Ab initio calculations and spectral simulation of the

P2Hð ~X2A0ÞKP2H

Kð ~X1A0Þ photodetachment process

Wu Jun, Zhang Xianyi *, Chen Feng, Cui Zhifeng

Department of Physics, Anhui Normal University, Beijing east Road, Wuhu 241000, People’s Republic of China

Received 30 April 2006; received in revised form 31 May 2006; accepted 31 May 2006

Available online 8 June 2006

Abstract

Geometry optimization and harmonic vibrational frequency calculations were performed on the ~X2A0 state of P2H and ~X

1A0 state of P2H

K at

the MP2, B3LYP, QCISD and CCSD levels. Franck–Condon factors were computed to simulate the recently observed, photoelectron spectrum of

the P2HK anions [K. M. Ervin and W. C. Lineberger, J. Chem. Phys. 122 (2005) 194303]. The theoretical spectra obtained by employing density-

functional theory (DFT) with 6-311CG(2p,d) values are in excellent agreement with the observed one. In addition, Franck–Condon analyses and

spectral simulations confirm the assignment of the observed spectrum to the ~X2A0K ~X

1A0 photodetachment process of P2H

K. Using iterative

Franck–Condon analysis procedure in the spectral simulations, it is concluded that the reliable variation of geometry is 0.0026 nm for bond length

R(PP), 0.0068 nm for bond length R(PH), and 8.38 for bond angle :(PPH) from ~X2A0 state of P2H to ~X

1A0 state of P2H

K.

q 2006 Elsevier B.V. All rights reserved.

Keywords: Franck–Condon analysis; Duschinsky effect; Photoelectron spectra; Spectral simulation

1. Introduction

Phosphorus hydride compounds and radicals are of interest

in planetary atmospheres and other astrophysical environments

[1,2]. They are also important because of the role of organo-

phosphorus compounds in catalysis of radical recombination

reactions involved in combustion [3,4] and because of the use

of phosphine in chemical-vapor deposition phosphide semi-

conductors [5–7]. Whereas neutral phosphanes have been

studied extensively [8], their radical and anionic fragments

are less well characterized. Recently, Ervin and Lineberger

reported a theoretical and experimental study of photoelectron

spectroscopy of phosphorus hydride anion [9]. The photo-

electron spectrum of P2HK was obtained through measuring

the kinetic energy of photodetached electrons. With the aid of

B3LYP/aug-cc-pVTZ calculations of molecular vibrational

constants and CCSD(T) calculations of electron affinity, the

observed spectrum was assigned to the P2Hð ~X2A0ÞKP2H

Kð ~X1

A0Þ photodetachment process. This is the first report of an

experimental observation of this radical. Also, the electron

affinity from the optimized fits, EA0(P2H)Z1.514G0.010 eV,

0166-1280/$ - see front matter q 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.theochem.2006.05.055

* Corresponding author. Tel./fax: C86 553 3869748.

E-mail address: xyzhang@mail.ahnu.edu.cn (Z. Xianyi).

was determined, and the vibrational spectrum of P2Hð ~X2A0Þ

was observed in the region within 1 eV of its ground state

vibrational levels for the first time.

In this paper, theoretical study of photoelectron spectrum of

P2HK were performed by combining ab initio calculations

of correlative electronic states with spectral simulation of

vibrational structure based on the computed Franck–Condon

factors (FCFs). Geometry optimization and harmonic

vibrational frequency calculations were performed on the ~X2

A0 state of the neutral molecule P2H, and the ~X1A0 state of the

negative ion P2HK, iterative Franck–Condon (IFCA) analysis

and spectral simulation were carried out on the first photo-

electron band of P2HK (i.e. ~X

2A0K ~X

1A0 transition). It will be

shown that, the assignment of the photoelectron spectra

observed by Ervin and Lineberger [9] to the transition,~X

2A0K ~X

1A0, of P2H

K can be firmly confirmed. In addition,

the rather accurate equilibrium geometry of the ~X1A0 state of

P2HK can be derived.

