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Ionisation energies of CH2F2 calculated by the SCF Xα technique
Volume 44, number 3
IONISATION ENERGIES OF CH,F,
CALCULATED
M. BARBER, J.D. CLARK, A. IlINCIILIFFE Chemistry Departrncnt, h?anchester M60 iQD,
15 Deccmbcr 1976
CIIC:hlICAL PHYSICS LETTERS
University UK
BY THE SCF Xa TECHNIQUE
and S. MANN
of Mkwchester Instrtute of Science and Technology,
Rcccivcd 16 AuguG 1976
Ioniation cncrgics h.~ve been Aculntcd for CIIzF2 using the SW Xor technique. Agreement with expcrnncnt is cxcclIcnt, and the results rlrc compared with those from conventional IIartree-Pock calculations.
1. Introduction The He1 and He11 photoe!cctron spectra of CH;FZ have been reported [I 1, and the C and F 1s binding energies measured using 1254 eV X-rays [2]. Ionisation energies have been assigned on the basis of Hartree-Fock LCAO MO calculations with large gaussian basis sets generally invoking Koopmans theorem [I, 31, and in the case of the Is binding energies both by hole-state calculations and by the equivalent cores method [4]. Despite the obvious deficiencies of the caiculations - Koopmans-theorem-type calculations ignore changes in correlation energy and electronic relaxation on ionisation whilst hole-state calculations in gxtxd cannot be t;u~rantecd to bc variational upper bounds, the photoelectron spectra of CHZFZ are well understood. There is growing interest in the application to large molecules of Slater’s Xol approximation to the Hartree-Fock exchange term, coupled with the use of “muffin-tin” potentials [S, 61; apart from the obvious advantage that the method (the SCF Xa method) permits Hartree--Fock calculations to be performed on large molecules [S], use of the transition state technique [6] permits a much more realistic estimate of ionisation energies to be made. Such calculations are still rarely seen in the literature, so the aim of this paper is to report ionisation energies for CH2F, dculated by the SCF Xo method. WC also compare the results with those produced by conventional HartreeFock theory. 526
2.Calculations All calculations were performed on the University of Manchester Regional Computer Ccntre’s CDC 7600 computer. The geometry used for CH,F, exchange factors (0~)and sphere radii are given in table 1: the latter were chosen so that the C and F radii arc proportional to the Slatcr radii [7), whilst the II and outer sphere radii were chosen so that they just touched the C and F spheres. No overlap of spheres was permitted. Spherical harmonics were needed on each centre, to permit convergence of the potential, as follows: H, I = 0; C and F: up to I = 1; outer sphere: up to I = 2.
Table 1 Cartcsidn coordirztcs, cxchangc factors (a) [S] and sphere radd for CH2P2. Atomic unit oflcngth a0 TJ0.529 X lO-‘o a
Radius
1 .I559 1.1559 0 -1.5030
0.9780 0.9780 0.7585 0.7365
0.5665 0.5665 1.4970 1.0692
-1.5030
0.7365
1.0692
O&375
3.6355
C;lrtesian coordinates x(a0)
111
0
112
0 0 2.0801
C PI F2 outer sphere
-2.0801 0
u(a0)
1.6620 -1.6620 0 0 0 0
[9] 2670)
0
m
Volume 44, number 3
CHEMICAL PHYStCS LETTERS
Table 2 Ionisation energies for Cki21;2 by the SW Xa method. Gaussmn orbital SCP + Koopmdns thcorcm (KT) [ 1.31 dnd e\pcrlment [I] _-_--.-_--_ Orbital Iomsation energy (cV) SCFXor
- ____
--__ 14.09
16.66 16.97 17.80 19.45 19.63 20.16 23.86 36.63 37.75 296.72 679.98 __-_-
3.
