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An electron momentum spectroscopy study of the outer valence orbitals of chlorodifluoromethane
Chemical Physics 299 (2004) 17–24 www.elsevier.com/locate/chemphys
An electron momentum spectroscopy study of the outer valence orbitals of chlorodifluoromethane XuHuai Zhang, XiangJun Chen *, Chunkai Xu, ChangChun Jia, XiaoFeng Yin, Xu Shan, Zheng Wei, KeZun Xu Laboratory of Bond-Selective Chemistry, Laboratory of Atomic and Molecular Physics, Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230027, PR China Received 17 October 2003; accepted 25 November 2003
Abstract Electron momentum spectroscopy (EMS) has been used to measure the momentum profiles of outer valence orbitals of chlorodifluoromethane (CHF2 Cl), which are compared with Hartree–Fock (HF) and density functional theory (DFT) calculations using different-sized basis sets. Overall, DFT calculation employing B3LYP hybrid functional and the largest basis set that we used provides the best agreement with experiment. But the minimum improvement gained by replacing the 6-311++G** basis set with AUG-cc-pVQZ suggests that basis set saturation has been approached, at least for some orbitals of CHF2 Cl, and a computationally affordable method which addresses effects that current theoretical treatment neglects, such as distorted wave and electron relaxation, is sorely needed. Ó 2003 Elsevier B.V. All rights reserved. Keywords: Electron momentum spectroscopy; Density functional theory; Chlorodifluoromethane
1. Introduction On account of its unique ability to measure the momentum densities for individual molecular orbitals, electron momentum spectroscopy (EMS) is capable of investigating the molecular electronic structure. Momentum profiles (MP) of orbitals are most sensitive to the wave functionsÕ long-range behavior in the chemically important region, which is far from the nuclei but plays a central role in determining the moleculeÕs chemical properties. Therefore, EMS has been increasingly employed as a powerful tool for assessing the validity of quantum chemical calculations [1–6]. EMS measurements of halomethanes have been the subjects of studies by several authors. Cambi et al. [7–9] have reported binary ðe; 2eÞ and many body GreenÕs function studies of series molecules CHn F4 n . The results of their experiments and calculations clear showed *
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significant many-body effects for the inner valence orbitals. However, their experiment is seriously limited by low energy resolution (2.6 eV) and poor statistics. Minchinton et al. [10–12], in a series papers, have investigated the electronic structure of monohalomethanes CH3 X (X ¼ F, Cl, Br and I) with electron momentum spectroscopy accompanied by GreenÕs function calculations. It was found that employing polarized basis sets improved theoretical calculations but the agreement between experiments and theoretical calculations still remained for the heavy halogen substituted methanes such as CH3 Br and CH3 I. Furthermore, EMS studies of series molecules CHn Cl4 n [13] as well as CF4 [14] have also been published. It is interesting to extend these studies to halomethanes including more than one species of halogen atoms. Chlorodifluoromethane (CHF2 Cl), also denoted as F22 as a member of Freon family, is one of the hydrochlorofluorocarbons (HCFCs), which show low values of ozone-depleting potential (ODP). At present, HCFCs, especially CHF2 Cl, are used as interim substitutes for chlorofluorocarbons (CFCs) in applications
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such as detergents, solvents, and refrigerants. This makes the detailed knowledge of electronic structure of CHF2 Cl molecule important. CHF2 Cl has been studied by photoelectron spectroscopy (PES) [15,16]. To our knowledge, no EMS study of chlorodifluoromethane has been reported so far. In this paper, we report the first electron momentum profiles for the outer valence orbitals of CHF2 Cl measured using ðe; 2eÞ electron momentum spectrometer at a total energy of 1200 eV plus binding energy and symmetric non-coplanar geometry. The experimental momentum profiles are also compared with Hartree–Fock (HF) and density functional theory (DFT) calculations using various basis sets.
2. Experimental and theoretical background Electron momentum spectroscopy is based on the kinematically complete ðe; 2eÞ collision experiment, which is an electron impact single ionization process. Within several approximations, including the binary encounter approximation (in which the residual ion is a mere spectator and hence the collision operator depends only on the incident and recoil electrons), and planewave impulse approximation (PWIA), the triple differential cross-section (TDCS) for the random oriented molecules is proportional to the spherically averaged momentum distribution of the corresponding Dyson orbital [1–6,17] Z 2 rEMS / dXjh~ pWfN 1 jWN0 ij ; ð1Þ the integrand of which is the square of the momentum representative of the overlap between the N-electron wave function describing the initial state of the target and the ðN 1Þ-electron wave function for the final ion state. The random orientation of the molecule is allowed for by the isotropic integration over the whole solid angle of the incident electronÕs momentum ~ p. Eq. (1) can be further simplified in most cases within target Hartee– Fock approximation (THFA), in which the initial state wave function is approximated by a single determinant of the ground state target Hartree–Fock orbitals, and freezing orbital approximation (FOA), in which the relaxation effect is ignored and consequently the Dyson orbital can be approximated with an initial (neutral) state canonical HF orbital. Then the TDCS becomes [1–6] Z 2 rEMS / Sqðf Þ dXjuHF ð2Þ q ðpÞj ; where uHF q ðpÞ is the one-electron momentum space canonical HF wavefunction for the qth orbital, from which the electron was ejected. The quantity Sqðf Þ is called spectroscopic factor or pole strength, which is the
possibility of finding such a one-hole configuration in the symmetry manifold f . It is essentially unity if we adopt THFA and FOA. For more general Dyson orbitals, we have the sum rule X Sqðf Þ ¼ 1; ð3Þ f
which is because of a closure relation, the completeness of the final ion states. Eq. (1) can also be simplified by using the more recent target Kohn–Sham approximation (TKSA) [18–20] in which the Dyson orbital can be approximated with an initial (neutral) state canonical Kohn–Sham orbital obtained by solving the Kohn–Sham equation [21]. By simply replacing the HF orbital wavefunction with the Kohn–Sham orbital wavefunction uKS q ðpÞ the TDCS then becomes Z 2 ðf Þ rEMS / Sq ð4Þ dXuKS q ðpÞ : A detailed description of the present electron momentum spectrometer has been given elsewhere [22]. In brief, it consists of an electron gun, a reaction chamber, two hemispherical electron energy analyzers each having a five-element cylindrical retarding lens and a one-dimensional position sensitive detector. In this work, since the symmetric non-coplanar geometry was employed, the polar angles of two analyzers were kept fixed at 45°. The relative azimuthal angle / was varied by rotating one analyzer around the incident electron beam while keeping the other one fixed. The incident electron energy was 1200 eV plus binding energy and the two outgoing electrons have essentially equal energies (600 eV). The coincident energy resolution of the spectrometer was measured to be 1.5 eV (FWHM) using Ar 3p ionization. The momentum resolution was estimated to be 0.15 a.u. by comparing the experimental momentum profile of the Ar 3p orbital with the theoretical one.
