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On the controversial assignment of the ionization potentials of formaldehyde
VoIume34,
number 1
CHEhlICAL PHYSICS LETTERS
ON THE CONTROVERSIAL OF THE IONIZATION
1 July 197.5
ASSIGNMENT
POTENTIALS
OF FORMALDEHYDE
L.S. CEDERBAUM, W. DOMCKE and W. VON NIESSEN * Plr_~ls;k-Deparrnlrrlt
der Technischen
Universirijt
Miinciren.
T;ireoretisclze
Physik,
8016
Garching.
Germany
Rcccived 3 March I?75
The Hartrce-i:ock calculations and the SCF Xa scattered-wave method using overlapping spheres predict B different ordering of the ionization potentials of formaldehyde. To clarify the problem a Green’s function approach includiq many-body effects is used. The caiculatcd ionization potentiais as well as th: vibrational structure of the bands asrce well with experiment. We conclude the Hartrec-Fock assignment to bc the correct one.
The He1 photoelectron spectrum of formaldehyde [I,;] shows three bands, rhe last bnnd containing two ionization potentials (IP’s). The assignment of these two IP’s has been controversial. From arguments which are based on an examination of the vibrational structure of the last band, Turner et al. [2J conclude the third and fourth IP’s to be assigned to the lb2 and Sal orbitals of formaldehyde, respectively. The Hartree-Fock (HF) calculations (3,4] on this molecule predict, however, the third IP to be the 5a, IP (see table 1). To clarify the problem, Batra and Robaux [5] have performed calculations using the SCF Xol scattered-wave method [6] which has become very popular in the last few years. With this method they obtain the same ordering of IP’s as found from the HF ca!culation. To improve the physical rea!ism of the approach and the quantitative agreement with experiment they then use the scheme of overlapping spheres [7]. The best results obtained for the values of the IP’s wi’lh this method have also been found to improve the virial ratio and the total energy. The ordering of IP’s determined in this case is in agreement with the ordering origlmllly proposed by Turner et al. (see table 1). Surprised by the strong sensitivity of the IP’s to the overlap of the atomic spheres we decided to per* Permanent address: Lehrstuhl fiir Theorctische Chemie der TeFhnischcn UnivcrsitZt Minchen, Munich, Germany. 60 .
form an extensive ab initio calculation on formaldehyde including many-body effects within a Green’s function approach. The HF calculation used as a starting point is very similar to the one performed recently [4], which to the knowledge of the authors has the lowest total energy cited in the literature. The main difference is that our calculation contains only one set of d-type functions on each of the C and 0 atoms instead of two sets. The total energies and the orbital energies of both calculations are shown in table 1. The IP’s have been calculated with the Green’s function method described in detail in refs. [8,9]. The results (table 1) indicate that in all steps of the calculation the ordering of the IP’s is the same as predicted by the I-IF calculation. In the second order of the perturbation expansion of the self-ener,v part we find remarkable shifts for all orbitals (3.3 eV for the 5al orbital!)_ In third order the orbitals are strongly shifted back towards the HF values. The good agreement of the final IP’s with the experimental values permits us to conclude that the assignment given by the. EIF calculation is the correct one. To remove any doubt about this conchrsion we have also calculated the vibrational structure of the bands in the photoelectron spectrum. The method we use takes account of many-body effects and is described in detail in ref. [lo]. The present calculation is the first of its kind for a polyatomic molecule
Votume 34, number
1
CHEMICAL PHYSICS LETTERS
Table 1 Results for formaldehyde. E zre the orbital energies, IP(2) = IP calculated in second order, IP(3) = IP in third order, IP(f) = final result for the IP. The Siare the vibrational coupling parameters. Total energies in au, all other energies ineV
1 July 1975
:I
Orbital 2bT_ IPa) I P b) (Xa) IP c) (Xa) -e d) --E e) IP(2) IP(3) IPW H2C0 St s2 S3 &CO St
-
Ibt
531
Lb2
14.5 16.60 14.44 14.60
16.2 17.49 16.87 17.77
17.0 17.78 15.29 18.82
10.9 13.14 11.13 12.03 12.0s 9.21 11.45 10.84 0.033 0.129 0.126
14.63
i7.76
18.87
13.50 14.67 14.29 0.036 2.792 0.270
14.42 17.!9 16.36 0.004 1.156 0.301
16.63 17.59 17.13 0.757 0.195 1.533
0.092
0.414
0.098
0.635
s-2
0.122
2.611
0.765
0.950
s3
0.090
0.011
0.855
1.534
Escrd)
= -113.91494’
EScFe)
= -113.90117 ---
3)
Estimated centre of gravity of the
knds
in the esperimen-
tal spectrum
of ref. f2] for HzCC). b) SCF Xcr results of ref. [S ] : no overlap of spheres. Cl SCP Xa results of ref. I.5 ] : with optimum overlap. d) Hartree-Fock resutts of ref. (41. e, This work.
