HeI photoelectron spectra of PH2 and PF2: comparison between simulation and experiment

Chemical Physics

ELSEVIER Chemical Physics 224 (1997) 157 - 173

HeI photoelectron spectra of PH 2 and PF 2" comparison between simulation and experiment

Foo-Tim Chau a,*, John M. Dyke b, Edmond P.F. Lee a,b Abed Ridha b, De-Chao Wang a

a Department of Applied Biology and Chemical Technology, The Hong Kong Polytechnic University, Hung Horn, Kowloon, Hong Kong b Department of Chemistry, Southampton Universi~, Southampton S017 IBJ, UK

Received 4 June 1997

Abstract

Molecular orbital calculations on PH 2 and PF 2 and some of their low-lying cationic states, followed by Franck-Condon calculations, have been performed with the objective of simulating HeI photoelectron bands of these radicals. The molecular orbital calculations involved MP2 and CCSD(T) geometry optimization and frequency calculations, with basis sets of size up to 6-311G(3df,2p), and as well as G 1/G2 calculations. Franck-Condon simulations of photoelectron bands were performed using force constants derived from the ab initio calculations.

Based on comparison between simulated and observed spectra, the first adiabatic ionization energy of PH 2 has been confirmed as (9.84+0.01) eV and the lowest singlet-triplet separation in PHi- (1AI-3B t) has been deduced as (0.78 ___ 0.04) eV. Also, the first adiabatic ionization energy of PF 2, corresponding to the ionization PFf JA 1 ,-- PF 2 X2Bt, has been established as (8.84 + 0.01) eV. The vibrational structure observed in the first band of PF 2 has been assigned to excitation of the symmetric stretching mode (u I) in PFf (X ~AI) and the vibrational structure observed in the second band of PH 2 has been assigned to excitation of the deformation mode (u 2) in PH~-(a3B1). © 1997 Elsevier Science B.V.

1. Introduct ion

U.v. photoelectron spectra recorded for the F + PH 3 reaction have been reported only briefly by the Southampton p.e.s, group in a review [1] and in a paper on the photoelectron spectrum on PF [2]. In summary, the F + PH 3 reaction gives PH 2 as the primary reaction product and this shows maximum intensity in the photoelectron spectrum at 0.5 ms reaction time, under the conditions used. On increas- ing the reaction time at constant reagent partial

* Corresponding author. Fax: + 852 2364 9932.

pressures, the PH 2 signal decreases to be replaced by PH (which maximizes at 1 ms reaction time) and P2, PF and PF 2 which maximize at --~ 2 ms. As the reaction time is increased further, the PH and PF signals decrease to zero (by = 3 ms) but the PF 2 signal persists until 5 ms. At long reaction times, > 10 ms, only photoelectron bands of the final reaction products (PF 3 and HF) are observed. These characteristics mean that PH 2 bands can be observed early in the reaction (at = 0.5 ms) and PF z can be observed at longer reaction times when the partial pressures of all other reaction intermediates have decreased to zero.

Although only a brief account of this work has

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158 F.-T. Chau et a l . / Chemical Physics 224 (1997) 157-173

been presented previously [1], it has been referred to on two occasions by other research groups in relation to the lowest singlet-triplet separation in PH + [3] and the value of the first adiabatic ionization energy (AIE) of PF 2 [4]. In view of this interest in PH 2 and PF 2, the u.v. photoelectron spectra of these radicals have been simulated and compared with the PH 2 and PF 2 photoelectron spectra recorded from the F + PH 3 reaction. The main objectives were to determine the first adiabatic ionization energies of these radicals and determine the lowest singlet-triplet separation in PH2, values which have received considerable atten- tion from theoreticians [3-11] and spectroscopists [3,4,12] but are not yet fully established.

In principle, photoelectron spectroscopy is well suited to measuring the energy separation of two cationic states. This can only be achieved, however, if the adiabatic components can be identified in the associated photoelectron bands [1,13]. Problems will be experienced if one or more of the bands associated with the states of interest are overlapped by other bands or if the Franck-Condon envelope associated with ionization to one of the ionic states corresponds to a large geometry change on ionization and hence is very broad, as is the case in the first photoelectron bands of HCO [13] and NH 2 [14]; the adiabatic component is then difficult to identify.

In the case of PH 2, although the first band is a typical non-bonding type envelope with the adiabatic ionization energy (AIE) equal to the vertical ionization energy (VIE), the second photoelectron band is broad, with the AIE not equal to the VIE. The second PH 2 band is also heavily masked by a number of overlapping bands arising from other species present in the F + PH 3 reaction mixture, notably P2 and unreacted PH 3. In the present study simulations of the first two bands of PH 2 have been performed. The aim is to use the vibrational components that are observed, with the computed envelopes, to allow the first two adiabatic ionization energies to be obtained and hence to enable the lowest singlet-triplet separation in PHi- to be determined.

In the case of PF2, a recent resonance enhanced multiphoton ionization (REMPI) and ab initio study [4] suggested a lower first AIE ( = 8.73 eV) than that obtained from both photoelectron spectroscopy ((8.84 _+ 0.01) eV; see later text and [1]) and photoionization mass spectrometry ((8.85 _+0.01) eV

[15]). The lower value in the REMPI study [4] arose from the fact that a number of low-lying Rydberg states could be more reasonably fitted to Rydberg series using a first adiabatic ionization energy of 8.73 eV rather than 8.84 eV, and ab initio calculations for the isogyric reaction PF 2 + SiF+--* PF 2 + SiF +, at the QCISD(T)/6-311 + + G ( 3 d f ) / / QCISD(T)/6-31G* level, gave an AIE of PF 2 of 8.77 eV. In order to clarify this situation, the first photoelectron band of PF 2 has been simulated for comparison with the experimental first band, which is vibrationally resolved.

A number of ab initio molecular orbital studies of the minimum energy geometries, harmonic vibrational frequencies and relative electronic energies of the PH 2 and PF 2 radicals and their cations have been reported previously (see later text). However, none of them employed the size-consistent perturbative MP2 and/or the CCSD(T) methods apart from a very recent study on PFf and related triatomics [ 16]. The MP2 method is attractive for calculating minimum-energy geometries and harmonic vibrational frequencies because of the availability of analytic first and second energy derivatives in most com- monly used quantum chemical packages. Although analytic first and second derivatives are not readily available for the CCSD(T) method, it has been shown recently that the coupled-cluster (CC) approach is remarkably good in describing non-dynamic electron correlation and is more accurate in computing ionization energies than non-size-extensive CI type methods [17]. In addition, a recent systematic comparison of experimental and calculated minimum energy bond lengths for some organic molecules, computed using different methods, has come to the conclusion that the computed bond lengths converged to the CCSD/TZ2P + f values [18].