3. Calculations The spherically averaged momentum distributions in Eqs. (2) and (4) were calculated within the PWIA and THFA or TKSA for all the outer valence orbitals of CHF2 Cl. The corresponding position–space canonical HF or Kohn–Sham orbital wavefunctions were calculated at the equilibrium geometries using the GAUSSIAN 98W program [23]. The molecular geometry was optimized by DFT-B3LYP calculation with 6-311++G** basis set. The canonical HF orbitals for CHF2 Cl were then calculated using the 6-31G, 6-311++G**, and an augmented quadruple-zeta (QZ) basis set (AUG-cc-pVQZ). The Kohn–Sham orbitals were obtained by carrying out DFT calculations employing the B3LYP hybrid functional with the same
X.H. Zhang et al. / Chemical Physics 299 (2004) 17–24 Table 1 Calculated total energies and dipole moments for CHF2 Cl Method HF/6-31G HF/6-311++G** HF/AUG-cc-pVQZ B3LYP/6-31G B3LYP/6-311++G** B3LYP/AUG-cc-pVQZ
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Table 2 Outer valence shell IP of CHF2 Cl (in eV)
Total energy (a.u.)
Dipole momentum (D)
)696.690 )696.897 )696.956 )698.490 )698.692 )698.749
2.1506 1.8077 1.6577 1.7520 1.5893 1.4599
three basis sets, respectively. In HF calculations, only the exchange energy resulting from the fermionic nature of electron is included. In DFT calculations, on the other hand, both exchange energy and correlation effect are included. The keyword B3LYP refers to BeckeÕs three-parameter hybrid functional using the LYP correlation functional [24]. The total energies and dipole moments calculated for CHF2 Cl using various methods are shown in Table 1. An outer-valence-shell Green function (OVGF) [25] calculation of ionization potentials (IPs) and pole strengths for outer valence orbitals of CHF2 Cl has also been performed with the 6-31++G** basis set.
4. Results and discussion CHF2 Cl contains 42 electrons and has Cs symmetry point group. Its ground state electronic configuration can be written as
Orbital
PES Ref. [15]
8a0 5a00 7a0 6a0 4a00 3a00 5a0 2a00 4a0 3a0 a
Theoretical Ref. [16]
12.6
12.56
14.0 15.9
13.91 15.94
18.7 19.7
18.87 19.98
23.0
23.1
This work (OVGF)a Ionization potential
Pole strength
12.381 12.478 13.987 16.187 16.350 17.134 19.323 20.043 20.713 24.246
0.94 0.94 0.94 0.93 0.93 0.93 0.92 0.92 0.92 0.90
With 6-31++G** basis set.
lence orbitals were measured at 13 different out-of-plane azimuthal angles. Fig. 1 shows two of them, which were measured at azimuthal angles 1° and 8°. Gaussian peaks fitted to the individual transitions, or in some cases ‘‘bands’’ formed by the overlap of several near degenerate (with respect to the energy resolution of the spectrometer) transitions, for example 8a0 +5a00 , are shown by dotted curves while their sum is shown by a solid curve. The positions of each individual peak are given by the IP determined by high-resolution PES [16]. The widths of the peaks are the combinations of the EMS instrumental energy resolution (1.5 eV in this work) and the Franck–Condon width of the corresponding bands determined by high-resolution PES [16].
ðcoreÞ16 ðla0 Þ2 ðla00 Þ2 ð2a0 Þ2 ð3a0 Þ2 ð4a0 Þ2 ð2a00 Þ2 ð5a0 Þ2 ð3a00 Þ2 ð4a00 Þ2 ð6a0 Þ2 ð7a0 Þ2 ð5a00 Þ2 ð8a0 Þ2 |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} inner valence shell
outer valence shell
The valence shell contains 13 molecular orbitals and can be divided into two sets: three inner valence orbitals and 10 outer valence orbitals. The IP ordering of the outer valence orbitals can be established by combining PES experiments and theoretical calculations, except for 4a00 and 6a0 orbitals, which will be discussed later. Table 2 compiles the IPs of the 10 outer valence orbitals predicted by theoretical calculation along with those observed by PES. The discrepancy between calculation and PES results becomes larger for inner valence orbitals. OVGF calculation also gives the pole strength for each outer valence orbital. As can be seen from the Table 2, the pole strengths for ionization from all outer valence orbitals can be regarded as unity to some extent. 4.1. Binding energy spectra The binding energy spectra of CHF2 Cl over the energy range 5–30 eV that covers all of the 10 outer va-
In Fig. 1, the first peak at 12.56 eV represents ionization of the highest occupied molecular orbital (HOMO), which is the chlorine lone-pair orbital and contains two orbitals: 8a0 and 5a00 . They cannot be resolved even by the high-resolution PES [16]. The theoretical calculations in present work give the ordering of 8a0 and 5a00 (in ascending order of ionization potential, default for all orbitals). The second peak at 13.91 eV corresponds to the C–Cl bonding orbital (7a0 ) ionization. The first two peaks are not well resolved due to the poor energy resolution of EMS. The third peak at 15.94 eV belongs to the fluorine lone-pair orbital ionization, which contains three orbitals: 6a0 , 4a00 and 3a00 . These orbitals are also too close to be distinguished by high-resolution PES. The ordering of 3a00 orbital can be determined by our calculations in this work, which indicates that it has the highest IP of the three. But the ordering of 6a0 and 4a00 remains unclear because different calculation methods give different results. DFT-
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culated by DFT-B3LYP method employing AUG-ccpVQZ basis set. The instrumental angular resolution (0.15 a.u.) has been folded into the theoretical momentum profiles using the GWPG method [26].
Fig. 1. Binding energy spectra of CHF2 Cl at azimuthal angles / ¼ 1° and 8°. The dotted curves represent Gaussian curves fitted to the transitions or ‘‘bands’’ and the solid curve represents their sum. The positions of individual transitions determined by high-resolution PES [16] are shown as bars with numbers 1–6.
