, H. Koch, J. Noga, J. Chem. Phys. 106 Ž1997. 9639. w14x J.M.L. Martin, Chem. Phys. Lett. 259 Ž1996. 669. w15x D.P. Chong, S.R. Langhoff, J. Chem. Phys. 84 Ž1986. 5606. w16x B.A. Hess, Phys. Rev. A 33 Ž1986. 3742. w17x C.E. Moore, Atomic energy levels; US National Bureau of Standards: Washington, DC, 1949; circular 467. w18x R.J. Kee, F.M. Rupley, J.A. Miller, SAND87-8215B. Sandia National Laboratories: Albuquerque, NM, 1991. w19x Gaussian 98, Revision A.6, M.J. Frisch et al., Gaussian, Inc., Pittsburgh, PA, 1998. w20x MOLPRO is a package of ab initio programs written by H.-J. Werner, P.J. Knowles, with contributions from J. Almlof ¨ et al. The closed shell CCSD program is described in C. Hampel, K. Peterson, H.-J. Werner Chem. Phys. Lett. 190 Ž1992. 1. w21x MOLECULE-SWEDEN is an electronic structure program written by J. Almlof ¨ et al. w22x K.P. Huber, G. Herzberg, Constants of Diatomic Molecules, Van Nostrand Reinhold, New York, 1979. w23x G. Mamantov, D.G. Vickroy, E.J. Vasini, T. Maekawa, M.C. Moulton, Inorg. Nucl. Chem. Lett. 6 Ž1970. 701. w24x D.F. Smith, J. Chem. Phys. 21 Ž1953. 609. w25x O. Madelung, Landolt-Bornstein: Numerical Data and Func¨ tional Relationships in Science and Technology, Vol. IIr15, Springer, Berlin, 1987. w26x C.W. Bauschlicher, A. Ricca, J. Phys. Chem. A 102 Ž1998. 8044. w27x L.V. Gurvich, I.V. Veyts, C.B. Alcock, Thermodynamic Properties of Individual Substances, CRC Press, Boca Raton, 1994.
A. Ricca r Chemical Physics Letters 323 (2000) 498–505 w28x L.A. Curtiss, K. Raghavachari, P.C. Redfern, J.A. Pople, J. Chem. Phys. 106 Ž1997. 1063. w29x G.A. Petersson, D.K. Malick, W.G. Wilson, J.W. Ochterski, J.A. Montgomery, M.J. Frisch, J. Chem. Phys. 109 Ž1998. 10570.
505
w30x D. Feller, K.A. Peterson, J. Chem. Phys. 110 Ž1999. 8384. w31x M.W. Chase, C.A. Davies, J.R. Downey, D.J. Frurip, R.A. McDonald, A.N. Syverud, J. Phys. Chem. Ref. Data 14, Suppl. 1., 1985. w32x The values can be found at http:rrwww.ipt.arc.nasa.gov.
Chemical Physics Letters 323 Ž2000. 498–505 www.elsevier.nlrlocatercplett
Heats of formation for ClFn žn s 1–3/ Alessandra Ricca) Eloret Corporation NASA Ames Research Center Mail Stop 230-3 Moffett Field, CA 94035, USA Received 2 February 2000; in final form 11 April 2000
Abstract Accurate heats of formation have been computed for ClFn Ž n s 1–3.. The accuracy of the results is strongly dependent on the basis set quality and it is crucial to add at least one tight d function to Cl. The atomization energies are corrected for scalar relativistic, core-valence, spin–orbit, thermal effects, and zero-point energy. Our heats of formations are in very good agreement with the experimental values reported by Gurvich therefore suggesting that the JANAF values are slightly underestimated. q 2000 Elsevier Science B.V. All rights reserved.
