J. Phys. Chem. 1996, 100, 19455-19460
19455
Analysis of X-ray Photoelectron Spectra of Eight Polymers by deMon Density-Functional Calculations Using the Model Oligomers Kazunaka Endo,*,† Yasuo Kaneda, and Hiroyuki Okada Tsukuba Research Laboratory, Mitsubishi Paper Mills, LTD., 46 Wadai, Tsukuba-City, Ibaraki 300-42, Japan
Delano P. Chong* and Patrick Duffy Department of Chemistry, 2036 Main Mall, UniVersity of British Columbia, VancouVer, BC, Canada V6T 1Z1 ReceiVed: April 16, 1996; In Final Form: September 20, 1996X
The X-ray photoelectron spectra of eight polymers [(CH2CH2)n, (CH2CH2NH)n, (CH2O)n, (CH2CH2S)n, (CH2CHX)n, and (CH2CX2)n (X ) F, Cl)] were analyzed by the deMon density-functional method using the model oligomers. Calculated AIK R valence photoelectron spectra were obtained using Gaussian line shape functions of an approximate line width (0.10Ik), where Ik ) Ik′ - WD, Ik′ is the vertical ionization potential of each MO, and WD is a shift to account for sample work function, polarization energy, and other effects. The theoretical spectra showed good agreement with the experimental spectra of the polymers between 0 and 40 eV. The core-electron binding energies (CEBEs) of C1s, N1s, O1s, F1s, S2p, and Cl2p of the model oligomers were calculated by unrestricted generalized transition-state models. The difference between the calculated and the experimental CEBEs reflects the trend in WDs of the polymers.
Introduction spectroscopy1-3
has become a powerful X-ray photoelectron tool for providing precise information concerning the core-level binding energies and the valence electronic structure of polymers. The theoretical studies4-22 on X-ray photoelectron spectra (XPS) and ultraviolet photoelectron spectra of polymers showed that information on the polymer electronic structure can be obtained through MO calculations for simple model oligomers or using a crystal model of one-dimensional periodicity. Some XPS studies8,10,11,23 of simple model oligomers and saturated hydrocarbons demonstrated that information on the conformation and tacticity dependence can be obtained through spectral simulation by MO calculations. Recently, Delhalle et al.24 found evidence of a folded structure at the surface of polyethylene lamellae in the XPS valence band. In our previous papers,16-18,20 we used syndiotactic model molecules for analysis of XPS of polymers, because we found that the tacticity had little effect on the calculated energy structure, in contradiction to the results of other workers.23,24 In previous studies,19-22 we showed that earlier workers used Koopmans’ theorem and the δ-SCF method to analyze the photoelectron spectra of polymers. The method of δ-SCF gave quite reliable values14,15 of the core-electron binding energies (CEBEs) but suffers from occasional failures. For better assignment20-22 of the valence XPS of polymers involving carbon, nitrogen, oxygen, and fluorine, we tested the performance of the semiempirical hydrogenic-atoms-in-molecule, version 3 (HAM/3) MO method25-27 in that the results can be directly compared with experiment, because it uses the idea of “transition state”28 rather than Koopmans’ theorem to predict vertical ionization potentials (VIPs). In recent studies of density-functional theory (DFT) using the deMon DFT program29 which uses the idea of transition state, Chong and co-workers30-34 offered the methods of calculating accurate VIPs and CEBEs of small molecules. Except for an energy shift WD to account for solid-state effects, the present paper follows the same procedures of DFT to † X
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[email protected]. Abstract published in AdVance ACS Abstracts, November 1, 1996.