B3LYP calculations give the ordering af 4a00 and 6a0 , but HF calculations give a contradicting result. The next peak positioned approximately at 19 eV actually contains two peaks: the C–H bonding (5a0 ) ionization peak at 18.87 eV and the C–F bonding ionization peak at 19.98 eV. The latter contains two molecular orbitals, which cannot be resolved by PES, in the ordering of 2a00 and 4a0 determined by theoretical calculations in this work. The last peak at the ionization potential of 23.1 eV corresponds to the ionization from the innermost outer valence orbital of 3a0 . 4.2. Experimental and theoretical momentum distributions 4.2.1. Normalization The experimental momentum profiles are extracted by deconvoluting the same peak from the sequentially obtained binding energy spectra at different azimuthal angles or momentum [1]. In order to compare the experimental momentum distributions with the theoretical ones, we need one normalization factor common for all bands. Usually, this normalization factor is determined by normalizing the experimental and theoretical momentum distributions of the outermost valence ionization to the common intensity scale, since the outermost valence ionizations are expected to exhibit pole strength close to unity. In this work, as shown in Fig. 1, the three outermost orbitals 8a0 , 5a00 and 7a0 cannot be resolved clearly, so we use the sum of these three orbitals to determine this normalization factor. ItÕs reasonable to do so because the pole strengths of these three orbitals are nearly the same and close to unity. The theoretical momentum distribution used for normalization is cal-
4.2.2. 8a0 , 5a00 and 7a0 orbitals Fig. 2 shows the summed experimental MP of 8a0 , 5a00 and 7a0 orbitals compared with DFT-B3LYP and HF calculations employing 6-31G, 6-311++G** and AUGcc-pVQZ basis sets. It can be seen that the B3LYP/ AUG-cc-pVQZ calculation gives the proper intensity in low-momentum region and the correct position of the maximum. All other calculations underestimate the observed intensity in low-momentum region and shift the position of the maximum a little to high-momentum end. The first peak in the binding energy spectra (Fig. 1) is due to the ionization of the HOMOs, which contains two orbitals (8a0 and 5a00 ). As explained above, these two orbitals are too closely spaced, so we treat them as one peak. The second peak, which is only 1.35 eV away from the first one, corresponds to 7a0 orbital ionization. Fig. 3 shows the experimental and theoretical momentum profiles of the 8a0 + 5a00 orbitals (a) and 7a0 orbital (b), from which we can see that the theoretical MP is relatively high for 8a0 + 5a00 orbitals and low for 7a0 orbital. The theoretical and experimental MPs fit well in shape for 8a0 + 5a00 orbitals, but are quite inconsistent for 7a0 orbital in shape and magnitude. Orbitals 8a0 and 5a00 belong to the lone pairs of chlorine and are dominantly ÔatomicÕ, as can be easily seen from their momentum profiles, which resemble that of the 3p atomic orbital of chlorine. On the whole, the individual MPs of these two peaks have not been well described. But it would be premature to consider the predictions a complete failure, since these two peaks are not well
Fig. 2. The summed experimental and theoretical momentum profiles for 8a0 , 5a00 and 7a0 orbitals of CHF2 Cl.
X.H. Zhang et al. / Chemical Physics 299 (2004) 17–24
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Fig. 3. Experimental and theoretical momentum profiles for 8a0 , 5a00 orbitals (a) and 7a0 orbital (b) of CHF2 Cl.
resolved (the energy resolution of our spectrometer is 1.5 eV plus Franck–Condon width) and deconvolution uncertainties may have been introduced to both peaks. Therefore, a possible explanation is that the experimental momentum profile of 7a0 orbital is mixed with part of 8a0 + 5a00 orbitals. A much more definite conclusion can be expected with the upcoming spectrometers with an energy resolution well under 1 eV. 4.2.3. 6a0 , 4a00 and 3a00 orbitals This peak is due to fluorine lone-pair orbital ionization, and contains three orbitals: 6a0 , 4a00 and 3a00 , which cannot be resolved. The comparison of the summed experimental momentum distribution with the theoretical calculations is shown in Fig. 4. The experimental momentum profile shows a peak at p 0:5 a.u. and has no discernible shoulder beyond the peak. All theoretical calculations predict the peak at 0.5 a.u. except the one calculated with DFT-B3LYP method employing 6-31G basis set, which shift the maximum about 0.04 a.u. to high-momentum end. In this figure, we can see that all calculations severely underestimate the observed inten-
Fig. 4. The summed experimental and theoretical momentum profiles for 6a0 , 4a00 and 3a00 orbitals of CHF2 Cl.
sity in the peak region. The best match is provided by DFT-B3LYP calculation with AUG-cc-pVQZ basis set, which, in comparison with other calculations, shows the highest maximum intensity at p 0:5 a.u. and no significant shoulder around 1.3 a.u. The MP calculated using the same method with 6-311+G** basis set does not exhibit much difference, which indicates that DFTB3LYP calculations using the basis sets larger than 6311++G** will not provide much better agreement with the experimental results for this peak. The HF calculations using 6-311++G** and AUG-cc-pVQZ basis sets are in good agreement with each other too, but the intensity of the maximum is much lower than DFT calculations using the same basis sets and there is an obvious shoulder at p 1:3 a.u. For 6-31G basis set, the DFT calculation shows an even lower intensity of the peak and an obvious shoulder beyond it, and the HF calculation shows two maximum due to the depression of the peak at p 0:5 a.u. 4.2.4. 5a0 orbital The next orbital is 5a0 , which corresponds to C–H bonding orbital. Fig. 5 shows the experimental momentum distribution of this orbital (predominantly ÔptypeÕ), together with the calculations. The 6 theoretical curves in this figure are divided into two groups according to the calculation methods, which indicates that theoretical method is more important than basis set in reproducing the experimental momentum distribution for this orbital. This is easily understandable, since the atoms forming the bond are small and adding more polarization and diffuse terms to the basis set is unlikely to improve the quality of the calculation. We can see that DFT-B3LYP calculations give the better fit, while HF calculations underestimate the observed intensity. The best fit is still given by B3LYP/AUG-cc-pVQZ calculation, in both shape and intensity. There is little difference between the calculations using same method with different basis sets in the low-momentum region of p < 0:9 a.u., but in the high-momentum region beyond 0.9 a.u. The calculations with AUG-cc-pVQZ basis set
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Fig. 5. The experimental and theoretical momentum profiles for 5a0 orbital of CHF2 Cl.
differ from that with the other two basis sets. This can also be expected, for high-momentum region roughly corresponds to the area close to nuclei in coordinate space, where wave functions of the molecule tend to have large gradients. Large basis sets have an inherent advantage in describing wave functions in such an area. As for the same calculation method, the momentum profile calculated with AUG-cc-pVQZ basis set shows higher intensity and fits better with the experimental data than those calculated with 6-31G and 6-311++G** basis sets, which are in good agreement with each other, in the region of p > 0:9 a.u.
4.2.5. 2a00 and 4a0 orbitals The next band is due to the ionization of 2a00 + 4a0 orbitals which correspond to C–F bond. Fig. 6(a) shows the summed experimental momentum distribution of these two orbitals compared with the theoretical momentum distributions. The individual theoretical momentum distributions are shown in Fig. 6(b) and (c). All of the theoretical calculations are in good agreement with the experimental MP in the region of p > 0:8 a.u. But in the region of p < 0:8 a.u., the theoretical calculations significantly differ from each other and none of them fits the experimental MP very well. It can be seen that DFT-B3LYP calculations employing 6-311++G** and AUG-cc-pVQZ basis sets have little difference with each other, and both provide very good agreement with the observed data in the region of p > 0:3 a.u. In the region of p < 0:3 a.u., each of these two calculations predicts a continuous rising curve with the descent of the momentum, but experimental data turn flat at about 0.3 a.u. and exhibit a platform. Both of the DFT-B3LYP calculations using 6311++G** and AUG-cc-pVQZ basis sets overestimate the experimental MP in this region. The HF calculations with 6-311++G** and AUG-cc-pVQZ basis sets turn flat at 0.8 a.u., and consequently underestimate the observed intensity in the region of p < 0:8 a.u. As for the calculations using 6-31G basis set, the DFT-B3LYP method predicts a shoulder around 1.0 a.u. and turns up at p 0:5 a.u., and the HF method shows a similar profile as calculated with 6-311++G** basis set, except
Fig. 6. (a) The summed experimental and theoretical momentum profiles for 2a00 and 4a0 orbitals of CHF2 Cl. The theoretical calculations for individual orbital 2a00 and 4a0 are shown in (b) and (c) respectively.