In the present study on PH 2 and PF 2, the MP2 and CCSD(T) methods have, therefore, been chosen with both small and large basis sets, to obtain minimum energy geometries, vibrational frequencies and relative energies for each radical in its ground state and its low-lying ionic states. Although PH 2 and PF 2 have recently been studied by density functional theory using different functionals [7,19,20], this approach was not adopted in this work as the computed values are likely to be less reliable than those obtained by the MP2 and CCSD(T) methods.

F.-T. Chau et aL / Chemical Physics 224 (1997) 157-173 159

2. Computational details

Geometry optimizations and frequency calculations were performed at the MP2 and CCSD(T) levels of theory employing the Gaussian 94 [21] suite of programs with the available basis sets. G1 [22] and G2 [23] energies were also computed for the ground states of PH 2 and PF 2, and some low-lying states of their cations. In addition to the AIEs obtained from the above calculations, VIEs were also calculated for some ionization processes to assist spectral assignments. Unrestricted wavefunctions were used for open-shell species and spin-annihilated energies, PUMP2, were used at the MP2 level unless otherwise stated. (It should be noted that all the states considered in this work are in each case the lowest state of a particular spin symmetry).

The computer program used for Franck-Condon spectral simulation has been developed for the MAT- LAB [24] environment on a PC. It is based on the method of Chen [25] and has been described else- where [26,27]. It makes use of the cartesian displace- ments of the normal co-ordinates obtained from a Gaussian 94 frequency calculation. In this method, the Duschinsky effect is included and the harmonic oscillator model is employed for both the neutral and cationic states to evaluate Franck-Condon factors. Vibrational components within a photoelectron band were simulated using gaussian functions with the experimental FWHM (full width at half-maximum) value.

3. Experimental

All photoelectron spectra were recorded using a single detector photoelectron spectrometer specifi- cally designed for the study of short-lived molecules in the gas phase [1]. A flow reactor described in reference [28] was used to study the F + PH 3 reaction. Fluorine atoms were generated by a microwave discharge (2.45 GHz) of a 5% mixture of molecular fluorine in helium and this typically gave 95% disso- ciation. The photoelectron spectra recorded for phos- phine were in good agreement with that reported previously [29]. The reagent mixing distance above the photon beam could be varied in the range 0-10 cm, corresponding to reaction times of approxi-

mately 0 -5 ms. All photoelectron spectra were recorded with HeI (21.22 eV) radiation. The best PH 2 spectra that could be obtained were recorded at short mixing distances ( ~ 1 cm) whereas the opti- mum PF 2 spectra were recorded at longer mixing distances (4-8 cm). Calibrated spectra were acquired by adding calibrants (e.g. methyl iodide and argon) to the ionization region under reaction conditions.

4. Results and discussion

The electronic ground state configuration of PH 2 is:

- - - (2bz)2(5a~)2(2b~) ' , X2B~

where the half-filled molecular orbital, the 2b I orbital, is essentially a phosphorus 3p orbital perpendicular to the PH 2 plane. The 5a I orbital consists of P3s, P3p and Hls orbitals, and is weakly bonding in the P - H directions and bonding between the hydro- gen atoms. In contrast, the 2b 2 orbital is bonding in the P - H direction and antibonding between the hy- drogen atoms. The (2b 1) l, (5al)-1 and (262) -1 ionizations are expected to give the ~A 3.1 1, B 1 and 3'~A 2 ionic states and ab initio molecular orbital calculations performed in this work show that the PH 2 ionic states occur in this order.

An experimental spectrum recorded at 1 cm mixing distance above the photon beam is shown in Fig. la. A band was observed at (9.84 + 0.01) eV, which had a non-bonding envelope. Its behaviour with mixing distance was consistent with it being associated with a primary reaction product, as it maximised in intensity at 1.0 cm mixing distance at constant reagent partial pressures and then decreased. Also, the position of this band is in excellent agreement with the value of (9.83 _ 0.02) eV obtained for the first adiabatic ionization energy of PH 2 by McAllister and Lossing [30] by electron impact mass spectrometry and a value of (9.824 + 0.002) eV obtained by Berkowitz and co-workers [3] by photoionization mass spectrometry. A band was also observed in the 11.0-11.5 eV ionization energy region which was proportional in intensity to the first band of PH~ as the experimental conditions changed. This band showed four clear vibrational components, at l l.00,

160 F.-T. Chau et al. / Chemical Physics 224 (1997) 157-173

11.11, 11.22 and 11.33 eV, and was assigned on the basis of the results of ab initio molecular orbital calculations to the second band of PH 2, corresponding to the PH~-(3B1)*--PHe(X2BI) ionization. The most intense vibrational component was the feature at (11.11 + 0.01) eV and this was taken as the VIE. Unfortunately, no other vibrational components to lower ionization energy of the 11.0 eV feature could be observed because of overlap with bands associated with unreacted PH 3 and the reaction products P2, P and PH in the 10.0-11.0 eV region.

In the case of PF 2, assignment of the band shown in Fig. 2a to the first photoelectron band of this radical was achieved on the basis of the following evidence: 1. it was the longest-lived reaction intermediate ob-

served in the F + PH 3 reaction, clearly being derived from a series of consecutive reactions;

2. the measured first adiabatic ionization energy, (8.84 ___ 0.01) eV, agrees well with the value determined by photoionization mass spectrometry ((8.85 +__ 0.01) eV [15]);

3. the experimental vertical ionization energy, (9.09 + 0.01) eV, is in good agreement with the values

is:

computed in this work using molecular orbital theory. The electronic ground state configuration of PF 2

- - - ( 5 b 2 ) 2 ( 8 a l ) 2 ( 3 b l ) 1 X 2 B 1

where the half-filled level, the 3b~ orbital, consists of a large contribution from a P3p orbital and a small contribution from fluorine 2p orbitals, perpendicular to the PF 2 plane. The 3b I molecular orbital is antibonding in the P - F direction and bonding in the F - F direction. Ab initio molecular orbital calculations have been carried out f o r PF2(XZBx ) and the ~A1, 3'IB 1 a n d 3'lA 2 ionic states arising from the (3bl) -~, (8a l ) - l and (5b2)-l ionizations, although clear evidence was only obtained for the PF~(XIA1)* - PF2(X2BI) band because of problems with overlapping bands at higher ionization energy.