1. Introduction Chemical vapor deposition ŽCVD. processes require a periodic cleaning of the chamber to remove the material that deposits on the walls. To minimize the damage to the equipment the cleaning reagent must be able to react without the need of ion bombardment. ClF3 is now widely used to clean in situ semiconductor process tools w1x. It reacts readily at room temperature and decomposes to generate fluorine atoms and ClFx fragments. The reactions of ClF3 are usually spontaneous and can be violent. To improve the handling and safety, it is important to know the thermodynamic properties of ClF3 and its fragments. While the heats of formation of ClF and ClF3 are known from experiment very few data are available for ClF2 which is weakly bound. Theory is particularly well-suited to provide the data for molecules difficult to study experimentally. In the present paper we report accurate heats of formation for ClF3 , ClF2 , and ClF, computed using the coupled )
Fax: q1-650-604-0350; e-mail: [email protected]
cluster singles and doubles approach w2x, including a perturbational estimate of the triple excitations w3x, CCSDŽT., in conjunction with extrapolation to the complete basis set ŽCBS. limit.
2. Methods Geometries are first optimized using density functional theory ŽDFT., in conjunction with the hybrid w4x B3LYP w5x approach. We use both the 6-31GU and the 6-311 q GŽ2df. basis sets w6x. For comparison we also optimize the geometries at the CCSDŽT. level using the augmented-correlation-consistent polarized valence ŽAVNZ. sets developed by Dunning and co-workers w7–10x, namely the triple-zeta ŽAVTZ., quadruple-zeta ŽAVQZ., and quintuple-zeta ŽAV5Z. sets. For open-shell molecules, energetics are computed using the restricted coupled cluster singles and doubles approach w2,11x, including the effect of connected triples determined using perturbation theory w3,12x, RCCSDŽT.. In these CCSDŽT. calculations only the valence electrons are correlated
0009-2614r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 0 0 9 - 2 6 1 4 Ž 0 0 . 0 0 5 6 2 - 5
A. Ricca r Chemical Physics Letters 323 (2000) 498–505
Žthe Cl 3s and 3p and the F 2s and 2p.. The harmonic frequencies are computed at the B3LYPr6-31GU level of theory and the zero-point energy is computed as one half the sum of the harmonic frequencies, which are not scaled. To study the effect of additional tight d functions on chlorine, we add one and two tight d functions to the AVNZ basis sets to yield the AVNZq 1d and the AVNZq 2d basis sets, respectively. The tight d functions are even-tempered with a b value of 3.0. Core-valence ŽCV. calculations are performed by including the F 1s and the Cl 2s and 2p electrons in the correlation treatment. The F and Cl basis sets used in these CV calculations are derived from the AVTZ valence basis sets. The F basis set is derived by contracting the first five s primitives to one function. The rest of the s functions and all the p functions are uncontracted. The Cl basis set is derived by contracting the first eight s primitives to two functions and the first four p primitives to one function. Three even-tempered tight d functions and two even-tempered tight f functions are added to both F and Cl. A b value of 2.5 is used for the d functions and a value of 3.0 is used for the f functions. The a values are the tightest existing exponents. The core-valence results are not corrected for basis set superposition error ŽBSSE.. To improve the accuracy of the results, several extrapolation techniques are used. We use the twopoint Ž ny3 . scheme described by Helgaker et al. w13x. We also use the two-point Ž ny4 ., three-point Ž ny4 q ny6 ., and variable a Ž nya . schemes described by Martin w14x. The scalar relativistic effect is computed at the modified coupled pair functional w15x ŽMCPF. level of theory using the AVTZ basis set as the difference between the results using the nonrelativistic and the Douglas Kroll ŽDK. approaches w16x. In the DK calculations, the same primitive basis sets are used and contracted in the same manner as in the nonrelativistic calculations, but the contraction coefficients are taken from DK atomic calculations. The atomic spin–orbit contribution to the atomization energy is taken from experiment w17x and we use the difference between the lowest J component and the weighted average energy. The heat capacity, entropy, and temperature dependence of the heat of formation are computed for
499
300 to 4000 K using a rigid rotorrharmonic oscillator approximation. We include the effect of electronic excitation for the atoms using the data from Moore w17x. These results are fit in two temperature ranges, 300–1000 K and 1000–4000 K using the Chemkin w18x fitting program and following their constrained three step procedure. The B3LYP calculations are performed using Gaussian98 w19x, the RCCSDŽT. are performed using Molpro w20x, and the MCPF calculations are performed using Molecule– Sweden w21x. The DK integrals are computed using a modified version of the program written by Hess w16x.