X.H. Zhang et al. / Chemical Physics 299 (2004) 17–24
for the depression at about 0.5 a.u. Both of them fit the experimental data poorly in both shape and intensity. In comparison with other calculations, the theoretical MP calculated by DFT-B3LYP method employing AUG-ccpVQZ basis set gives the best fit. Individually, for 2a00 orbital shown in Fig. 6(b), the theoretical calculations exhibit Ôp-typeÕ momentum profiles, and do not show much difference with each other. The maximum position predicted by these calculations various from 0.9 a.u. to 1.0 a.u., and the DFT-B3LYP/AUG-cc-pVQZ calculation gives the lowest intensity. In comparison with 4a0 orbital, the intensity of the theoretical MP of this orbital is much lower, and thus contributes to the shoulder of the summed distribution only. For the 4a0 orbital shown in Fig. 6(c), all calculations show mainly Ôs-typeÕ (slightly mixed with Ôp-typeÕ) momentum profiles, but they differ from each other significantly in the region of p < 1:0 a.u. This is the main cause of the difference between the calculations of the summed distribution in this region. The momentum profiles calculated by DFT method show steeper slopes and intensities in this region than those calculated by HF method. From Fig. 6(c) we can see that the difference between DFT and HF calculations is very large, which indicates that calculation method is more important for the MP of this orbital. Comparing the calculations using the same method, 6-311++G** and AUG-cc-pVQZ basis sets are in good agreement with each other, and the main difference between them and 6-31G basis set is that the latter shows an obvious shoulder around 1.0 a.u. This shoulder depresses its intensity in the region of p < 1:0 a.u. 4.2.6. 3a0 orbital The last orbital of the outer-valence-shell is 3a0 . The experimental momentum distribution is presented in Fig. 7, together with the theoretical calculations. All
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calculations give predominantly Ôp-typeÕ momentum distributions for this orbital and are in good agreement with the experimental data in the region of p > 0:7 a.u.. But all of them severely underestimate the observed intensity in low-momentum region, where experimental MP shows a strong Ôturn-upÕ indicating more ‘‘s-type’’ component than theoretical predictions. This is unlikely to be introduced via deconvolution uncertainties, since this peak is well isolated from other peaks. From this figure, we can see that the theoretical calculations are divided into three groups according to the basis set employed, which indicates that basis sets are more important than calculation methods when predicting the momentum distribution for this orbital. In the region of p > 0:7 a.u., the calculations employing AUG-cc-pVQZ basis set give the best fit. But in low-momentum region, we cannot tell which method is better due to the ÔturnupÕ of the experimental data. 5. Summary In summary, we have reported the first measurement of the momentum profiles for all 10 outer valence orbitals of CHF2 Cl by ðe; 2eÞ electron momentum spectroscopy. The experimental momentum profiles are compared with the theoretical ones. The results show that DFT calculations using the B3LYP hybrid functional are better than HF calculations in predicting the momentum distributions of the outer valence orbitals of CHF2 Cl. In this work, we employed the largest basis set (AUG-ccpVQZ) that our computing resources allowed for the CHF2 Cl calculations. But this does not bring much improvement of the results over those calculated with 6-311++G**. Therefore it indicates that basis set saturation has been approached and it is necessary to improve the calculation method. Figs. 4 and 7 exhibit significant discrepancies between experiment and theory for 6a0 + 4a00 + 3a00 and 3a0 orbitals, which implies that these orbitals are subjected to effects that the current theoretical treatment has not given full consideration, such as the electron correlation, relaxation, and distorted wave effects. Our work makes imperative the need to develop a computationally affordable approach that addresses these effects, since for molecular systems current methods that do so, such as CI (configuration interaction) and DWIA (distorted wave impulse approximation) calculations, are prohibitively demanding on computing power. Acknowledgements
0
Fig. 7. The experimental and theoretical momentum profiles for 3a orbital of CHF2 Cl.
Financial support for this research work was provided by the National Natural Science Foundation of China (Grants No. 19974040 and 10134011). We gratefully
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acknowledge Professor C E Brion from the University of British Columbia (UBC) in Canada for supplying the HEMS and RESFOLD programs. References [1] I.E. McCarthy, E. Weigold, Phys. Rep. C 27 (1976) 275. [2] C.E. Brion, Int. J. Quantum Chem. 29 (1986) 1397. [3] K.T. Leung, in: Z.B. Maksic (Ed.), Theoretical Models of Chemical Bonding, Part 3, Springer, Berlin, 1991, p. 339. [4] C.E. Brion, in: T. Andersen et al. (Eds.), The Physics of Electronic and Ionic Collisions, American Institute of Physics Press, New York, 1993, p. 350. [5] M.A. Coplan, J.H. Moore, J.P. Doering, Rev. Mod. Phys. 66 (1994) 985. [6] E. Weigold, I.E. McCarthy, Electron Momentum Spectroscopy, Kluwer-Academic, New York, 1999. [7] R. Cambi, G. Ciullo, A. Sgamellotti, F. Tarantelli, R. Fantoni, A. Giardini-Guidoni, A. Sergio, Chem. Phys. Lett. 80 (1981) 295. [8] R. Cambi, G. Ciullo, A. Sgamellotti, F. Tarantelli, R. Fantoni, A. Giardiniguidoni, M. Rosi, R. Tiribelli, Chem. Phys. Lett. 90 (1982) 445. [9] R. Cambi, G. Ciullo, M. Rosi, A. Sgamellotti, F. Tarantelli, R. Fantoni, A. Giardiniguidoni, Int. J. Mass Spectrom. 46 (1983) 261. [10] A. Minchinton, J.P.D. Cook, E. Weigold, W. von Niessen, Chem. Phys. 93 (1985) 21. [11] A. Minchinton, J.P.D. Cook, E. Weigold, W. von Niessen, Chem. Phys. 113 (1987) 251. [12] A. Minchinton, A. Giardiniguidoni, E. Weigold, P.P. Larkins, R.M. Wilson, J. Electron Spectrosc. Relat. Phenom. 27 (1982) 191. [13] A.M. Grisogono, R. Pascual, W. von Niessen, E. Weigold, Chem. Phys. 135 (1989) 317.