The computational results and the comparison of the simulated and experimental photoelectron spectra will now be considered for (a) PH 2 and PH2 ~, and (b) PF 2 and PF~-.

Table 1 The computed geometries and harmonic vibrational frequencies of PH2 X2B t at different levels of theory

Method PH HPH ~'l u 2 u 3 Ref.

(,~.) (°) (cm - ') (cm- l ) (cm- ')

MP2/6-3 IG " 1.4192 92,61 2486.5 1181.4 MP2/6-311G(3df,2p) 1.4124 92.02 2458.5 1148.8 CCSD(T)/6-311G * * 1,4202 91.83 2418.7 1143.5 CCSD(T)/6-311G(2df,2p) 1.4222 91.77 2353.8 1131.3 UHF/TZ2p 1.405 90.5 UHF/6-31G * 1.407 93.4 2295 1258 MCSCF/TZP 1.442 92.9 CASSCF/SOCP 1.426 90.5 M R D C I / ~ DZ2P + sp(bond) 1.420 91.1 2330 1110 absorption/emission 1.428 91.5 1102 absorption spectrum 1.418 91.7 refined analysis 1.429 91.7 LIF 1.423 91.7 pes o fPH 2 2270 + 80 FIR-LMR 1102 Raman (high temp.) 2310 _ 2

2500.6 2467.5 2425.0 2362.7

2577

2495

[31] [32] [33] [9] [34] [35] [36] [37] b

[381 [39] [401 [41]

aBasis sets used: P [7s6p3d2flg]; H [8s5pld]. bin [37], the visible absorption spectrum of PH 2 has been recorded with more intensity than earlier work and re-analysed.

F.-T. Chau et al./ Chemical Physics 224 (1997) 157-173

Table 2 The computed geometries and harmonic vibrational frequencies of PHi- X IA 1 at different levels of theory

161

Method PH HPH ~'l ~'2 u3 Ref. (,~.) (°) (cm- I ) (cm- ' ) (cm ')

MP2/6-3 IG * 1.4155 93.4 2545.3 1191.9 2567.2 MP2/6-311G(3df,2p) 1.4129 92.4 2480.0 1168.8 2492.3 CCSD(T)/6-311 G* * 1.4178 92.6 2463.3 1152. I 2473.5 CCSD(T)/6-311G(2df,2p) 1.4217 92.5 2390.5 1138.3 2380.1 HF/6-31 G* 1.400 93.4 2668 1274 2682 [3,6] GVB/DZVP 1.436 94.0 [5] casscf(6,6)/TZP 1.438 94.2 2353 1111 2335 [7] casscf/SOCI 1.426 92.6 [9] MRSDCI + D / ~ TZ2P 1.414 93.0 [11] MRCI 1.423 92.9 2399 1112 2413 [51 ]a

aRef. [51] quotes an unpublished experimental value for v 2 of PH~ XIAI of 1101 cm-t.

4.1. PH 2 and PH2 +

4.1.1. Computed geometries and uibrational frequencies

The computed minimum-energy geometries and harmonic vibrational frequencies obtained in this work (all at the MP2 and CCSD(T) levels) for the X2B~ state of PH 2 and the X~A~, a3Bl and A~Bj states of PHi- are presented in Tables 1-4, respectively, together with earlier computed and experimentally determined values. The highest level of calculations performed previously are the large basis C A S S C F / S O C I calculations of Balasubramanian [9]. For PH 2(X 2 B ~ ), experimentally derived geometries and some experimental vibrational frequencies are available for comparison. The MP2 and CCSD(T) minimum energy geometries reported here agree,

within experimental uncertainty, with the available experimental geometries, except that the M P 2 / 6 - 31G * computed bond angle is slightly high. Inspec- tion of the computed vibrational frequencies shows that the CCSD(T)/6-311G(2df,2p) values are in the best agreement with available experimental values.

For PH ~-, it appears that there are no experimental determinations of the equilibrium geometry or vibrational frequencies for any of the low-lying electronic states. The MP2 and CCSD(T) minimum energy geometries obtained here change only slightly with change of basis sets, suggesting that they are near convergence for all three cationic states studied. It is difficult to make any comment on the minimum energy geometries obtained in previous calculations because, other than the differences in the s ize/quality of the basis sets used, the active/configurational spaces used are different in the MCSCF a n d / o r C1

Table 3 The computed geometries and harmonic vibrational frequencies of PHi- a3Bi at different levels of theory

Method PH HPH l~ I /~2 1"3 Ref. (,~) (°) (cm- i ) (cm- i ) (cm- I)

MP2/6-3 IG * 1.4028 122.0 2554.1 1011.9 2637.6 MP2/6-311G(3df,2p) 1.4002 121.8 2477.6 1000.3 2554.5 CCSD(T)/6-311G* " 1.4048 121.6 2463.0 984.2 2542.5 CCSD(T)/6-311G(2df,2p) 1.4097 121.8 2383.5 967.8 2441.6 HF/6-31G* 1.387 121.4 [3,6] GVB/DZVP 1.411 I 21.5 [5] casscf(6,6)/TZP 1.420 122.0 2442 954 2357 [7] casscf/SOCI 1.416 121.8 [9] MRSDCI + D / ~ TZV2P 1.399 121.9 [11]

162 F.-T. Chau et a l . / Chemical Physics 224 (1997) 157-173

Table 4 The computed geometries and harmonic vibrational frequencies of PH~ AIBI at different levels of theory

Method PH HPH v I u 2 u 3 Ref.