3. Results and discussion The computed and experimental geometries of ClFn Ž n s 1–3. are reported in Table 1 and the harmonic frequencies are reported in Table 2. For all the systems, the systematic improvement of the basis set from AVTZ to AV5Zq 1d has the effect of reducing the Cl–F bond length. The geometries are practically converged for the AV5Z basis set. ClF has a 1 Sq ground state with an experimental Cl–F ˚ w22x. The geometries combond length of 1.628 A puted at the B3LYPr6-311q GŽ2df. and at the CCSDŽT.rAVTZ levels of theory are very similar to each other, but differ from the experimental geometry. It is necessary to use at least the AV5Z basis set in conjunction with the CCSDŽT. approach to obtain close agreement with experiment. ClF2 in its 2A 1 ground state has a bent structure with C2 Õ symmetry. The two Cl–F bonds are longer than the Cl–F bond in ClF indicating a weaker bonding. Experimentally the F–Cl–F angle is known to be 140 " 19 w23x. The geometry of ClF2 is sensitive to the theoretical treatment used and, as for ClF, a basis set of at least AV5Z quality and the CCSDŽT. approach must be used. ClF3 has a 1A 1 ground state with C2 Õ symmetry. The geometry has a T shape with one short axial Cl–F bond and two long equatorial Cl–F bonds. The axial bond is similar to the Cl–F bond in ClF whereas the two equatorial bonds are very close to the ones in ClF2 . We do not include tight d functions to the AV5Z basis set to optimize the ClF3 geometry as they have little effect on the geometry of ClF and ClF2 . Two experimental geometries have been re-
A. Ricca r Chemical Physics Letters 323 (2000) 498–505
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Table 1 Geometries of ClFn Ž n s 1–3. optimized at the B3LYPr6-311q GŽ2df., CCSDŽT.rAVTZ, CCSDŽT.rAVQZ, CCSDŽT.rAV5Z, and CCSDŽT.rAV5Zq 1d levels of theory. The experimental values are given for comparison. The calculated r e values are compared with the experimental r e ones. The units are in angstroms and in degrees r ŽCl–F.
/ŽF–Cl–F.
ClF 1 Sq ClF2 2A 1 ClF3 1A 1
Ž C`Õ . Ž C2 Õ . Ž C2 Õ .
B3LYPr6-311q GŽ2df. 1.648 1.740 1.624 Fax 1.730 Feq
153.96 87.91 Fax ClFeq 175.81 FeqClFeq
ClF 1 Sq ClF2 2A 1 ClF3 1A 1
Ž C`Õ . Ž C2 Õ . Ž C2 Õ .
CCSDŽT.rAVTZ 1.646 1.726 1.613 Fax 1.717 Feq
152.04 86.98 Fax ClFeq 173.96 FeqClFeq
ClF 1 Sq ClF2 2A 1 ClF3 1A 1
Ž C`Õ . Ž C2 Õ . Ž C2 Õ .
CCSDŽT.rAVQZ 1.637 1.715 1.603 Fax 1.706 Feq
152.42 87.05 Fax ClFeq 174.10 FeqClFeq
ClF 1 Sq Ž C`Õ . ClF2 2A 1 Ž C2 Õ . ClF3 1A 1 Ž C2 Õ .
CCSDŽT.rAV5Z 1.630 1.706 1.595 Fax 1.698 Feq
152.84 87.12 Fax ClFeq 174.24 FeqClFeq
CCSDŽT.rAV5Zq 1d 1.629 1.705
152.97
ClF 1 Sq Ž C`Õ . ClF2 2A 1 Ž C2 Õ .