[14] K.T. Leung, C.E. Brion, Chem. Phys. 91 (1984) 43. [15] J. Doucet, P. Sauvageau, C. Sandorfy, J. Chem. Phys. 58 (1973) 3708. [16] I. Novak, T. Cvitas, L. Klasinc, J. Chem. Soc. Faraday Trans. 2 77 (1981) 2049. [17] A.O. Bawagan, C.E. Brion, E.R. Davidson, D. Feller, Chem. Phys. 113 (1987) 19. [18] P. Duffy, D.P. Chong, M.E. Casida, D.R. Salahub, Phys. Rev. A 50 (1994) 4707. [19] M.E. Casida, Phys. Rev. A 51 (1995) 2005. [20] P. Duffy, Can. J. Phys. 74 (1996) 763. [21] W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133. [22] B.X. Yang, X.J. Chen, W.N. Pang, M.H. Chen, F. Zhang, B.L. Tian, K.Z. Xu, Acta Phys. Sin. (in Chinese) 5 (1997) 862. [23] M.J. Frisch, G.W. Trucks, H.B. Schlegel, G.E. Scuseria, M.A. Robb, J.R. Cheeseman, V.G. Zakrzewski, J.A. Montgomery Jr., R.E. Stratmann, J.C. Burant, S. Dapprich, J.M. Millam, A.D. Daniels, K.N. Kudin, M.C. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G.A. Petersson, P.Y. Ayala, Q. Cui, K. Morokuma, P. Salvador, J.J. Dannenberg, D.K. Malick, A.D. Rabuck, K. Raghavachari, J.B. Foresman, J. Cioslowski, J.V. Ortiz, A.G. Baboul, B.B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R.L. Martin, D.J. Fox, T. Keith, M.A. Al-Laham, C.Y. Peng, A. Nanayakkara, M. Challacombe, P.M.W. Gill, B. Johnson, W. Chen, M.W. Wong, J.L. Andres, C. Gonzalez, M. Head-Gordon, E.S. Replogle, J.A. Pople, Gaussian 98 revision A3, Gaussian Inc., Pittsburgh PA, 1998. [24] A.D. Becke, J. Chem. Phys. 98 (1993) 5648. [25] J.V. Ortiz, V.G. Zakizewski, O. Bolgounircheva, in: J.L. Calais, E. Kryachko (Eds.), Conceptual Perspectives in Quantum Chemistry, Kluwer, New York, 1997, p. 465. [26] P. Duffy, M.E. Casida, C.E. Brion, D.P. Chong, Chem. Phys. 159 (1992) 347.
An electron momentum spectroscopy study of the outer valence orbitals of chlorodifluoromethane XuHuai Zhang, XiangJun Chen *, Chunkai Xu, ChangChun Jia, XiaoFeng Yin, Xu Shan, Zheng Wei, KeZun Xu Laboratory of Bond-Selective Chemistry, Laboratory of Atomic and Molecular Physics, Department of Modern Physics, University of Science and Technology of China, Hefei, Anhui 230027, PR China Received 17 October 2003; accepted 25 November 2003
Abstract Electron momentum spectroscopy (EMS) has been used to measure the momentum profiles of outer valence orbitals of chlorodifluoromethane (CHF2 Cl), which are compared with Hartree–Fock (HF) and density functional theory (DFT) calculations using different-sized basis sets. Overall, DFT calculation employing B3LYP hybrid functional and the largest basis set that we used provides the best agreement with experiment. But the minimum improvement gained by replacing the 6-311++G** basis set with AUG-cc-pVQZ suggests that basis set saturation has been approached, at least for some orbitals of CHF2 Cl, and a computationally affordable method which addresses effects that current theoretical treatment neglects, such as distorted wave and electron relaxation, is sorely needed. Ó 2003 Elsevier B.V. All rights reserved. Keywords: Electron momentum spectroscopy; Density functional theory; Chlorodifluoromethane
1. Introduction On account of its unique ability to measure the momentum densities for individual molecular orbitals, electron momentum spectroscopy (EMS) is capable of investigating the molecular electronic structure. Momentum profiles (MP) of orbitals are most sensitive to the wave functionsÕ long-range behavior in the chemically important region, which is far from the nuclei but plays a central role in determining the moleculeÕs chemical properties. Therefore, EMS has been increasingly employed as a powerful tool for assessing the validity of quantum chemical calculations [1–6]. EMS measurements of halomethanes have been the subjects of studies by several authors. Cambi et al. [7–9] have reported binary ðe; 2eÞ and many body GreenÕs function studies of series molecules CHn F4 n . The results of their experiments and calculations clear showed *
Corresponding author. Tel.: +86-5513601170; 5513601164. E-mail address: [email protected] (XJ. Chen).
fax:
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0301-0104/$ - see front matter Ó 2003 Elsevier B.V. All rights reserved. doi:10.1016/j.chemphys.2003.11.036
significant many-body effects for the inner valence orbitals. However, their experiment is seriously limited by low energy resolution (2.6 eV) and poor statistics. Minchinton et al. [10–12], in a series papers, have investigated the electronic structure of monohalomethanes CH3 X (X ¼ F, Cl, Br and I) with electron momentum spectroscopy accompanied by GreenÕs function calculations. It was found that employing polarized basis sets improved theoretical calculations but the agreement between experiments and theoretical calculations still remained for the heavy halogen substituted methanes such as CH3 Br and CH3 I. Furthermore, EMS studies of series molecules CHn Cl4 n [13] as well as CF4 [14] have also been published. It is interesting to extend these studies to halomethanes including more than one species of halogen atoms. Chlorodifluoromethane (CHF2 Cl), also denoted as F22 as a member of Freon family, is one of the hydrochlorofluorocarbons (HCFCs), which show low values of ozone-depleting potential (ODP). At present, HCFCs, especially CHF2 Cl, are used as interim substitutes for chlorofluorocarbons (CFCs) in applications
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such as detergents, solvents, and refrigerants. This makes the detailed knowledge of electronic structure of CHF2 Cl molecule important. CHF2 Cl has been studied by photoelectron spectroscopy (PES) [15,16]. To our knowledge, no EMS study of chlorodifluoromethane has been reported so far. In this paper, we report the first electron momentum profiles for the outer valence orbitals of CHF2 Cl measured using ðe; 2eÞ electron momentum spectrometer at a total energy of 1200 eV plus binding energy and symmetric non-coplanar geometry. The experimental momentum profiles are also compared with Hartree–Fock (HF) and density functional theory (DFT) calculations using various basis sets.