and is therefore also of interest on its own. The calculation takes account of all three normal modes f 11i ~1, ~2 and “3 _The corresponding normaI coordinates are linear combinations of the internal symmetry coordinates representing the C-O and C-H stretching and the L HCH deformation. The results are expressed in terms of ~brationai coupling parameters [lo] Si, i= 1,2,3, the magnitude Of Si being a measure of the probability of the excitation of the normal vibration vi due to ionization. The calculated S; are shown in tabte 1 for H,CO as well as for R,CO. The details of this calculation will be published elsewhere. To have a simple way of comparing the results with the expriment we have drawn the calculated bands Sal and lb2 togther with the corresponding experimental spectra (fig. 1). For clarity the ca.lcu-
176
1'12
1SB
i&
li0
156
eV
i
Fig. 1. A comparison of the cslcukted and the experimental phoroetectron spectra of ff2CO and DzCO. (1, The c&xIated lb2 band of tI2CO. (2) The cs!culated 5at band of HzCO. (3) The last band in the esperimenta1 spectrum of H2C0. (4) The crtlcufatcd lb2 band of D2CO. (5) The calculated 5at band of DzCO. (6) The last band in rhe esperimento1 spectrum of D2CO. bed
bands have not been overlapped. The individual vibrational lines have been drawn as Lorer.tzians with a half-width representing the experimental resolution. let us only briefiy discuss the resuIts. For the 531 orbital of &CO we hwe found the vibrational coupling to be mostly due to the p2 mode. For the Sal
orbital of D,CO the situation is quite different.
Here
61
Volume 34, number
CHEMICAL
1
both the v2 and v3 modes cwple strongly leading to the complex structure observed. The vibrational coupling for the !b, orbital is also strong, but clearly different. All three coupling parameters are considerable for D,CO, whereas only v1 zod v3 couple strongly for H,CO. k comparison of the calculated and the observed vibrational structure revea!s - most evidcntly in-the case.of D2C0 - that the lower II’ has to be assigned as Sal, the tligher a~ 1 b,. It is thus the case that, at least for formaldehyde, the SCF Xa scattered-wave method predicts the correct assignment of the IP’s in the photoelectron spectrum although the quantitative agreement of the calculated IP’s with the experimental ones is poor. Using overlapping spheres le;lds to a wrong assignment ‘of the P’S although the virial ratio is clearly improved and the total energy compares well with the exprimental value. It seems that these quantities cannot be used as criteria for the physical relevance r,f an -SCF Xol scattered-wave calculation. We also hope to have demonstrated that the
Green’s function method is very suitable for obtaining theoretical
photoelectron
spectra
for the permission tc use their HF progams and W. Brenig, i. Schirrner and FL Schijnhammer for interesting discussions.
References 111 CR. Trundle 314.
thank
G.‘Diercksen
Chem.
Commun.
(19673
Turner, C. Baker, A.D. Baker and C.R. Brundlc, hIolecu!nr photoelectron spectroscopy (Mley, New York, 1970). and I.W. hloskowitz, J. Chcm. Phys.. 50 131 D.B. Neumann (1969) 2216. H.F. Schaefer and W.A. Lester, J. Chcm. 14) B.S. Garrison,
Phys. 61 (1974) 3039. [51 I.P. Batra and 0. Robaus, Chem. Phys. Letters 28 (1974) 529. Advan. Quantum Chem. 7 (1973) 143, [61 K.H. Johnson, and rererenccs
therein.
Chem. Phys. Letters 24 171 N. Riisch and K.H. Johnson, (lS74) 179. 181 L.S. Cederbaum, Theoret. Chim. Acta 31 (1973) 239.
(91 L.S. Cederbsum, IlO1 L.S. Ccdcrhaum
of molecules. and W. Kraemer
and D.W. Turner,
I21 D.W.
2878. T. Shimanouchi
J. Phys. B, to be published. and \V. Domckc, 5. Chem. Fhys.
(1974)
[Ill The authors
1 July 1975
PHYSICS LETTERS
(1965)
296.
and I. Suzuki,
J. Chem.
Phys.