(~.) (°) (cm- ' ) (cm- L ) ( cm- ' )

MP2/6-31G * 1.4112 123.2 2481.2 1004.6 2569.9 MP2/6-311G(3df,2p) 1.4071 123.5 2421.9 989.9 2507.6 CCSD(T)/6-311G * * 1.3997 122.4 2495.4 982.2 2602.1 CCSD(T)/6-311G(2df,2p) 1.4062 122.4 2386.1 954.1 2473.0 GVB/DZVP 1.418 126.6 casscf /SOCI 1.431 124.0 MRSDCI + D / ~ TZV2P 1.419 124.7 MRCI 1.427 124.5 2259 914 2292

[5] [9] [ll] [51]

type calculations reported. Inspection of Tables 2 -4 shows that the computed minimum energy geometries obtained in previous calculations also differ from each other significantly. If the computed vibrational frequencies are considered, the CCSD(T)/6- 311G(2df,2p) values seem to be the most reliable.

4.1.2. Computed adiabatic and vertical ionization energies of PH 2

Computed AlEs and VIEs at different levels of theory are given in Table 5, while the computed XIA1-a3BI and XIA1-AIBI PHi- separations are

given in Table 6, together with previous theoretical and experimental values. From Table 5, it can be seen that the computed value for the first AlE coin- cides with the corresponding computed value for the first VIE at almost all levels of calculation in agreement with the experimental first band envelope (see Fig. 1). The computed AIE/VIE values converge at 9.72 eV, which is smaller than the experimental value by 0.12 eV. The CCSD(T)/6-311G(2df,2p) ionization energies are virtually identical to the G 1/G2 values.

For the second AlE, the C C S D ( T ) / 6 - 31 lG(2df,2p) and G 1 /G 2 values of 10.46 and 10.60

Table 5 The computed adiabatic ionization energies (VIE values are in brackets)

(AIEs, in eV) from PH 2 X2BI to the various ionic states of PHi- at different levels of theory

AIE (VIE) X IA i,(bl ) - i a 3 B t ,(al ) - L A I B I,(al ) - i

MP2/6-31G * 9.54 (9.54) 9.92 (10.46) 11.08 (11.58) a MP2/6-311G(3df,2p) 9.80 (9.80) 10.37 (10.90) 11.25 (11.79) b CCSD(T)/6-311G* * 9.45 (9.45) 10.13 (10.65) 10.44 (10.99) CCSD(T)/6-31 lG(2df,2p) 9.71 (9.71) 10.46 (10.97) 10.80 (11.33) GI 9.71 10.60 G2 9.72 10.60 photoionization mass c 9.824 ± 0.002 ~ 10.534 photoionization mass d 10.525 11.74 photoelectron e 9.84 (9.84) 10.62 f (11.11)g

aThese are from the PUMP2 energies; the corresponding values from the UMP2 energies are 10.65 (11.23) eV (large spin contamination; see text). bAs for a; the corresponding values from the UMP2 energies are 11.02 (11.61) eV. CRef. [3]. dRef. [12]. e Experimental uncertainties -t- 0.01 eV. fThe derived value from comparison of simulated and experimental spectra (see text). gThe strongest peak that could be observed (see text).

F.- T. Chau et al. / Chemical Physics 224 (1997) 157-173

Table 6 The energies (in eV) of the low-lying 3Bj and J B I states of PHi- relative to the ground XIA] state

163

Method 3B 1 i B i Ref. Remark

MP2/6-31G * 0.34 1.54 MP2/6-311CK3df,2p) 0.57 1.45 CCSD(T)/6-311G * * 0.68 0.99 CCSD(T)/6-311G(2df,2p) 0.75 1.09 G1 0.89 G2 0.88 GVB + CI/DZVP 0.70 2.12 [5] MP4(combined) 0.92 [6] a MP4(combined) 0.87 [6] b casscf/MRCISD(Q) 0.71 [7] G2 0.88 [8] casscf/SOCI 0.769 1.954 [9] casscf/SOCl + Q 0.771 1.938 [9] best est. 0.78 [9] MRDCI 0.59 2.05 [10]

(0.75) [10,12] MRSDCI + D / ~ TZ2P 0.61 1.95 [11] est. full CI 0.72 2.03 [11] MRCI - 1.97 [51] photoionization mass _> 0.71 [3] photoionization mass 0.70 1.92 [ 12] photoelectron 0.78 1.1 c

GVB/DZVP, geometries HF/6-31G ~ geometries HF/6-31G * geometries

ZPE + core-val. + rel.

at PH = 1.40 ,~; see [12]

+ 0.05

aEffectively MP4/6-31 + G(2df, p)/ /HF/6-31G ~ + ZPE level; isogyric process; Ref. [6a]. bEffectively MP4/6-311 + G(2df, p)//HF/6-31G * + ZPE level; modified isogyric process; Ref. [6b]. c Franck-Condon simulation for this work.

eV, respectively, agree well with the experimental value of = 10.53 eV obtained from photoionization mass spectrometry [3]. The experimental second VIE of (11.11 ___ 0.01) eV is in good agreement with the CCSD(T) /6 -311G(2df ,2p) value of 10.97 eV. The computed values for the A l E - V I E separation at all levels of calculation are = 0.5 eV, suggesting a broad photoelectron band, consistent with the experimental observation. This will be discussed later together with the band simulations.

The computed values for the third AlE and VIE also suggest a broad photoelectron band. The CCSD(T) results indicate that the third band overlaps the second. However, the computed CCSD(T) AlE values of the third band differ from the MP2 computed AlE values and the photoionization mass spectrometric AlE posit ion [12] by = 0.5 and 1.0 eV, respectively. It should be noted that there is signifi- cant spin contamination ( (S 2) ca. 1.0; ( S ) ca. 0.2) in the UHF wavefunctions for the open-shell A~B2 state for all the MP2 and CCSD(T) calculations.

Since it has been shown that coupled-cluster methods, such as CCSD, usually remove a great deal of spin contamination [42,43], the CCSD(T) results would presumably be more reliable than the MP2 results. Although the third IE has not been reported in previous computational studies, the position of the A ~B~ state relative to the X ~A t state has been quoted in a number of theoretical studies, together with the X ]A l - a3Bl separation (see Table 6). The X - a separation in PHi- is discussed in the next section.