KT
-_-
cxpcrimcnt ----_--.-
14.89 16.94 17.23 18.22 20.38(3b1) 21.13 21.54(1b2) 26.76 43.78 45.66 311.09 715.79 _-- _---.---
idlabJtiC __-- --_.--_
- --_.
vcrt1cal __-_-
12.72
13.27
14.5
15.3
18.20
18.9
23.1
23.9
The SCF Xa ionisation energjes agree better with expcrimcnt than the results of the gaussian SCF + Koopmans theorem calculation, which generally overestimates the experimental ionisation energy by about 10%. The two calculation; give different orderings to the I b, and 3b, ionisations, but th&c arc predicted to be very close in energy.
Acknowledgement We thank Dr. M. Quinn who kindly gave us access to some of the programs used in this study.
References 296.3 _- --
693.1 ____- _ _ -___
Results and discussion
Ionisation energies were calculated by the transition - that is, if an electron is to be ionired from orbital I)~, the SCF Xa calculation is repeated with pi half occupied [G] . Spin polarisation was included, and in table 2 we show the ionisation energies, together with those of a conventional gaussian state method
SCP calculation, The experimental
15 December 1976
ussuming Koopmans theorem 131. results arc given for CompariSOfl.
Trundle, h1.B. Robin and If. Basch. 5. Chcm. Whys. 53 (1970) 2196. [2] T.D. Thomas, I. Am. Chcm. Sot. 92 (1970) 4182. 131 E.K. Crimmcln~nn and J.P. Chesick. f. Chem. Phys. 55 (1971) 1690; E. Clcmenti and A. Routh. Intern. I. Quantum Chcm. 6 [l 1 C.R.
(1972) 525. 141 LLB. Adams and D.T. Clark. Thcorct. Chirn. Acta 31 (1973) 171. [S] J.C. Slatcr, Quantum theory of n~oIccuIcr and solids,
Vol. 4 (McGraw-Ml, New York. 1974). 161 K.A. Johnson and FS. Smith. Phys. Rev. B.5 (L972) 831. [7] J.C. Slatcr. Quantum theory of mokcuks and solids, Vol. 2 (McGraw-IIilI, New York. 196.5) p. 5.5. [S] K. Schwarr, Phys. Rev. i25 (1972) 2466. [9] Interatomic Distances. ~hcmkd Society SpcciA Publictron. NC>.1 1 <1952).
527
IONISATION ENERGIES OF CH,F,
CALCULATED
M. BARBER, J.D. CLARK, A. IlINCIILIFFE Chemistry Departrncnt, h?anchester M60 iQD,
15 Deccmbcr 1976
CIIC:hlICAL PHYSICS LETTERS
University UK
BY THE SCF Xa TECHNIQUE
and S. MANN
of Mkwchester Instrtute of Science and Technology,
Rcccivcd 16 AuguG 1976
Ioniation cncrgics h.~ve been Aculntcd for CIIzF2 using the SW Xor technique. Agreement with expcrnncnt is cxcclIcnt, and the results rlrc compared with those from conventional IIartree-Pock calculations.
1. Introduction The He1 and He11 photoe!cctron spectra of CH;FZ have been reported [I 1, and the C and F 1s binding energies measured using 1254 eV X-rays [2]. Ionisation energies have been assigned on the basis of Hartree-Fock LCAO MO calculations with large gaussian basis sets generally invoking Koopmans theorem [I, 31, and in the case of the Is binding energies both by hole-state calculations and by the equivalent cores method [4]. Despite the obvious deficiencies of the caiculations - Koopmans-theorem-type calculations ignore changes in correlation energy and electronic relaxation on ionisation whilst hole-state calculations in gxtxd cannot be t;u~rantecd to bc variational upper bounds, the photoelectron spectra of CHZFZ are well understood. There is growing interest in the application to large molecules of Slater’s Xol approximation to the Hartree-Fock exchange term, coupled with the use of “muffin-tin” potentials [S, 61; apart from the obvious advantage that the method (the SCF Xa method) permits Hartree--Fock calculations to be performed on large molecules [S], use of the transition state technique [6] permits a much more realistic estimate of ionisation energies to be made. Such calculations are still rarely seen in the literature, so the aim of this paper is to report ionisation energies for CH2F, dculated by the SCF Xo method. WC also compare the results with those produced by conventional HartreeFock theory. 526
2.Calculations All calculations were performed on the University of Manchester Regional Computer Ccntre’s CDC 7600 computer. The geometry used for CH,F, exchange factors (0~)and sphere radii are given in table 1: the latter were chosen so that the C and F radii arc proportional to the Slatcr radii [7), whilst the II and outer sphere radii were chosen so that they just touched the C and F spheres. No overlap of spheres was permitted. Spherical harmonics were needed on each centre, to permit convergence of the potential, as follows: H, I = 0; C and F: up to I = 1; outer sphere: up to I = 2.