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simulate the valence XPS of eight polymers involving C, N, O, F, S, and Cl atoms and to calculate the CEBEs. The simulation of the valence spectra was performed on the model oligomers using standard convolution techniques by a Gaussian line shape and using the Gelius model35 for molecular photoionization cross section. The line width of a peak of ionization energy Ik was taken to be 0.10Ik (proportional to the ionization energy) as in previous studies.20-22 The CEBEs of C1s, N1s, O1s, F1s, S2p, and Cl2p of the model oligomers were calculated using the deMon DFT program with scaled pVTZ basis sets. Our results showed much better correspondence with experiment than those predicted by Koopmans’ theorem. Theoretical Background For the comparison between calculations for single molecules of the trimer or dimer model and experiments on a solid polymer, we must shift each computed VIP (or CEBE) Ik′ by a quantity WD36 as Ik(EF) ) Ik′ - WD, to convert to ionization energy Ik(EF) relative to the Fermi level. This quantity WD denotes the sum of the work function of the sample and other energy effects, such as the polarization energy, the width of the interchain band formation, and the peak broadening in the solid state.37-42 Now, let us consider an electronic process of ionization or excitation for single molecules using Slater’s transition-state (TS) method at fixed molecular geometry. Following Duffy and Chong’s work,32 we define
E(x) ) ∑xkEk ) E0 + xE1 + x2E2 + x3E3 + x4E4 + ‚‚‚
(1)
where E(0) and E(1) correspond to the initial and final states, respectively, and x is assumed to be a continuous variable. From eq 1, the endothermicity we seek is given by
∆E ) E(1) - E(0) ) E1 + E2 + E3 + E4 + ‚‚‚
(2)
If we define the first derivative (F(x) ) ∂E(x)/∂x), in Slater’s transition-state concept, ∆E is approximated by © 1996 American Chemical Society
19456 J. Phys. Chem., Vol. 100, No. 50, 1996
F(1/2) ) E1 + E2 + 3E3/4 + E4/2 + ‚‚‚
Endo et al.
(3)
with an error of
dTS ) -E3/4 - E4/2 + ‚‚‚
(4)
For ionization of an electron from molecular orbital (MO) φk, for example, we can apply the Janak theorem43 and set F(1/2) to -k at X ) 1/2. In the generalized transition-state (GTS) method, Williams et al.44 proposed the use of
F(2/3) ) E1 + 4E2/3 + 4E3/3 + 32E4/27 + ‚‚‚
(5)
Therefore, ∆E can be approximated by
∆E ) [F(0) + 3F(2/3)]/4 ) E1 + E2 + E3 + 8E4/9 + ‚‚‚ (6)
TABLE 1: Scaling Factors for Gaussian-type Orbitals of C, N, O, F, S, and Cl atoms atomic
1s
2s
C N O F S Cl
1.071 775 5 1.060 924 7 1.052 923 4 1.046 779 6 1.000 617 8 1.000 581 1
1.390 775 9 1.321 17y0 2 1.272 548 4 1.236 681 7 1.044 852 8 1.041 666 1
dGTS ) -E4/9 + ‚‚‚
The transition-state model and GTS model can be applied in two ways. In what is labeled “restricted” (G)TS, we remove the same set of fractional electrons from molecular orbitals for both R and β electrons, rather than the MO for R electron(s) only in the “unrestricted” (G)TS model. (1) Valence Region of XPS of Polymers. For the VIPs of the valence regions, we use the so-called diffuse ionization (DI) model which A° sbrink et al.25 proposed in the HAM/3 method. In the rDI model, half of an electron is removed evenly from the valence MOs and the negative of the resulting orbital energies correspond to calculated VIPs. This allows us to obtain all the valence VIPs in a single calculation. The C2H2 molecule, with 5 valence MOs and 10 valence electrons, can be used as an example. For the rDI model, each valence MO of C2H2 has 0.95 R and 0.95 β electrons. (2) Core-Electron Binding Energies. Following Chong,33,34 we used the GTS model to compute CEBEs and added relativistic correction (Crel) for C to F using Crel ) KInrN where K ) 2.198 × 10-7, N ) 2.178, and Inr is the nonrelativistic