4.1.3. The X - a separation in Pi le +

From Table 6, it is clear that the computed X - a separation is dependent on the level and type of theoretical method used. Of the previously computed values, the X - a separation computed at the highest level is the best estimate of Balasubramanian [9], 0.78 eV. This agrees well with the C C S D ( T ) / 6 - 311G(2df,2p) value of 0.75 eV computed in the present work. Based on the observed change in the values of the computed X - a separation at the


CCSD(T) level with the two basis sets used (Table 6), with a larger basis set the CCSD(T) value would probably converge to the best estimate of Balasubra- manian [9]. The corresponding values from the com- posite methods, G1, G2 and MP4 (combined), however, are slightly higher - - in the region of 0.9 eV. For the MP4 (combined) approach, the H F / 6 - 3 1 G * geometries were used and they differ considerably from those obtained with correlated methods. This may be the cause of the larger singlet-triplet separation with this approach. For the G1 and G2 ap-

proaches, the energy of the 3B 1 state is too high, as the G 1 / G 2 second AlEs are higher than the CCSD(T)/6-311G(2df,2p) value (by 0.14 eV), but the first AIEs from all these three approaches are the same (see Table 5). This may be due to the additivity assumption a n d / o r the empirical correction made in the G 1 / G 2 approach being inappropriate for the PH ~- 3 B 1 state.

For the XIA~-A 1B1 separation, all MCSCF a n d / o r CI type calculations give values of ca. 2.0 eV, in reasonably good agreement with the value

IQO

d

P '

' c'.o ' o o ' r F x v

i

11.5 110 105

J I0.0 9.5

Fig. 1. (a) Observed and simulated photoelectron bands for the ionizations PH~(XtA i, a3B i, AI B~) ~ PH2X2 BI. The simulations employed CCSD(T)/6-311G(2df,2p) computed minimum energy geometries and adiabatic ionization energies (AlEs = 9.71, 10.46 and 10.80 eV for the three ionizations). A FWHM = 55 meV was used for the vibrational component envelopes. In the experimental spectrum (upper trace), the dotted envelope represents the estimated contribution from the first band of unreacted PH 3. (b) The simulated first three bands of PH 2 (see text) as used in (a). The vibrational level labelling shown corresponds to PH i (v', u', O) ~ PH 2 (0, 0, 0) transitions, where the numbers shown above the vibrational bands are (t,', u') values.

F.-T. Chau et al. / Chemical Physics 224 (1997) 157-173 165

suggested by photoionization mass spectrometry of 1.92 eV [12]. However, the MP2 values of the present work are ca. 0.5 eV lower, while the CCSD(T) values are even lower, in the 1.0 eV region. Although the MP2 values are probably less reliable because of the high spin contamination in

the UHF wavefunctions, as mentioned previously, all these values from the perturbative methods change little with the different basis sets used. The cause of this discrepancy between the results of the perturbative methods used here and previous MCSCF/CI type methods is not clear. One possibility may be

I I I , I I l , l , l , l j l t , I

o o o o o o o o o ~

I

O9 t- @ t -

._>

n~

PH2 + AIB1 + a3B1

J I ' I '

12.0 11.5 I ' I

11.0 10.5

I I i I j f l I i I i l l J i i I

o o o o o o o O O o

AIB1

, , l l I I I I , , I ,

XIA1

I 10.0

I 12.0

a3B1

, I , I ' I

11.5

l i ,I i , , i I I ; I

11.0 10.5

Ionization Energy/eV Fig. 1 (continued).

I 10.0

166 F.-T. Chau et al. / Chemical Physics 224 (1997) I57-173

that the different computed energy separations are actually associated with two different ~ B ~ PF~ states, and it is noted that, for the low-lying excited states of PF 2, the supposedly lowest 2A 1 and 2B 2 PF~ states from an MRDCI study [44] were found to be the second lowest states by later C A S P T 2 / / C A S - SCF [45] and C A S S C F / M R S D C I studies [46]. Of course, it is also possible that the CCSD(T) method has not removed the effect of large spin contamination in the A~B~ state a n d / o r the single reference methods are inadequate for this case.

4.1.4. The o b s e r v e d a n d s i m u l a t e d spec t ra

The simulated first three bands in the Hel photoelectron spectrum of PH 2 are shown in Fig. 1, together with the experimental spectrum recorded for the F + PH 3 reaction at short mixing distance (1.0 cm). The simulated spectrum (Fig. lb) has employed the CCSD(T) /6-311G(2df ,2p) minimum energy geometries, vibrational frequencies and relative energies of the states involved (Tables 1-5). The first simulated band is just a sharp band with the AIE equal to the VIE and essentially no vibrational structure, in excellent agreement with the experimental first band envelope . Wi th the C C S D ( T ) / 6 - 311G(2df,2p) AIEs, the simulated second and third photoelectron bands overlap as shown (Fig. l b). Since the a3B~ and N B~ states are computed to have

similar minimum energy geometries and vibrational frequencies (Tables 3 and 4), the vibrational structure and F ranck-Condon factors for the second and third bands are similar. The band associated with ionization to the 3B~ state has been simulated assum- ing an intensity three times that for ionization to the ~B~ state in accordance with the 3BI:~B ~ spin-multi- plicity ratio. The relative intensity of the first and second / th i rd bands is not known, but for comparison with the experimental spectrum this ratio has been set to be the estimated ratio on the experimental spectrum.

The observed second band of PH 2 shows four clear vibrational components at 1 1.00, 11.1 1, 11.22 and 11.33 eV (see Fig. 1). The strongest component in a large number of spectra, al lowing for the contribution from unreacted PH 3, is the feature at (1 1.1 1 + 0.01) eV. Setting the VIE to this value and making use of the computed envelope, the AIE of the second photoelectron band is placed at 10.62 eV, giving a PH + X I A l - a 3 B l separation of (0.78 _+ 0.04) eV. This agrees very well with the best theoretical estimate of Balasubramanian (0.78 eV [9]) and the CCSD(T) /6-31 1G(2df,2p) value (0.75 eV). This assignment means that the VIE at 1 1.11 eV corresponds to the (0,4,0)PH~-a3B1 ~ (0,0,0)PH 2 X2BI component.