42
60
number 1
CHEhlICAL PHYSICS LETTERS
ON THE CONTROVERSIAL OF THE IONIZATION
1 July 197.5
ASSIGNMENT
POTENTIALS
OF FORMALDEHYDE
L.S. CEDERBAUM, W. DOMCKE and W. VON NIESSEN * Plr_~ls;k-Deparrnlrrlt
der Technischen
Universirijt
Miinciren.
T;ireoretisclze
Physik,
8016
Garching.
Germany
Rcccived 3 March I?75
The Hartrce-i:ock calculations and the SCF Xa scattered-wave method using overlapping spheres predict B different ordering of the ionization potentials of formaldehyde. To clarify the problem a Green’s function approach includiq many-body effects is used. The caiculatcd ionization potentiais as well as th: vibrational structure of the bands asrce well with experiment. We conclude the Hartrec-Fock assignment to bc the correct one.
The He1 photoelectron spectrum of formaldehyde [I,;] shows three bands, rhe last bnnd containing two ionization potentials (IP’s). The assignment of these two IP’s has been controversial. From arguments which are based on an examination of the vibrational structure of the last band, Turner et al. [2J conclude the third and fourth IP’s to be assigned to the lb2 and Sal orbitals of formaldehyde, respectively. The Hartree-Fock (HF) calculations (3,4] on this molecule predict, however, the third IP to be the 5a, IP (see table 1). To clarify the problem, Batra and Robaux [5] have performed calculations using the SCF Xol scattered-wave method [6] which has become very popular in the last few years. With this method they obtain the same ordering of IP’s as found from the HF ca!culation. To improve the physical rea!ism of the approach and the quantitative agreement with experiment they then use the scheme of overlapping spheres [7]. The best results obtained for the values of the IP’s wi’lh this method have also been found to improve the virial ratio and the total energy. The ordering of IP’s determined in this case is in agreement with the ordering origlmllly proposed by Turner et al. (see table 1). Surprised by the strong sensitivity of the IP’s to the overlap of the atomic spheres we decided to per* Permanent address: Lehrstuhl fiir Theorctische Chemie der TeFhnischcn UnivcrsitZt Minchen, Munich, Germany. 60 .
form an extensive ab initio calculation on formaldehyde including many-body effects within a Green’s function approach. The HF calculation used as a starting point is very similar to the one performed recently [4], which to the knowledge of the authors has the lowest total energy cited in the literature. The main difference is that our calculation contains only one set of d-type functions on each of the C and 0 atoms instead of two sets. The total energies and the orbital energies of both calculations are shown in table 1. The IP’s have been calculated with the Green’s function method described in detail in refs. [8,9]. The results (table 1) indicate that in all steps of the calculation the ordering of the IP’s is the same as predicted by the I-IF calculation. In the second order of the perturbation expansion of the self-ener,v part we find remarkable shifts for all orbitals (3.3 eV for the 5al orbital!)_ In third order the orbitals are strongly shifted back towards the HF values. The good agreement of the final IP’s with the experimental values permits us to conclude that the assignment given by the. EIF calculation is the correct one. To remove any doubt about this conchrsion we have also calculated the vibrational structure of the bands in the photoelectron spectrum. The method we use takes account of many-body effects and is described in detail in ref. [lo]. The present calculation is the first of its kind for a polyatomic molecule
Votume 34, number
1
CHEMICAL PHYSICS LETTERS
Table 1 Results for formaldehyde. E zre the orbital energies, IP(2) = IP calculated in second order, IP(3) = IP in third order, IP(f) = final result for the IP. The Siare the vibrational coupling parameters. Total energies in au, all other energies ineV
1 July 1975
:I
Orbital 2bT_ IPa) I P b) (Xa) IP c) (Xa) -e d) --E e) IP(2) IP(3) IPW H2C0 St s2 S3 &CO St
-
Ibt
531
Lb2
14.5 16.60 14.44 14.60
16.2 17.49 16.87 17.77
17.0 17.78 15.29 18.82
10.9 13.14 11.13 12.03 12.0s 9.21 11.45 10.84 0.033 0.129 0.126
14.63
i7.76
18.87
13.50 14.67 14.29 0.036 2.792 0.270
14.42 17.!9 16.36 0.004 1.156 0.301
16.63 17.59 17.13 0.757 0.195 1.533
0.092
0.414
0.098
0.635
s-2
0.122
2.611
0.765
0.950
s3
0.090
0.011
0.855
1.534
Escrd)
= -113.91494’
EScFe)
= -113.90117 ---
3)
Estimated centre of gravity of the
knds
in the esperimen-
tal spectrum
of ref. f2] for HzCC). b) SCF Xcr results of ref. [S ] : no overlap of spheres. Cl SCP Xa results of ref. I.5 ] : with optimum overlap. d) Hartree-Fock resutts of ref. (41. e, This work.