CEBE. Since the corresponding Crel expressions have not been determined for S and Cl, we did not add Crel for those atoms in the present study. Practical Details of Calculation (1) MO Calculations. The model molecules [H(CH2CH2)3H, H(CH2CH2NH)2H), H(CH2O)3H, H(CH2CH2S)2H, H(CH2CHX)2H, and H(CH2CX2)2H (X ) F, Cl)] were calculated by the density-functional method using the deMon program.29 For the geometry of the molecules, we used the optimized Cartesian coordinates from the semiempirical AM1 (version 6.0) method.45 The Koopmans’ values were calculated using the HONDO7 program.46 For C and O atoms, we used (3s2p) basis sets and for H and (Cl, S) atoms we used (2s) and (4s3p) basis sets, respectively, reported by Huzinaga et al.47 and Dunning et al.48 The deMon calculations were performed with the exchangecorrelation potential labeled as B88/P86, made from Becke’s 1988 exchange functional49 and Perdew’s 1986 correlation functional.50 In the program, we used a nonrandom grid and consistent-correlation polarized valence triple-ζ (cc-pVTZ) basis sets of Dunning and co-workers48 to calculate VIPs of model molecules with auxiliary fitting functions labeled (4, 4:4, 4) for C, N, O, and F, (3, 1:3, 1) for H, and (5, 4:5, 4) for S and Cl. Furthermore, we calculated the CEBEs of the model molecules to study the effect of basis set. Using the B88/B86 functional and the unrestricted GTS (uGTS) model, we compared the performance of the scaled polarized valence triple-ζ
3p
atomic
orbital
Al KR (Heh42)
H C
1s 2s 2p 2s 2p 2s 2p 2s 2p 3s 3p 3s 3p
0.0041 1.0000 0.0323 1.7925 0.1364 2.8602 0.3910 4.2797 1.0256 2.9098 1.5835 4.4481 2.9353
N
F
(7)
3s
TABLE 2: Relative Photoionization Cross Section of Each Atomic Orbital for H, C, N, O, F, S, and Cl Atoms (Relative to C2s)
O
with an error of only
2p
1.441 367 9 1.357 065 9 1.299 702 8 1.258 183 3 1.037 368 3 1.169 978 6 1.215 861 5 1.034 421 4 1.152 198 9 1.193 060 6
S Cl
set (scaled-pVTZ)34 with a polarized valence double-ζ (DZVP) basis29 of (621/41/1*) for C, N, O, and F, (41) for H, and (6321/ 521/1*) for (S, Cl). In the CEBE calculations with scaled pVTZ basis, we used the new scaling factors for the Gaussian-type orbitals (GTO)s of S and Cl atoms with the factors for the second-period atoms as given by Chong and co-workers.34 Recently, Chong has modified the screening constants of Si to Ar atoms in the uGTS model for 2s or 2p holes
Sig(1s) ) 0.3(n1s - 1) + 0.0072(n2s + n2p) + 0.0169(n3s + n3p) Sig(2s) ) (1.7208 × 0.5)n1s + 0.3536(n2s + n2p + 1) + 0.196(n3s + n3p) Sig(2p) ) 0.93575n1s + 0.3536n2s + 0.3326(n2p - 1) 0.0773n3s - 0.0161n3p Sig(3s) ) n1s + 0.77745(n2s + n2p) + 0.2866(n3s + n3p - 1) Sig(3p) ) n1s + 0.8476625(n2s + n2p) + 0.2866n3s + 0.3803(n3p - 1) where n1s, n2s, n2p, n3s, and n3p are the number of 1s, 2s, 2p, 3s, and 3p electrons, respectively. Table 1 summarizes the scaling factors for the GTOs of S and Cl atoms with C, N, O, and F atoms. (2) Spectral Simulation. In order to simulate the valence XPS of polymers theoretically, we constructed from a superposition of peaks centered on the VIPs Ik. As was done in previous works,19-22 each peak was represented by a Gaussian curve. The intensity was estimated from the relative photoionization cross section for Al KR radiation using the Gelius intensity model.35 For the relative atomic photoionization cross section, we used the theoretical values from Yeh (Table 2).51 In the case of the line width (WH(k)), we used WH(k) ) 0.10Ik for the models, as adopted in previous works.20-22
deMon Density-Functional Calculations of Polymers
Figure 1. (a) Valence XPS of PE with the simulated spectra of the trimer model molecule as calculated using deMon DFT. (b) Valence XPS of PMG with the simulated spectra of the trimer model molecule using deMon.