This result means that the C C S D ( T ) / 6 -

Table 7 The computed geometries and harmonic vibrational frequencies of P F 2 X2BI at different levels of theory

Method PF FPF u I t, 2 v~ Ref. (A) (°) (cm-i) (cm i) (cm-i)

casscf(9,8)/6-31G * 1.605 l 98.5 867.3 356. l 863.7 MP2/6-31G * 1.6096 99.2 884.2 344.5 884.2 MP2/6-311G(2df) 1.5835 99.0 878.9 372.7 867.9 CCSD(T)/6-31 I G * 1.6056 98.7 844.4 356.7 831.4 CCSD(T)/6-31 lG(2d) 1.5939 98.6 848.8 357.0 839.7 CCSD(T)/6-311G(2df) 1.5835 98.8 875.4 372.0 864.8 casscf(3,8)/6-311 + G(2d) 1.5661 97.5 [45] QCISD(T)/6-3 IG* 1.613 98.7 874 343 874 [4] MRSDCI/DZP 1.577 98.5 830 378 859 [44] casscf/MRSDCI a 1.600 97.94 [46] microwave 1.5792 (18) 98.48 (21) 864 (14) 365.3 (1 l) 848 (24) [47] IR matrix 831.4 853.1 [48] IR matrix 847.0 329 826 [49] Jacox 841 (4) 367 (1) 848 (24) [50]

aFrom all-electron calculations using a QZV3P (for P) and TZV2P (for F) quality basis set; using RECP with TZ2P for thc valence space, the casscf/MRSDCI calculations gave PF = 1.610 A and FPF = 97.50 °.

F.-T. Chau et al. /Chemical Physics 224 (1997) 157-173

Table 8 The computed geometries and harmonic vibrational frequencies of PF2 + XIAI at different levels of theory

167

Method PF FPF v t v 2 v 3 / Re f .

(,~) (°) (cm- I ) (cm- I ) (cm- l )

casscf(8,8)/6-31G" 1.5260 99.8 1022.0 418.6 1077.6 MP2/6-31G * 1.5342 102.5 1022.6 386.7 1072.9 MP2/6-311G(2df) 1.5059 103.2 1030.9 415.1 1076.9 CCSD(T)/6-311G * 1.5209 102.3 1002.2 406.9 1040.1 CCSD(T)/6-31 lG(2d) 1.5120 102.5 1000.6 402.1 1045.6 CCSD(T)/6-311G(2df) 1.5045 103.0 1028.4 416.7 1074.9 GVB/DZVP 1.513 101.6 QCISD(T)/6-31G * 1.536 102.2 1006 384 1058 casscf/MRSDCI a 1.525 102.3 CCSD(T)/cc-pVQZ 1.5045 102.59 1017.8 411.3 1058.4 corrected structure 1.4949 102.74 experimental b 980 4- 30

[5] [4] [46] [16] [16]

aUsing RECP with a TZ2P quality basis for the valence shells. bFrom HeI photoelectron spectrum; see text and Fig. 2.

311G(2df ,2p) first AIE of 9.71 eV has to be in-

c reased by 0.13 eV to g ive the exper imenta l value o f

9.84 eV, and the C C S D ( T ) / 6 - 3 1 1 G ( 2 d f , 2 p ) second

A l E of 10.46 eV has to be increased by 0.16 eV to

g ive the der ived value o f 10.62 eV.

I f the X - a PHi- separat ion f rom M C S C F a n d / o r

M R C I type calcula t ions is used (e.g., [51] der ive an

X - a value o f 1.92 eV f rom M R C I calculat ions)

rather than the C C S D ( T ) / 6 - 3 1 l G(2df ,2p) value o f

1.09 eV, then the third PH 2 band in the s imulat ion in

Fig. 1 is p laced at 0.83 eV higher ionizat ion energy.

This has no effect , however , on the re la t ive intensi ty

o f the first six vibrat ional componen t s in the s imu-

lated second band of PH 2. It therefore does not

affect the use o f the observed second VIE of PH 2

with the computed enve lope to establish the second

A l E of PH 2.

4.2. PF 2 and PF2 +

4.2.1. Computed geometries and vibrational frequen-

cies The m i n i m u m energy geomet r ies and harmonic

vibrat ional f requencies computed in this work are shown in Tables 7 - 9 . For the X 2 B t state o f PF 2, the

exper imenta l geomet ry and vibrat ional f requencies are avai lable for compar i son (Table 7). The M P 2 / 6 -

311G(2df) and C C S D ( T ) / 6 - 3 1 1 G ( 2 d f ) computed

m i n i m u m energy bond lengths are nearly identical,

suggest ing that h igher -order correlat ion has little ef-

fect on the value o f the computed bond length.

Howeve r , the MP2 computed bond angles are sl ightly

too large compared with the exper imenta l value o f 98.48 °, whi le the C C S D ( T ) bond angles agree wel l

with the exper imenta l value. For the bond length, a

very large basis set seems to be required for an

accurate value to be obtained. The C A S S C F /

M R S D C I calculat ions o f Lat i fzadeh and Balasub-

Table 9 Optimized geometries and harmonic vibrational frequencies of PF 2 X2BI and low-lying ionic states of PF~- at the MP2/6-31G * level

States PF FPF v I v 2 v 3 (~.) (o) (cm - ') (cm- ' ) (cm- I)

PF 2 X2Bt 1.6096 99.2 8 8 4 . 2 344.5 884.3 PF~ XlAt 1.5342 102.5 1022.6 3 8 6 . 7 1072.9 a3Bt 1.5474 a 118 .7 928.6 3 0 3 . 8 1093.6 AJB~ 1.5541 b 118 .5 929.9 299.8 1311.5 b3A2 1.7097 66.9 863.4 5 0 0 . 8 2970.3 c3B2 1.7175 83.3 8 0 5 . 8 3 2 7 . 7 1197.3

aThe casscf/MRSDCI/RECP-TZ2P optimized geometry from [46]: PF = 1.591 A; FPF = 117.0°; the GVB/DZVP optimized geometry from [5]; PF = 1.522 A; FPF = 116.5% bThe casscf/MRSoDCI/RECP-TZ2P optimized geometry from [46]: PF = 1.600 A; FPF = 116.3°; the GVB/DZVP optimized geometry from [5]: PF = 1.547 A; FPF = 119.7 °.


ramanian [46], which are the highest level of calculations performed previously, give a geometry which seems to be inferior to the CCSD(T) geometries obtained here, when compared with the experimental geometry; this is so even for the all electron calculations performed by Latifzadeh and Balasubramanian [46] with a QZV3P basis. The poor agreement be-

tween the RECP-TZ2P computed geometry of [46] and the experimental geometry also suggests that a very good basis set is required for an accurate computed geometry of this system. Nevertheless, the computed vibrational frequencies shown in Table 7 agree reasonably well with the available experimental values.