Experiment 1.628 a
ClF 1 Sq Ž C`Õ . ClF2 2A 1 Ž C2 Õ . ClF3 1A 1 Ž C2 Õ .
a b c d
Ref. Ref. Ref. Ref.
1.598 1.698
c
1.584 1.703
d
c
d
140 " 19 b 87.5 c Fax ClFeq
Fax Feq Fax Feq
87.0
d
Fax ClFeq
w22x. w23x. w24x. w25x.
ported for ClF3 w24,25x. Both have a T shape with C 2 Õ symmetry. The Cl–Feq bond lengths agree to
˚ whereas the Cl–Fax bond lengths within 0.005 A ˚ Overall the two experimenagree to within 0.014 A.
Table 2 The computed harmonic frequencies, in cmy1 ClF ClF2 ClF3
785 245Ža 1 . 305Ža 1 .
543Žb 2 . 314Žb1 .
552Ža 1 . 402Žb 2 .
542Ža 1 .
739Ža 1 .
755Žb 2 .
A. Ricca r Chemical Physics Letters 323 (2000) 498–505 Table 3 Total Cl d populations of ClFn Ž ns1–3. computed at the B3LYP level of theory by a Mulliken population analysis. The geometries are optimized at the B3LYPr6-311qGŽ2df. level of theory
ClF ClF2 ClF3
AVTZ
AVTZq1d
AVTZq2d
0.07 0.16 0.28
0.08 0.19 0.35
0.08 0.19 0.35
tal geometries are very similar. Our best results at the CCSDŽT.rAV5Z level of theory agree somewhat better with the experimental geometry of Smith w24x. In Table 3 we report the total Cl d populations of ClFn Ž n s 1–3. obtained at the B3LYP level of theory by a Mulliken population analysis. To show the influence of the tight d orbitals on the d population we report the Cl d populations as a function of the AVTZ, AVTZq 1d, and AVTZq 2d basis sets. Adding one tight d function on Cl has a large effect particularly on the Cl d population of ClF3 , whereas the addition of a second tight d has essentially no effect on the Cl d populations of ClFn Ž n s 1–3.. We suspect that the addition of one tight d function on Cl will also affect the energetics.
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The computed and extrapolated atomization energies are reported in Tables 4 and 5. In Table 4 we report the atomization energies at the AVTZ, AVQZ, and AV5Z levels with and without additional tight d functions. For ClF3 the addition of tight d functions to the AV5Z basis set makes the calculations prohibitively large and we could not perform them. The AVNZq 1d and the AVNZq 2d results are extrapolated using the TZ,QZ ny4 scheme. To obtain the CBS values we correct the TZ,QZ ny4 results by the average difference between the ny4 q ny6 and the ny4 results for ClF and ClF2 . The results for ClF and ClF2 show that for the AVNZq 1d basis set the ny4 q ny6 values differ from the ny4 ones by y0.26 kcalrmol while for the AVNZq 2d basis set they differ by y0.40 kcalrmol. We use these two corrections to obtain our final ClF3 AVNZq 1d and AVNZq 2d CBS values. The addition of one tight d has the largest effect on the atomization energy and this effect increases going from ClF to ClF3 as the systems becomes increasingly more hypervalent. Adding a second tight d function modifies only slightly the CBS value. We have previously shown w26x that by comparing the results of various extrapolations it is possible to pick the most reliable basis set. The three-point
Table 4 Atomization energies Žin kcalrmol. computed at the CCSDŽT. level of theory and without including zero-point energies. The geometries used are optimized at the CCSDŽT.rAVNZ ŽNZ s TZ, QZ, and 5Z. levels of theory. The CBS values are obtained using the three-point Martin Ž ny4 q ny6 . extrapolated values unless noted otherwise Basis set
TZ
AVNZ AVNZq 1d AVNZq 2d
ClF 58.44 59.21 59.44
60.97 61.58 61.67
62.16 62.21 62.22
63.36 62.65 62.57
AVNZ AVNZq 1d AVNZq 2d
ClF2 70.70 72.57 73.08
74.66 76.10 76.30
76.76 77.12 77.14
79.00 77.88 77.71
AVNZ AVNZq 1d AVNZq 2d
ClF3 115.86 119.62 120.62
122.80 125.57 125.96
126.65
130.82 128.75 128.65
a b
QZ
5Z
Obtained using the two-point Martin Ž ny4 . value corrected by y0.26 kcalrmol. Obtained using the two-point Martin Ž ny4 . value corrected by y0.40 kcalrmol.