For eight polymers, we cited the valence XPS and the CEBEs by Beamson and Briggs.3 Results and Discussion As mentioned in the Introduction, VIPs predicted by Koopmans’ theorem are often too high, by approximately 8%.52 In contrast, the VIPs of small molecules calculated by the deMon density-functional program have an absolute deviation of 0.4 eV from experiment,32 and the deviation of over 50 calculated CEBEs from observed values is within 0.29 eV.33,34 On the basis of such performance, we have some confidence in modeling polymers by applying the density-functional method on the model dimer or trimer. The agreement between simulated and experimental XPS of polymers gives us further assurance about or interpretation of the different regions of the spectra. (1) PE, PMG, PEI, PETHS, PVF, PVDF, PVC, and PVDC Polymers in Valence XPS. A new feature of the present study is the use of the rDI model using the deMon program for the simulation of valence spectra of S- and Cl-containing polymers, since we were only able to calculate the valence XPS of polymers involving C, N, O, and F atoms with the HAM/3 method. Figures 1a,b, 2a,b, and 3a,b indicate the simulated spectra of (CH2CH2)n (PE), (CH2O)n (PMG), (CH2CH2NH)n (PEI), (CH2CH2S)n (PETHS), (CH2CHF)n (PVF), and (CH2CF2)n (PVDF) using the model dimer or trimer molecules with the experimental spectra. We show the orbital characters of PMG and PETHS in Tables 3 and 4 (we omitted similar tables for PE, PEI, PVF, and PVDF as described in previous works).20,22
J. Phys. Chem., Vol. 100, No. 50, 1996 19457
Figure 2. (a) Valence XPS of PEI with the simulated spectra of the dimer model molecule using deMon. (b) Valence XPS of PETHS with the simulated spectra of the dimer model molecule using deMon.
For (CH2CHCl)n (PVC) and (CH2CCl2)n (PVDC) (Figure 4a,b), the intense peaks (at around 6 or 5 eV) are due to 3p lone-pair orbitals of the pendant Cl of the polymers, respectively. Broader spectra between 15 and 22 eV are determined by the C13s main contributions, respectively. We show the orbital characters of PVC in Table 5 (a similar table for PVDC was omitted). The WD was estimated as 4.0 and 3.5 eV for the models of PVC and PVDC polymers, respectively. The WDs of PE, PMG, PEI, PVF, and PVDF polymers as obtained using the deMon program were 1.0-1.5 eV lower than those using HAM/3 program (Table 6). For the simulated spectra using model dimer or trimer molecules, the spectra appeared to show good agreement with the experimental ones, when we used an approximate line width of 0.10Ik. It is very interesting that we can observe the characteristic spectra which are due to the photoionization cross section of any contributing atomic orbitals of the constituent elements of the functional groups. For these eight polymers, we have clarified the orbital nature of the fingerprint spectra which were characterized from the constituent elements (C, N, O, F, S, and Cl) in the range of 5-30 eV. (2) CEBEs of Eight Polymers. The computed CEBEs of eight polymers (PE, PMG, PEI, PVF, PVDF, PETHS, PVC, and PVDC) using the uGTS model are also in much better agreement with experimental values than were those predicted by Koopmans’ theorem, as shown in Table 6. In the case of the CEBEs with scaled pVTZ basis set including the relativistic corrections for second-period atoms, we obtained values for ∆CEBE (the difference between the calculated and experimental CEBEs) closer to the estimated WD than those from the DZVP
19458 J. Phys. Chem., Vol. 100, No. 50, 1996
Endo et al.
Figure 3. (a) Valence XPS of PVF with the simulated spectra of the dimer model molecule using deMon. (b) Valence XPS of PVDF with the simulated spectra of the dimer model molecule using deMon.
basis. These ∆CEBEs also follow the trend of the WD values assumed for the valence region of the XPS. We may therefore consider these new ∆CEBEs as another estimate of WD.
Figure 4. (a) Valence XPS of PVC with the simulated spectra of the dimer model molecule using deMon. (b) Valence XPS of PVDC with the simulated spectra of the dimer model molecule using deMon.