I0© (a)

I

0.0

i I

J

9.0

130

110

1 0

(b)

i

9 0 8 8 8.6 -101 q i i

0 0 9 8 9 6 9.4 9 2

IonizatJon Ener0y/B v

Fig. 2. (a) The first band of PF 2 recorded with HeI radiation. (b) The simulated first photoelectron band of PF 2 using CCSD(T)/6-31 lG(2df) minimum energy geometries for PF~-(X JA I ) and PF2(X 2 B t ). A FWHM of 45 meV and an AlE of 8.84 eV (computed G2 value) were used in this simulation (see text). The CCSD(T)/6-311G(2df) computed AIE is 8.56 eV. The computed AIE has therefore been increased by 0.28 eV to correspond to the experimental value.


No experimental geometries or vibrational frequencies are available for any of the states of PF~-, except that the average spacing in the first photoelectron band has been measured as (980 + 30) c m - l (Fig. 2a). For the X~A~, state of PF +, the M P 2 / 6 - 311G(2df) and CCSD(T)/6-311G(2df) results computed in this work (Table 8) agree well with those of the recent CCSD(T) /cc -pVQZ study [16]. The favoured computed minimum energy geometry for this state of PF2 +, based on the results shown in Table 8, would be R(P-F) = (1.500 _+ 0.001)A and the FPF angle = (103.0 _+ 0.5) °. Optimized geometries and harmonic vibrational frequencies of some low-lying excited states of PF f at the M P 2 / 6 - 3 1 G * level are shown in Table 9. Attempts to obtain the optimized geometries for the B~A~ and CIB2 states were made, but these were unsuccessful because of severe SCF convergence problems. Bands associated with these two singlet states would be expected to be one-third the intensity of the corresponding triplet state bands.

Table 11 Computed AIEs and VIEs (in eV) at the MP2/6-31G * level and the computed VIEs at the CCSD(T)/6-311G(2d) level to the various ionic states of PFf

Ionic MP2/6-31G * CCSD(T)/ casscf/ states 6-311G(2d) MRSDCI a

AIE VIE VIE AIE

X IA I 8.47 8.72 8.87 8.803 a3B~ 12.09 b 12.55 12.76 12.70 AtB~ 13.31 c 13.69 c 13.24 14.47 b3A2 14.02 14.39 15.52 c3B2 15.04 15.60 15.79

aCASSCF/MRSDCI/RECP calculations reference [46]. bThe G! and G2 AIEs have also been computed for this state and are 12.79 and 12.76 eV, respectively. CThese are from the unprojected UMP2 energies. The PUMP2 values are 14.04 and 13.79 eV for the AIE and VIE, respectively. Note that the AIE is higher than the VIE at the PUMP2 level. This is because of the large (($2) ca 1.08) and different spin contamination of the 1BI UHF wavefunction at two different geometries.

4.2.2. Computed adiabatic and vertical ionization

energies of PF z The computed ionization energies of PF 2 are

shown in Tables 10 and 11 for ionization to the ground and low-lying excited cationic states, respectively, together with available computed a n d / o r experimental values. From the computed CCSD(T)

Table 10 The computed AlEs and VIEs (in eV) for PF 2 X2BI~PF + XIAI +e- at different levels of theory

Method AIE VIE

casscf/6-3 IG * 7.84 MP2/6-31G * 8.47 8.72 MP2/6-31 IG(2df) 8.56 8.83 CCSD(T)/6- 311 G* 8.60 8.89 CCSD(T)/6-311G(2d) 8.74 8.87 CCSD(T)/6-3 ! IG(2df) 8.56 G1 8.88 G2 8.84 CASSCF/SOCI a QCISD(T)/6-311 + G(3df) b 8.77 REMPI(Rydberg series) b 8.73 photoionization mass c 8.847 __+ 0,010 photoelectron d 8.84 _+ 0.01 9.09 + 0.01

aRef. [46]. bRef. [4]. CRef. [15]. dRef. [1] and this work.

AlEs to the X IAI state (Table 10), obtained with the different basis sets used, it seems that the basis size effect has not been exhausted, as the computed AIEs have not converged. From all the computed values shown in Table 10, it is not conclusive as to whether or not the lower AlE suggested in the R E M P I / a b initio study [4] (8.73 eV) is more reliable than the photoelectron value of 8.84 + 0.01 eV (this work). Never the less , the M P 2 / 6 - 3 1 1 G (2df) and CCSD(T)/6-311G(2df) AIEs are almost identical, suggesting that higher order correlation is small in the computed AIE for this ionization, although larger basis sets are required than used in this work to remove the basis size effect.

For ionization to the a3Bl state, the MP2 and CCSD(T) AIEs obtained in this work agree reasonably well with the C A S S C F / M R S D C I AlE [46] (Table !1). However, similar to the PH 2 case, the MP2 and CCSD(T) AlEs to the A~BI state are significantly smaller than the C A S S C F / M R S D C I value. Spin contamination in the UHF wavefunction, used for the MP2 and CCSD(T) calculations, is high for this singlet state, as is the case for the PH ~ A ~ B j state (see footnote c of Table 11). As discussed previously for PHi- AIBi, the CCSD(T) values are expected to be more reliable than the MP2 values.

1 7 0 F.-T. Chau et al. / Chemical Physics 224 (1997) 157-173

4.2.3. Observed and simulated photoelectron spectra The observed and simulated first photoelectron

bands of PF 2 are shown in Figs. 2 and 3, and the full simulated spectrum is shown in Fig. 4. The simulated envelope was obtained using CCSD(T) /6 - 311G(2df) geometries, vibrational frequencies and relative energies. Apart from the first band, there is only one feature in the experimental spectrum, which is broad, relatively weak and shows no structure, which is observed at 14.90 eV (band maximum) and which could be associated with PF 2. Based on the computed ionization energies obtained in this work (Table 11) and the simulated photoelectron spectrum (Fig. 4), this structure may be due to the ionization PF~ b3A2 ~ PF 2 XZBI. All other bands of PF 2 are masked by more intense bands arising from other molecules, notably PF 3 and P2.

For the first band, the agreement between the simulated and observed spectra is good (Fig. 2). The simulation (Fig. 2b) suggests that the observed structure is due to a progression in the symmetric stretching mode, v 1, in the cation with only very minor contributions from the symmetric bending mode, ~'2. With a FWHM of 45 meV used in the simulation, it can be seen that the simulated vibrational components of the main v I progression are slightly asym- metric due to the contributions from the v 2 bending mode (components with tJ '> 2 in v 2 are computed to be too weak to be observed). However, due to the poor resolution in the experimental spectrum, it was not possible to resolve the vibrational structure due to the deformation mode, with spacings computed to be = 410 cm -1 (Table 8).