CBS
a b
A. Ricca r Chemical Physics Letters 323 (2000) 498–505
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Table 5 Extrapolated atomization energies Žin kcalrmol. ny3 QZ,5Z
ny4 TZ,QZ
ny4 QZ,5Z
ClF AVNZ ClF AVNZq 1d ClF AVNZq 2d
62.82 63.30 63.29
63.40 62.87 62.80
62.43 62.94 62.95
63.12 62.72 62.67
63.36 62.65 62.57
64.14 Ž2.334. 62.61 Ž4.743. 62.53 Ž5.058.
ClF2 AVNZ ClF2 AVNZq 1d ClF2 AVNZq 2d
77.56 78.68 78.65
78.96 78.19 78.02
76.95 78.14 78.16
78.47 77.95 77.82
79.00 77.88 77.71
81.57 Ž1.806. 77.83 Ž4.432. 77.65 Ž4.846.
ClF3 AVNZ ClF3 AVNZq 1d ClF3 AVNZq 2d
127.87 129.92 129.86
130.69
126.81 129.01 129.05
129.78
130.82
136.79 Ž1.603.
a
ny4 q ny6 TZ,QZ,5Z
a
ny3 TZ,QZ
Basis set
Variable a TZ,QZ,5Z
The a values are reported in parentheses.
Martin Ž ny4 q ny6 . values computed using the AVNZ basis set don’t agree well with the variable a ones and the a values are significantly smaller than 4.5. The disagreement between the ny4 q ny6 and the variable a extrapolated results increases going from ClF to ClF3 . By adding one tight d function the agreement between the ny4 q ny6 and the variable a extrapolations becomes very good for ClF and ClF2 and the a value increases significantly. Adding a second tight d function to Cl reduces slightly the extrapolated values. Clearly the AVNZ basis set is not adequate to describe the ClFn systems, particularly ClF2 and ClF3 which are hypervalent and a basis set of at least AVNZq 1d quality must to be used. For all the systems we use the AVNZq 2d extrapolated values as our AE CBS values. We assume that these extrapolated values are accurate to "1.0 kcalrmol based on the excellent agreement between
the ny4 q ny6 and the variable a extrapolation values. We correct the AE CBS values for scalar relativistic effects, spin–orbit effects, core-valence effects, zero-point energy, and thermal effects to obtain our best atomization energies at 0 K ŽAEŽ0.. and at 298 K ŽAEŽ298.. which are reported in Table 6. The core-valence and the scalar relativistic effects are negligible for ClF2 in agreement with the fact that the system is weakly bound. ClF and ClF3 have very similar core-valence and scalar relativistic effects as an indication that the bonding in ClF3 consists mainly of one Cl–F bond which is very similar in nature to the one in ClF. Our AEŽ0. and AEŽ298. values are used in conjunction with the D H f Ž0 K. and the D H f Ž298 K. values for Cl and F to obtain the heats of formation reported in Table 7. We assign an error bar of "1.0 kcalrmol to our computed heats of formation. Experimental values at 298 K are available for both ClF and ClF3 . The most recent
Table 6 Atomization energies Žin kcalrmol. computed at 0 K and 298 K and corrected for scalar relativistic effects, spin–orbit effects, core-valence effects, zero-point energy, and thermal effects AE CBS ClF ClF2 ClF3 a b
62.57 77.71 128.65
a
Rel
SO
CV
ZPE
Therm b
AEŽ0.