Table 1 Cartcsidn coordirztcs, cxchangc factors (a) [S] and sphere radd for CH2P2. Atomic unit oflcngth a0 TJ0.529 X lO-‘o a
Radius
1 .I559 1.1559 0 -1.5030
0.9780 0.9780 0.7585 0.7365
0.5665 0.5665 1.4970 1.0692
-1.5030
0.7365
1.0692
O&375
3.6355
C;lrtesian coordinates x(a0)
111
0
112
0 0 2.0801
C PI F2 outer sphere
-2.0801 0
u(a0)
1.6620 -1.6620 0 0 0 0
[9] 2670)
0
m
Volume 44, number 3
CHEMICAL PHYStCS LETTERS
Table 2 Ionisation energies for Cki21;2 by the SW Xa method. Gaussmn orbital SCP + Koopmdns thcorcm (KT) [ 1.31 dnd e\pcrlment [I] _-_--.-_--_ Orbital Iomsation energy (cV) SCFXor
- ____
--__ 14.09
16.66 16.97 17.80 19.45 19.63 20.16 23.86 36.63 37.75 296.72 679.98 __-_-
3.
KT
-_-
cxpcrimcnt ----_--.-
14.89 16.94 17.23 18.22 20.38(3b1) 21.13 21.54(1b2) 26.76 43.78 45.66 311.09 715.79 _-- _---.---
idlabJtiC __-- --_.--_
- --_.
vcrt1cal __-_-
12.72
13.27
14.5
15.3
18.20
18.9
23.1
23.9
The SCF Xa ionisation energjes agree better with expcrimcnt than the results of the gaussian SCF + Koopmans theorem calculation, which generally overestimates the experimental ionisation energy by about 10%. The two calculation; give different orderings to the I b, and 3b, ionisations, but th&c arc predicted to be very close in energy.
Acknowledgement We thank Dr. M. Quinn who kindly gave us access to some of the programs used in this study.
References 296.3 _- --
693.1 ____- _ _ -___
Results and discussion
Ionisation energies were calculated by the transition - that is, if an electron is to be ionired from orbital I)~, the SCF Xa calculation is repeated with pi half occupied [G] . Spin polarisation was included, and in table 2 we show the ionisation energies, together with those of a conventional gaussian state method
SCP calculation, The experimental
15 December 1976
ussuming Koopmans theorem 131. results arc given for CompariSOfl.
Trundle, h1.B. Robin and If. Basch. 5. Chcm. Whys. 53 (1970) 2196. [2] T.D. Thomas, I. Am. Chcm. Sot. 92 (1970) 4182. 131 E.K. Crimmcln~nn and J.P. Chesick. f. Chem. Phys. 55 (1971) 1690; E. Clcmenti and A. Routh. Intern. I. Quantum Chcm. 6 [l 1 C.R.
(1972) 525. 141 LLB. Adams and D.T. Clark. Thcorct. Chirn. Acta 31 (1973) 171. [S] J.C. Slatcr, Quantum theory of n~oIccuIcr and solids,
Vol. 4 (McGraw-Ml, New York. 1974). 161 K.A. Johnson and FS. Smith. Phys. Rev. B.5 (L972) 831. [7] J.C. Slatcr. Quantum theory of mokcuks and solids, Vol. 2 (McGraw-IIilI, New York. 196.5) p. 5.5. [S] K. Schwarr, Phys. Rev. i25 (1972) 2466. [9] Interatomic Distances. ~hcmkd Society SpcciA Publictron. NC>.1 1 <1952).
527