2. Experimental and theoretical background Electron momentum spectroscopy is based on the kinematically complete ðe; 2eÞ collision experiment, which is an electron impact single ionization process. Within several approximations, including the binary encounter approximation (in which the residual ion is a mere spectator and hence the collision operator depends only on the incident and recoil electrons), and planewave impulse approximation (PWIA), the triple differential cross-section (TDCS) for the random oriented molecules is proportional to the spherically averaged momentum distribution of the corresponding Dyson orbital [1–6,17] Z 2 rEMS / dXjh~ pWfN 1 jWN0 ij ; ð1Þ the integrand of which is the square of the momentum representative of the overlap between the N-electron wave function describing the initial state of the target and the ðN 1Þ-electron wave function for the final ion state. The random orientation of the molecule is allowed for by the isotropic integration over the whole solid angle of the incident electronÕs momentum ~ p. Eq. (1) can be further simplified in most cases within target Hartee– Fock approximation (THFA), in which the initial state wave function is approximated by a single determinant of the ground state target Hartree–Fock orbitals, and freezing orbital approximation (FOA), in which the relaxation effect is ignored and consequently the Dyson orbital can be approximated with an initial (neutral) state canonical HF orbital. Then the TDCS becomes [1–6] Z 2 rEMS / Sqðf Þ dXjuHF ð2Þ q ðpÞj ; where uHF q ðpÞ is the one-electron momentum space canonical HF wavefunction for the qth orbital, from which the electron was ejected. The quantity Sqðf Þ is called spectroscopic factor or pole strength, which is the
possibility of finding such a one-hole configuration in the symmetry manifold f . It is essentially unity if we adopt THFA and FOA. For more general Dyson orbitals, we have the sum rule X Sqðf Þ ¼ 1; ð3Þ f
which is because of a closure relation, the completeness of the final ion states. Eq. (1) can also be simplified by using the more recent target Kohn–Sham approximation (TKSA) [18–20] in which the Dyson orbital can be approximated with an initial (neutral) state canonical Kohn–Sham orbital obtained by solving the Kohn–Sham equation [21]. By simply replacing the HF orbital wavefunction with the Kohn–Sham orbital wavefunction uKS q ðpÞ the TDCS then becomes Z 2 ðf Þ rEMS / Sq ð4Þ dXuKS q ðpÞ : A detailed description of the present electron momentum spectrometer has been given elsewhere [22]. In brief, it consists of an electron gun, a reaction chamber, two hemispherical electron energy analyzers each having a five-element cylindrical retarding lens and a one-dimensional position sensitive detector. In this work, since the symmetric non-coplanar geometry was employed, the polar angles of two analyzers were kept fixed at 45°. The relative azimuthal angle / was varied by rotating one analyzer around the incident electron beam while keeping the other one fixed. The incident electron energy was 1200 eV plus binding energy and the two outgoing electrons have essentially equal energies (600 eV). The coincident energy resolution of the spectrometer was measured to be 1.5 eV (FWHM) using Ar 3p ionization. The momentum resolution was estimated to be 0.15 a.u. by comparing the experimental momentum profile of the Ar 3p orbital with the theoretical one.
3. Calculations The spherically averaged momentum distributions in Eqs. (2) and (4) were calculated within the PWIA and THFA or TKSA for all the outer valence orbitals of CHF2 Cl. The corresponding position–space canonical HF or Kohn–Sham orbital wavefunctions were calculated at the equilibrium geometries using the GAUSSIAN 98W program [23]. The molecular geometry was optimized by DFT-B3LYP calculation with 6-311++G** basis set. The canonical HF orbitals for CHF2 Cl were then calculated using the 6-31G, 6-311++G**, and an augmented quadruple-zeta (QZ) basis set (AUG-cc-pVQZ). The Kohn–Sham orbitals were obtained by carrying out DFT calculations employing the B3LYP hybrid functional with the same
X.H. Zhang et al. / Chemical Physics 299 (2004) 17–24 Table 1 Calculated total energies and dipole moments for CHF2 Cl Method HF/6-31G HF/6-311++G** HF/AUG-cc-pVQZ B3LYP/6-31G B3LYP/6-311++G** B3LYP/AUG-cc-pVQZ
19
Table 2 Outer valence shell IP of CHF2 Cl (in eV)
Total energy (a.u.)
Dipole momentum (D)
)696.690 )696.897 )696.956 )698.490 )698.692 )698.749
2.1506 1.8077 1.6577 1.7520 1.5893 1.4599
three basis sets, respectively. In HF calculations, only the exchange energy resulting from the fermionic nature of electron is included. In DFT calculations, on the other hand, both exchange energy and correlation effect are included. The keyword B3LYP refers to BeckeÕs three-parameter hybrid functional using the LYP correlation functional [24]. The total energies and dipole moments calculated for CHF2 Cl using various methods are shown in Table 1. An outer-valence-shell Green function (OVGF) [25] calculation of ionization potentials (IPs) and pole strengths for outer valence orbitals of CHF2 Cl has also been performed with the 6-31++G** basis set.
4. Results and discussion CHF2 Cl contains 42 electrons and has Cs symmetry point group. Its ground state electronic configuration can be written as
Orbital
PES Ref. [15]
8a0 5a00 7a0 6a0 4a00 3a00 5a0 2a00 4a0 3a0 a
Theoretical Ref. [16]
12.6
12.56
14.0 15.9
13.91 15.94
18.7 19.7
18.87 19.98
23.0
23.1
This work (OVGF)a Ionization potential
Pole strength
12.381 12.478 13.987 16.187 16.350 17.134 19.323 20.043 20.713 24.246
0.94 0.94 0.94 0.93 0.93 0.93 0.92 0.92 0.92 0.90
With 6-31++G** basis set.
lence orbitals were measured at 13 different out-of-plane azimuthal angles. Fig. 1 shows two of them, which were measured at azimuthal angles 1° and 8°. Gaussian peaks fitted to the individual transitions, or in some cases ‘‘bands’’ formed by the overlap of several near degenerate (with respect to the energy resolution of the spectrometer) transitions, for example 8a0 +5a00 , are shown by dotted curves while their sum is shown by a solid curve. The positions of each individual peak are given by the IP determined by high-resolution PES [16]. The widths of the peaks are the combinations of the EMS instrumental energy resolution (1.5 eV in this work) and the Franck–Condon width of the corresponding bands determined by high-resolution PES [16].
ðcoreÞ16 ðla0 Þ2 ðla00 Þ2 ð2a0 Þ2 ð3a0 Þ2 ð4a0 Þ2 ð2a00 Þ2 ð5a0 Þ2 ð3a00 Þ2 ð4a00 Þ2 ð6a0 Þ2 ð7a0 Þ2 ð5a00 Þ2 ð8a0 Þ2 |fflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflffl} |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} inner valence shell
outer valence shell
The valence shell contains 13 molecular orbitals and can be divided into two sets: three inner valence orbitals and 10 outer valence orbitals. The IP ordering of the outer valence orbitals can be established by combining PES experiments and theoretical calculations, except for 4a00 and 6a0 orbitals, which will be discussed later. Table 2 compiles the IPs of the 10 outer valence orbitals predicted by theoretical calculation along with those observed by PES. The discrepancy between calculation and PES results becomes larger for inner valence orbitals. OVGF calculation also gives the pole strength for each outer valence orbital. As can be seen from the Table 2, the pole strengths for ionization from all outer valence orbitals can be regarded as unity to some extent. 4.1. Binding energy spectra The binding energy spectra of CHF2 Cl over the energy range 5–30 eV that covers all of the 10 outer va-
In Fig. 1, the first peak at 12.56 eV represents ionization of the highest occupied molecular orbital (HOMO), which is the chlorine lone-pair orbital and contains two orbitals: 8a0 and 5a00 . They cannot be resolved even by the high-resolution PES [16]. The theoretical calculations in present work give the ordering of 8a0 and 5a00 (in ascending order of ionization potential, default for all orbitals). The second peak at 13.91 eV corresponds to the C–Cl bonding orbital (7a0 ) ionization. The first two peaks are not well resolved due to the poor energy resolution of EMS. The third peak at 15.94 eV belongs to the fluorine lone-pair orbital ionization, which contains three orbitals: 6a0 , 4a00 and 3a00 . These orbitals are also too close to be distinguished by high-resolution PES. The ordering of 3a00 orbital can be determined by our calculations in this work, which indicates that it has the highest IP of the three. But the ordering of 6a0 and 4a00 remains unclear because different calculation methods give different results. DFT-
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X.H. Zhang et al. / Chemical Physics 299 (2004) 17–24
culated by DFT-B3LYP method employing AUG-ccpVQZ basis set. The instrumental angular resolution (0.15 a.u.) has been folded into the theoretical momentum profiles using the GWPG method [26].