In Table 6, we gave three different WDs as obtained from the ∆CEBEs, from valence-region XPS based on DFT calcula-
TABLE 3: Observed Peaks, VIP, Main AO PICS, Orbital Nature, and Functional Group for Valence XPS of PMG (Shift between Observed and Calculated VIPs ) 4.0 eV) peak (eV) 26.0 (22-32)a 18.0 (13-21)a 12.0 (10.5-13)a 8.5 (8-10.5)a 6.0 (4-8)a
VIP (eV)
main AO PICS
30.55; 29.21; 27.91
O2s
18.18-21.24
C2s(0.7), O2p, O2s
14.69-16.38
O2p(0.6), C2s, O2s
12.11-13.84
O2p(0.6), O2s, C2s
9.21-11.46
O2p
orbital natureb
functional group
{sσ(O2s-C2s)-B, pσ(O2s-C2p)-B} s, pσ(C2s-C, O2s,2p)-B
-OCH2-
{pσ(C2s-C2p)-B, pπp(C2p-C2p)-B} {pσ(C2s-C2p)-B, pπp(C2p-C2p)-B} {pπ(lone-pair)-NB, pπp(O2p-C2p)-B}
-CH2O-
-OCH2-
-OCH2-OCH2-
a Shows the peak range. b π indicates the pseudo π orbitals of the CH -O groups. B and NB mean bonding and nonbonding, respectively. (C, p 2 O2p-C, O2s) means (C2p-C2s) and (O2p-O2s) and (O2p-C2s), and so on.
TABLE 4: Observed Peaks, VIP, Main AO PICS, Orbital Nature, and Functional Group for Valence XPS of PETHS (Shift between Observed and Calculated VIPs ) 5.0 eV) orbital natureb
peak (eV)
VIP (eV)
main AO PICS
18.7; 15.8 (14.4-22.4)a 12.7 (10-14.4)a 8.1 (6.9-10)a 5.5 (4.3-6.9)a 3.9 (2-4.3)a
{23.86; 22.79, 21.20; 19.20} 17.60; 16.92
S3s(0.7), C2s(0.2)
sσ(S3s-C2s)-B
-SC-
S3s(0.8), C2s(0.3)
{sσ, pσ(S3s,C2s-C2s,s3p)-B}
SC-,-CC
13.06-14.54
S3p(0.7), S3s(0.2)
pπ, σ(S3p,3s-C2p)-B
-SC
10.04-12.01
S3p(0.8), S3s
pπ(S3p-C2p)-B
-S-
S3p
pπ(lone-pair)-NB
-S-
7.63; 8.03
functional group
a Shows the peak range. b B and NB mean bonding and nonbonding, respectively. (S3p,3s-C2p) means (S3p-C2p) and (S3p-C2p), (S3s,C2sC2s,S3p) denotes (S3s-C2s), (C2s-C2s), and (C2s-S3p), and so on.
deMon Density-Functional Calculations of Polymers
J. Phys. Chem., Vol. 100, No. 50, 1996 19459
TABLE 5: Observed Peaks, VIP, Main AO PICS, Orbital Nature, and Functional Group for Valence XPS of PVC (Shift between Observed and Calculated VIPs ) 4.0 eV) orbital natureb
peak (eV)
VIP (eV)
20.5 (20-23)a 18.0 (16-20)a 14.5 (12-16)a 10.0 (9-12)a 6.5 (4-9)a
24.59; 23.47
C13s(0.7), C2s(0.3)
sσ(Cl3s-C2s)-B
ClC-
21.98; 21.16
C13s(0.8), C2s(0.2)
sσ, pσ(C13s-C2s,2p)-B
ClC-
18.89; 17.52
C2s(0.6), Cl3s, Cl3p
sσ, pσ(C2s-C2s,2p,Cl3s)-B
CC-, -CCl
(15.15; 14.63; 14.22; 13.55) 9.69-9.96 many adjacent levels 11.55-12.88
C13p(0.7), Cl3s, C2p
pπ(C2p-C2p,C13p)-B
CC-,-CCl
Cl3p
pπ(lone-pair)-NB
-Cl
Cl3p(0.9),C2p
pπ(C13p,C2p-C2p)-B
ClC-, -CC
a
main AO PICS
functional group
b
Shows the peak range. B and NB mean bonding and nonbonding, respectively. (Cl3s-C2s,2p) means (Cl3s-C2s) and (Cl3s-C2p), (C2pC2p, 2s, Cl3p) denotes (C2p-C2p), (C2p-C2s), and (C2p-Cl3p), and so on.