and is therefore also of interest on its own. The calculation takes account of all three normal modes f 11i ~1, ~2 and “3 _The corresponding normaI coordinates are linear combinations of the internal symmetry coordinates representing the C-O and C-H stretching and the L HCH deformation. The results are expressed in terms of ~brationai coupling parameters [lo] Si, i= 1,2,3, the magnitude Of Si being a measure of the probability of the excitation of the normal vibration vi due to ionization. The calculated S; are shown in tabte 1 for H,CO as well as for R,CO. The details of this calculation will be published elsewhere. To have a simple way of comparing the results with the expriment we have drawn the calculated bands Sal and lb2 togther with the corresponding experimental spectra (fig. 1). For clarity the ca.lcu-
176
1'12
1SB
i&
li0
156
eV
i
Fig. 1. A comparison of the cslcukted and the experimental phoroetectron spectra of ff2CO and DzCO. (1, The c&xIated lb2 band of tI2CO. (2) The cs!culated 5at band of HzCO. (3) The last band in the esperimenta1 spectrum of H2C0. (4) The crtlcufatcd lb2 band of D2CO. (5) The calculated 5at band of DzCO. (6) The last band in rhe esperimento1 spectrum of D2CO. bed
bands have not been overlapped. The individual vibrational lines have been drawn as Lorer.tzians with a half-width representing the experimental resolution. let us only briefiy discuss the resuIts. For the 531 orbital of &CO we hwe found the vibrational coupling to be mostly due to the p2 mode. For the Sal
orbital of D,CO the situation is quite different.
Here
61
Volume 34, number
CHEMICAL
1
both the v2 and v3 modes cwple strongly leading to the complex structure observed. The vibrational coupling for the !b, orbital is also strong, but clearly different. All three coupling parameters are considerable for D,CO, whereas only v1 zod v3 couple strongly for H,CO. k comparison of the calculated and the observed vibrational structure revea!s - most evidcntly in-the case.of D2C0 - that the lower II’ has to be assigned as Sal, the tligher a~ 1 b,. It is thus the case that, at least for formaldehyde, the SCF Xa scattered-wave method predicts the correct assignment of the IP’s in the photoelectron spectrum although the quantitative agreement of the calculated IP’s with the experimental ones is poor. Using overlapping spheres le;lds to a wrong assignment ‘of the P’S although the virial ratio is clearly improved and the total energy compares well with the exprimental value. It seems that these quantities cannot be used as criteria for the physical relevance r,f an -SCF Xol scattered-wave calculation. We also hope to have demonstrated that the
Green’s function method is very suitable for obtaining theoretical
photoelectron
spectra
for the permission tc use their HF progams and W. Brenig, i. Schirrner and FL Schijnhammer for interesting discussions.
References 111 CR. Trundle 314.
thank
G.‘Diercksen
Chem.
Commun.
(19673
Turner, C. Baker, A.D. Baker and C.R. Brundlc, hIolecu!nr photoelectron spectroscopy (Mley, New York, 1970). and I.W. hloskowitz, J. Chcm. Phys.. 50 131 D.B. Neumann (1969) 2216. H.F. Schaefer and W.A. Lester, J. Chcm. 14) B.S. Garrison,
Phys. 61 (1974) 3039. [51 I.P. Batra and 0. Robaus, Chem. Phys. Letters 28 (1974) 529. Advan. Quantum Chem. 7 (1973) 143, [61 K.H. Johnson, and rererenccs
therein.
Chem. Phys. Letters 24 171 N. Riisch and K.H. Johnson, (lS74) 179. 181 L.S. Cederbaum, Theoret. Chim. Acta 31 (1973) 239.
(91 L.S. Cederbsum, IlO1 L.S. Ccdcrhaum
of molecules. and W. Kraemer
and D.W. Turner,
I21 D.W.
2878. T. Shimanouchi
J. Phys. B, to be published. and \V. Domckc, 5. Chem. Fhys.
(1974)
[Ill The authors
1 July 1975
PHYSICS LETTERS
(1965)
296.
and I. Suzuki,
J. Chem.
Phys.
42
60