Fig. 1. Binding energy spectra of CHF2 Cl at azimuthal angles / ¼ 1° and 8°. The dotted curves represent Gaussian curves fitted to the transitions or ‘‘bands’’ and the solid curve represents their sum. The positions of individual transitions determined by high-resolution PES [16] are shown as bars with numbers 1–6.
B3LYP calculations give the ordering af 4a00 and 6a0 , but HF calculations give a contradicting result. The next peak positioned approximately at 19 eV actually contains two peaks: the C–H bonding (5a0 ) ionization peak at 18.87 eV and the C–F bonding ionization peak at 19.98 eV. The latter contains two molecular orbitals, which cannot be resolved by PES, in the ordering of 2a00 and 4a0 determined by theoretical calculations in this work. The last peak at the ionization potential of 23.1 eV corresponds to the ionization from the innermost outer valence orbital of 3a0 . 4.2. Experimental and theoretical momentum distributions 4.2.1. Normalization The experimental momentum profiles are extracted by deconvoluting the same peak from the sequentially obtained binding energy spectra at different azimuthal angles or momentum [1]. In order to compare the experimental momentum distributions with the theoretical ones, we need one normalization factor common for all bands. Usually, this normalization factor is determined by normalizing the experimental and theoretical momentum distributions of the outermost valence ionization to the common intensity scale, since the outermost valence ionizations are expected to exhibit pole strength close to unity. In this work, as shown in Fig. 1, the three outermost orbitals 8a0 , 5a00 and 7a0 cannot be resolved clearly, so we use the sum of these three orbitals to determine this normalization factor. ItÕs reasonable to do so because the pole strengths of these three orbitals are nearly the same and close to unity. The theoretical momentum distribution used for normalization is cal-
4.2.2. 8a0 , 5a00 and 7a0 orbitals Fig. 2 shows the summed experimental MP of 8a0 , 5a00 and 7a0 orbitals compared with DFT-B3LYP and HF calculations employing 6-31G, 6-311++G** and AUGcc-pVQZ basis sets. It can be seen that the B3LYP/ AUG-cc-pVQZ calculation gives the proper intensity in low-momentum region and the correct position of the maximum. All other calculations underestimate the observed intensity in low-momentum region and shift the position of the maximum a little to high-momentum end. The first peak in the binding energy spectra (Fig. 1) is due to the ionization of the HOMOs, which contains two orbitals (8a0 and 5a00 ). As explained above, these two orbitals are too closely spaced, so we treat them as one peak. The second peak, which is only 1.35 eV away from the first one, corresponds to 7a0 orbital ionization. Fig. 3 shows the experimental and theoretical momentum profiles of the 8a0 + 5a00 orbitals (a) and 7a0 orbital (b), from which we can see that the theoretical MP is relatively high for 8a0 + 5a00 orbitals and low for 7a0 orbital. The theoretical and experimental MPs fit well in shape for 8a0 + 5a00 orbitals, but are quite inconsistent for 7a0 orbital in shape and magnitude. Orbitals 8a0 and 5a00 belong to the lone pairs of chlorine and are dominantly ÔatomicÕ, as can be easily seen from their momentum profiles, which resemble that of the 3p atomic orbital of chlorine. On the whole, the individual MPs of these two peaks have not been well described. But it would be premature to consider the predictions a complete failure, since these two peaks are not well
Fig. 2. The summed experimental and theoretical momentum profiles for 8a0 , 5a00 and 7a0 orbitals of CHF2 Cl.
X.H. Zhang et al. / Chemical Physics 299 (2004) 17–24
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Fig. 3. Experimental and theoretical momentum profiles for 8a0 , 5a00 orbitals (a) and 7a0 orbital (b) of CHF2 Cl.
resolved (the energy resolution of our spectrometer is 1.5 eV plus Franck–Condon width) and deconvolution uncertainties may have been introduced to both peaks. Therefore, a possible explanation is that the experimental momentum profile of 7a0 orbital is mixed with part of 8a0 + 5a00 orbitals. A much more definite conclusion can be expected with the upcoming spectrometers with an energy resolution well under 1 eV. 4.2.3. 6a0 , 4a00 and 3a00 orbitals This peak is due to fluorine lone-pair orbital ionization, and contains three orbitals: 6a0 , 4a00 and 3a00 , which cannot be resolved. The comparison of the summed experimental momentum distribution with the theoretical calculations is shown in Fig. 4. The experimental momentum profile shows a peak at p 0:5 a.u. and has no discernible shoulder beyond the peak. All theoretical calculations predict the peak at 0.5 a.u. except the one calculated with DFT-B3LYP method employing 6-31G basis set, which shift the maximum about 0.04 a.u. to high-momentum end. In this figure, we can see that all calculations severely underestimate the observed inten-
Fig. 4. The summed experimental and theoretical momentum profiles for 6a0 , 4a00 and 3a00 orbitals of CHF2 Cl.
sity in the peak region. The best match is provided by DFT-B3LYP calculation with AUG-cc-pVQZ basis set, which, in comparison with other calculations, shows the highest maximum intensity at p 0:5 a.u. and no significant shoulder around 1.3 a.u. The MP calculated using the same method with 6-311+G** basis set does not exhibit much difference, which indicates that DFTB3LYP calculations using the basis sets larger than 6311++G** will not provide much better agreement with the experimental results for this peak. The HF calculations using 6-311++G** and AUG-cc-pVQZ basis sets are in good agreement with each other too, but the intensity of the maximum is much lower than DFT calculations using the same basis sets and there is an obvious shoulder at p 1:3 a.u. For 6-31G basis set, the DFT calculation shows an even lower intensity of the peak and an obvious shoulder beyond it, and the HF calculation shows two maximum due to the depression of the peak at p 0:5 a.u. 4.2.4. 5a0 orbital The next orbital is 5a0 , which corresponds to C–H bonding orbital. Fig. 5 shows the experimental momentum distribution of this orbital (predominantly ÔptypeÕ), together with the calculations. The 6 theoretical curves in this figure are divided into two groups according to the calculation methods, which indicates that theoretical method is more important than basis set in reproducing the experimental momentum distribution for this orbital. This is easily understandable, since the atoms forming the bond are small and adding more polarization and diffuse terms to the basis set is unlikely to improve the quality of the calculation. We can see that DFT-B3LYP calculations give the better fit, while HF calculations underestimate the observed intensity. The best fit is still given by B3LYP/AUG-cc-pVQZ calculation, in both shape and intensity. There is little difference between the calculations using same method with different basis sets in the low-momentum region of p < 0:9 a.u., but in the high-momentum region beyond 0.9 a.u. The calculations with AUG-cc-pVQZ basis set
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X.H. Zhang et al. / Chemical Physics 299 (2004) 17–24
Fig. 5. The experimental and theoretical momentum profiles for 5a0 orbital of CHF2 Cl.