AEŽ298.
y0.17 q0.08 y0.19
y1.23 y1.61 y2.00
q0.09 0.00 q0.08
y1.12 y1.92 y4.37
q0.93 q1.69 q2.85
60.14 74.26 122.17
61.07 75.95 125.02
Taken from Table 4. Therm s w H Ž298. y H Ž0.x trans q w H Ž298. y H Ž0.x rot q w H Ž298. y H Ž0.x vib q w H Ž298. y H Ž0.xelec .
0K
298 K
Theory PW ClF ClF2 ClF3 Cl F a
a
y13.1 y8.7 y38.2 w18.47x w87.25x
Theory PW y13.1 y9.0 y39.1 w28.99x w18.97x
Experiment G2 y14.0
Feller b
y38.4 b ,y39.6 c
d
y13.2
JANAF w31x
Gurvich w27x
y12.0"0.1
y13.3"0.1
y38.0"0.7 28.99 18.97
y39.3"1.2
Present work. The values given in square brackets for Cl and F are taken from Gurvich w27x. Original G2 w28x. c G2 modified to include spin–orbit corrections w29x. d Feller and Peterson w30x. To obtain their AEŽ0. value we correct the experimental D 0 value of 60.4 kcalrmol by y0.13 kcalrmol, which is the average between the errors of the three CBS extrapolations used by the authors. The AEŽ0. is converted to AEŽ298. using our thermal correction. b
A. Ricca r Chemical Physics Letters 323 (2000) 498–505
Table 7 Heats of formation Žin kcalrmol.
503
504
A. Ricca r Chemical Physics Letters 323 (2000) 498–505
compilation is the one by Gurvich w27x. On the theoretical side, G2 values have been computed for ClF and ClF3 w28x. For ClF3 the original G2 values have been improved to include spin–orbit corrections w29x. Feller and Peterson w30x have performed accurate calculations to obtain the D 0 value for ClF. We have converted their D 0 value to a D 298 value using our thermal correction, and then computed their heat of formation at 298 K. Our result for ClF at 298 K is in very good agreement with the result of Feller and Peterson and with the experimental value of Gurvich. The G2 value is somewhat too negative. For ClF3 our heat of formation at 298 K is in good agreement with the modified G2 value and with the experimental value of Gurvich. Overall our results are in excellent agreement with the experimental values of Gurvich which suggests that the JANAF w31x values are slightly underestimated. We use our heats of formation at 298 K, the CCSDŽT.rAV5Z optimized geometries and the B3LYP vibrational frequencies to compute the heat capacity, entropy, and heat of formation from 300 to 4000 K. The parameters obtained from the resulting fits can be found on the web w32x. 4. Conclusions The atomization energies of ClFn Ž n s 1–3. are computed at the CCSDŽT. level of theory. The basis set quality strongly affects the results. It is essential to add at least one tight d function to Cl to obtain accurate properties. The atomization energies are extrapolated to the CBS limit and corrected for scalar relativistic, core-valence, spin–orbit, thermal effects, and for zero-point energy. We combine the atomization energies with the heats of formation of Cl and F to obtain the heats of formation of ClFn Ž n s 1–3.. Our heats of formation agree with previous calculated values and are very similar to the experimental values reported by Gurvich. This suggests that the JANAF values are slightly underestimated. Acknowledgements A.R. would like to acknowledge helpful discussions with Charlie Bauschlicher. A.R. was supported
by NASA Contracts No. NAS2-14031 and No. NAS2-99092 to ELORET.
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w30x D. Feller, K.A. Peterson, J. Chem. Phys. 110 Ž1999. 8384. w31x M.W. Chase, C.A. Davies, J.R. Downey, D.J. Frurip, R.A. McDonald, A.N. Syverud, J. Phys. Chem. Ref. Data 14, Suppl. 1., 1985. w32x The values can be found at http:rrwww.ipt.arc.nasa.gov.