TABLE 6: Core-Electron Binding Energies (in eV) of Polymers by the deMon Program Using the Dimer Model observed
uGTS DZVP (∆b)
scaled pVTZ (∆b)
Koopmans’ theorema
(CH2CH2)n CEBE(C1s)[CH2-]
285.0
292.43 (7.4)
291.05 (6.1)c 〈〈5.5〉〉 (4.0)d
305.21
(CH2O)n CEBE(O1s)[-O-] CEBE(C1s)[CH2-]
533.1 287.9
540.82 (7.7) 295.54 (7.6)
539.09 (6.0) 294.12 (6.2) 〈〈5.0〉〉c (4.0)d
559.39 308.62
(CH2CH2NH)n CEBE(N1s)[-NH-] CEBE(C1s)[CH2-]
399.1 285.6
406.67 (7.8) 292.97 (7.4)
405.26 (6.2) 291.58 (6.0) 〈〈5.0〉〉c (4.0)d
422.38 305.80
(CH2CHF)n CEBE(F1s)[-F] CEBE(C1s)[-CHF] CEBE(C1s)[CH2-]
686.9 287.9 285.7
694.59 (7.7) 294.87 (7.0) 292.78 (7.1)
691.93 (5.0) 293.15 (5.3) 291.39 (5.7) 〈〈4.5〉〉c (3.0)d
714.69 308.35 306.23
(CH2CF2)n CEBE(F1s)[CF2] CEBE(C1s)[CH2-] CEBE(C1s)[CF2-]
688.2 286.4 290.9
695.38 (7.2) 293.23 (6.8) 297.56 (6.7)
693.26 (5.1)
715.87 307.45 311.68
(CH2CHCl)n CEBE(Cl2p)[-CHC1] CEBE(C1s)[CH2-] CEBE(C1s)[-CHCl]
200.6 285.9 287.0
208.39 (7.8) 292.89 (7.0) 294.13 (7.1)
207.11 (6.5) 291.47 (5.6) 292.77 (5.8) (4.0)d
217.93 306.74 308.10
(CH2CCl2)n CEBE(Cl2p)[CCl2] CEBE(C1s)[CH2-] CEBE(C1s)[CCl2-]
200.8 286.2 288.6
208.18 (7.4) 293.23 (6.8) 297.56 (6.7)
207.18 (6.4) 291.81 (5.7) 293.99 (5.4) (3.5)d
218.67 307.61 310.31
(CH2CH2S)n CEBE(S2p)[-S-] CEBE(C1s)[CH2-]
163.5 285.5
172.20 (8.7) 293.08 (7.6)
170.47 (7.0) 291.65 (6.2)
179.30 304.89
molecule
296.08 (5.2) 〈〈4.0〉〉c (3.0)d
a The values were calculated by the ab initio RHF-SCF MO method using the HONDO7 program. b The values denote the differences between the calculated CEBEs using uGTS model and the observed ones. c The values were obtained from analysis of valence XPS using HAM/3. d The values were obtained from analysis of valence XPS using deMon.
tions, and from valence-region XPS based on HAM/3 calculations. When we take into consideration the long acquisition times of valence-region XPS due to the 20- to 100-fold weaker intensities and hence the possible X-ray radiation damage, we conclude that the WD values from ∆CEBEs may very well be the most reliable ones among the choices in Table 6. This is true especially for values derived from CEBEs of C1s to F1s, for which the accuracy of CEBEs from the scaled pVTZ basis has been tested for over 60 cases.34,53 Consequently, the WD values may be underestimated by valence-region XPS based on HAM/3 calculations by 0.5-1.0 eV.
Conclusion We have calculated the core-electron binding energies and the valence XPS of C-, N-, O-, F, S-, and Cl-containing polymers by a deMon density functional method using the model dimers or trimer. We emphasize that the calculated VIPs and CEBEs of polymer models using rDI and uGTS models, respectively, by the deMon program showed better correspondence with experiment than those predicted by Koopmans’ theorem. The difference between the calculated and experimental CEBEs for C1s follows the trend of WD values we assume for VIPs in the valence region.
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