differ from that with the other two basis sets. This can also be expected, for high-momentum region roughly corresponds to the area close to nuclei in coordinate space, where wave functions of the molecule tend to have large gradients. Large basis sets have an inherent advantage in describing wave functions in such an area. As for the same calculation method, the momentum profile calculated with AUG-cc-pVQZ basis set shows higher intensity and fits better with the experimental data than those calculated with 6-31G and 6-311++G** basis sets, which are in good agreement with each other, in the region of p > 0:9 a.u.
4.2.5. 2a00 and 4a0 orbitals The next band is due to the ionization of 2a00 + 4a0 orbitals which correspond to C–F bond. Fig. 6(a) shows the summed experimental momentum distribution of these two orbitals compared with the theoretical momentum distributions. The individual theoretical momentum distributions are shown in Fig. 6(b) and (c). All of the theoretical calculations are in good agreement with the experimental MP in the region of p > 0:8 a.u. But in the region of p < 0:8 a.u., the theoretical calculations significantly differ from each other and none of them fits the experimental MP very well. It can be seen that DFT-B3LYP calculations employing 6-311++G** and AUG-cc-pVQZ basis sets have little difference with each other, and both provide very good agreement with the observed data in the region of p > 0:3 a.u. In the region of p < 0:3 a.u., each of these two calculations predicts a continuous rising curve with the descent of the momentum, but experimental data turn flat at about 0.3 a.u. and exhibit a platform. Both of the DFT-B3LYP calculations using 6311++G** and AUG-cc-pVQZ basis sets overestimate the experimental MP in this region. The HF calculations with 6-311++G** and AUG-cc-pVQZ basis sets turn flat at 0.8 a.u., and consequently underestimate the observed intensity in the region of p < 0:8 a.u. As for the calculations using 6-31G basis set, the DFT-B3LYP method predicts a shoulder around 1.0 a.u. and turns up at p 0:5 a.u., and the HF method shows a similar profile as calculated with 6-311++G** basis set, except
Fig. 6. (a) The summed experimental and theoretical momentum profiles for 2a00 and 4a0 orbitals of CHF2 Cl. The theoretical calculations for individual orbital 2a00 and 4a0 are shown in (b) and (c) respectively.
X.H. Zhang et al. / Chemical Physics 299 (2004) 17–24
for the depression at about 0.5 a.u. Both of them fit the experimental data poorly in both shape and intensity. In comparison with other calculations, the theoretical MP calculated by DFT-B3LYP method employing AUG-ccpVQZ basis set gives the best fit. Individually, for 2a00 orbital shown in Fig. 6(b), the theoretical calculations exhibit Ôp-typeÕ momentum profiles, and do not show much difference with each other. The maximum position predicted by these calculations various from 0.9 a.u. to 1.0 a.u., and the DFT-B3LYP/AUG-cc-pVQZ calculation gives the lowest intensity. In comparison with 4a0 orbital, the intensity of the theoretical MP of this orbital is much lower, and thus contributes to the shoulder of the summed distribution only. For the 4a0 orbital shown in Fig. 6(c), all calculations show mainly Ôs-typeÕ (slightly mixed with Ôp-typeÕ) momentum profiles, but they differ from each other significantly in the region of p < 1:0 a.u. This is the main cause of the difference between the calculations of the summed distribution in this region. The momentum profiles calculated by DFT method show steeper slopes and intensities in this region than those calculated by HF method. From Fig. 6(c) we can see that the difference between DFT and HF calculations is very large, which indicates that calculation method is more important for the MP of this orbital. Comparing the calculations using the same method, 6-311++G** and AUG-cc-pVQZ basis sets are in good agreement with each other, and the main difference between them and 6-31G basis set is that the latter shows an obvious shoulder around 1.0 a.u. This shoulder depresses its intensity in the region of p < 1:0 a.u. 4.2.6. 3a0 orbital The last orbital of the outer-valence-shell is 3a0 . The experimental momentum distribution is presented in Fig. 7, together with the theoretical calculations. All
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calculations give predominantly Ôp-typeÕ momentum distributions for this orbital and are in good agreement with the experimental data in the region of p > 0:7 a.u.. But all of them severely underestimate the observed intensity in low-momentum region, where experimental MP shows a strong Ôturn-upÕ indicating more ‘‘s-type’’ component than theoretical predictions. This is unlikely to be introduced via deconvolution uncertainties, since this peak is well isolated from other peaks. From this figure, we can see that the theoretical calculations are divided into three groups according to the basis set employed, which indicates that basis sets are more important than calculation methods when predicting the momentum distribution for this orbital. In the region of p > 0:7 a.u., the calculations employing AUG-cc-pVQZ basis set give the best fit. But in low-momentum region, we cannot tell which method is better due to the ÔturnupÕ of the experimental data. 5. Summary In summary, we have reported the first measurement of the momentum profiles for all 10 outer valence orbitals of CHF2 Cl by ðe; 2eÞ electron momentum spectroscopy. The experimental momentum profiles are compared with the theoretical ones. The results show that DFT calculations using the B3LYP hybrid functional are better than HF calculations in predicting the momentum distributions of the outer valence orbitals of CHF2 Cl. In this work, we employed the largest basis set (AUG-ccpVQZ) that our computing resources allowed for the CHF2 Cl calculations. But this does not bring much improvement of the results over those calculated with 6-311++G**. Therefore it indicates that basis set saturation has been approached and it is necessary to improve the calculation method. Figs. 4 and 7 exhibit significant discrepancies between experiment and theory for 6a0 + 4a00 + 3a00 and 3a0 orbitals, which implies that these orbitals are subjected to effects that the current theoretical treatment has not given full consideration, such as the electron correlation, relaxation, and distorted wave effects. Our work makes imperative the need to develop a computationally affordable approach that addresses these effects, since for molecular systems current methods that do so, such as CI (configuration interaction) and DWIA (distorted wave impulse approximation) calculations, are prohibitively demanding on computing power. Acknowledgements
0
Fig. 7. The experimental and theoretical momentum profiles for 3a orbital of CHF2 Cl.
Financial support for this research work was provided by the National Natural Science Foundation of China (Grants No. 19974040 and 10134011). We gratefully
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X.H. Zhang et al. / Chemical Physics 299 (2004) 17–24
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