It should be noted that the vibrational spacings in the simulated spectrum are slightly larger than those in the experimental spectrum. This is because of the slightly larger computed v'~ harmonic vibrational frequency (1028 c m - l ; see Table 8) used in the simulation compared to the experimental average separation of (980 5- 30) cm -1, and it could be that the harmonic oscillator model used is inadequate for this cationic state. Also, from Fig. 2, it can be seen that the simulated relative intensities of the vibrational components of the main ~,1 progression ap- pear to differ slightly from the observed relative intensities. It may be possible to improve the agreement between the simulated and experimental band envelope by variation of the geometry change be-

(v~" v:",O - 0,00) ' I I ' l ' l l l l ' l l ' 11 ' i~ l l l ' lT

o

e~

PF2 ÷ X1A1 ~ PF 2 X2B1

1 . . . . I , l , [ , I

1 0 0

l o n i z d o n Energy/eV

1,[, 91o

Fig. 3. The simulated first band of P~ as used in Fig. 2b. The vibrational level labelling shown corresponds to PFf 0/, v', 0) PF 2 (0, 0, 0) transitions, where the numbers shown above the vibrational bands are (v', t,') values.

tween the cationic and neutral state [25]. However, this has not been performed because it was felt that the slight rising background observed from about 9.0 eV and the somewhat limited signal-to-noise in the experimental spectra did not warrant such further calculations. Nevertheless, from comparison of the simulated and observed spectra as shown in Fig. 2, it is clear that the observed first vibrational component in the first band of PF 2 is the adiabatic component; that is, the measured position of the first component, (8.84 5-0.01) eV, is the first adiabatic ionization energy. This therefore implies that the value derived in the REMPI study [4], 8.73 eV, is too low and that the geometry change upon ionization between the neutral and cationic states is very close to that

F.- T. Chau et al. / Chemical Physics 224 (1997) 157-173 171

130

110 C=B2

J. 10

-10 I 16.5 15.5

I~F= + + e" < - - [~F=

baA= A~B * ~ '

L _] i I !

14.5 13.5 12.5

Ic~mli=n F-ner~/eV

I 11.5

XtAI < - X2B1

i 10.5 9.5 8.5

Fig. 4. Simulated band envelopes for the first five bands of PF 2 corresponding to the ionizations PF~-(X]AI, a3Bl, A]BI, b3A2, c3B2 ) ~ PF2(X2BI), computed using the CCSD(T)/6-311G(2df) computed equilibrium geometries, relative energies and vibrational frequencies for the first band and MP2/6-31G * values for the next four bands. A FWHM of 45 meV was used for all bands and the AlEs used were 8.84, 12.09, 13.31, 14.02 and 15.04 eV. All bands have been arbitrarily given the same height.

predicted by the MP2 and CCSD(T) calculations with the 6-311G(2df) basis set.

5. Concluding remarks

Observed and simulated photoelectron spectra of PH 2 and PF 2 have been reported. For PHi-, the XIA~-a3B~ energy gap was deduced on the basis of the observed and simulated spectra as (0.78 + 0.04) eV in agreement with the result of CCSD(T) /6 - 311G(2df,2p) calculations performed in this work and previous C A S S C F / S O C I [9] calculations, the highest-level calculations that have been performed on PHi-. This result means that the X - a separation deduced from photoionization mass spectrometric studies (0.71 eV; [3,12]) is slightly too low,

The next highest cationic state of PHi-, the A~B1 state, is computed by MP2 and CCSD(T) calculations to be --- 1.1 eV higher than the IA] state. This is, however, contrary to the results of previous CASSCF a n d / o r CI type calculations [5-11] and observations from photoionization mass spectrometry [3] that place the ~B~ state at ~ 2.0 eV above the

IA 1 state. Further theoretical and experimental inves- tigations are required to confirm the position of the A~B~ state in PHi-, although the lower separations obtained from MP2 and CCSD(T) calculations may arise from the presence of spin contamination and the inadequacy of a single reference configuration.

For PF 2, accurate computation of the position of the first AIE seems to be very demanding, particu- larly in terms of the basis set used. Nevertheless, simulation of the first photoelectron band clearly indicates that the observed first vibrational component in the first photoelectron band of PF 2 is the adiabatic component. The value derived for the first AIE, (8.84 ± 0.01) eV, agrees very well with the value derived from a previous photoionization mass spectrometric measurement [ 15]. The reason why this value differs from a value derived from REMPI measurements ([4], 8.73 eV) is that positions of Rydberg states with low principal quantum numbers have been used in [4] to derive an ionization energy. These may he too low in energy to have acquired full Rydberg character, making the fitting procedure used subject to some uncertainty.

The MP2 and CCSD(T) minimum-energy geome-


t r ies and h a r m o n i c v ib ra t iona l f r equenc ie s ob t a ined

in this work h a v e b e e n c o m p a r e d wi th p r ev ious

theore t ica l a n d / o r ava i l ab le expe r i m en t a l values . The

resul t s f r o m these pe r tu rba t ive m e t h o d s have b e e n

f o u n d to be re l iab le and super io r to those f rom

p rev ious CI - type ca lcu la t ions in some cases , whe re

e x p e r i m e n t a l va lues are ava i l ab le for compar i son . It

has been d e m o n s t r a t e d tha t c o m b i n i n g C C S D ( T ) (or

M P 2 ) ca lcu la t ions wi th F r a n c k - C o n d o n ca l cu la t ions

and spectra l s imu la t ion can y ie ld useful i n f o r m a t i o n

wh ich , w h e n c o m p a r e d wi th a v ib ra t iona l ly r e so lved

e x p e r i m e n t a l p h o t o e l e c t r o n band , can a l low the adia-

ba t ic c o m p o n e n t to be ident i f ied.

Acknowledgements

The au thors gra te fu l ly a c k n o w l e d g e suppor t f rom

the R e s e a r c h G r a n t Counc i l ( R G C ) of H o n g K o n g

and the E P S R C (U.K.) .

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HeI photoelectron spectra of PH2 and PF2: comparison between simulation and experiment