2. Theoretical method

Different methods [10–24] for calculating FCFs have been

presented in the literature. We choose the multidimensional

generating function method described by Sharp and Rosen-

stock [11] for Franck–Condon integrals. Briefly, the method is

based on the Born-Oppenheimer approximation, within the

harmonic oscillator model and includes the Duschinsky effect.

Journal of Molecular Structure: THEOCHEM 767 (2006) 149–153

www.elsevier.com/locate/theochem

W. Jun et al. / Journal of Molecular Structure: THEOCHEM 767 (2006) 149–153150

First, a transformation of the coordinates system of the two

electronic states is needed before one can compute vibrational

overlap integrals. Because of changes in bond lengths, angles,

force constants, or symmetry that accompany transitions, the

normal coordinates of the two electronic states are not the

same. The normal modes of the initial sate must be expressed

as a linear combination of the normal modes of the final sate (or

visa versa). This Duschinsky effect [11,25], or mode mixing, is

usually expressed as

Q0 Z JQCK; (1)

where the Q and Q 0 are the normal coordinates of the two

electronic states, respectively, and the matrix J and column

vector K define the linear transformation. To obtain the matrix

J and vector K in Eq. (1), in terms of displacements in

Cartesian coordinates [26–28], the general linear transfor-

mation of an arbitrary distortion X can be written as

X0 ZZXCR; (2)

where X and X 0 are distortions expressed as Cartesian displace-

ments from the equilibrium geometries of the neutral and

anion, respectively. RZZReqKR0eq is the change in equili-

brium geometry between the anion and the neutral in Cartesian

coordinates centered on the molecular center of mass, and Z is

a rotation matrix [29,30], which is a unit matrix for most

molecules of C2v or higher symmetry. In a conventional normal

mode analysis, the Q is related to Q 0 by

Q0 Z ðL0K1B0Þ½ZMK1ðLK1B0Þ†QCR�; (3)

where the superscript ‘†’ indicates the transpose of the matrix.

Eq. (3), substituted back into Eq. (1) gives expressions for Jand K:

JZ ðL0K1B0ÞZMK1ðLK1BÞ† and KZ ðL0K1B0ÞR: (4)

Having carried out the vibrational analyses for both the

initial and final electronic states to obtain B, L, B 0 and L 0, one

can use Eq. (4) for a description of the Duschinsky effect that is

valid even for large changes in geometry or force constants.

The Cartesian atom displacement matrix (ADM) is defined

as [31,32]

ADM ZMK1ðLK1BÞ†; (5)

which relates Q to X. M is a diagonal matrix with the atomic

masses on the diagonal.

Table 1

Summary of some computed and experimental geometrical parameters and vibratio

calculation

Method R(PP) (nm) R(PH) (nm) :(PPH

MP2/6-311CG(2d,p) 0.20488 0.14189 96.137

B3LYP/6-311G(2d,p) 0.20088 0.14324 98.089

B3LYP/6-311G(3df) 0.19982 0.14338 98.412

B3LYP/6-311CG(2d,p) 0.20085 0.14325 97.958

CCSD/6-311CG(2d,p) 0.20311 0.14223 97.183

QCISD/6-311CG(2d,p) 0.20316 0.14225 97.510

From Ref. [9] 0.2007 0.1435 98

For a molecule of N atoms, if we define a 3N!3NK6 matrix, g03, containing the normal mode output from

Gaussian 03, and a 3NK6!3NK6 diagonal matrix, V,

containing the reduced masses for each mode on the diagonal,

then

ADM Z ðg03ÞVK1=2; (6)

which removes the reduced-mass weighting. Finally, using

Eqs. (4)–(6), J and K in terms of the Gaussian 03 output for

the two electronic states are given by

JZ ½Mðg030ÞV0K1=2�†Zðg03ÞVK1=2 and

KZ ½Mðg030ÞV0K1=2�†R(7)

where, as usual, primed and unprimed quantities refer to the

initial state and the final state in the transition, respectively.

Having then computed J and K, the FCFs are easily produced

by using the more general algebraic expressions given in Ref.

[31–33].

The advantage of this approach is that the results are still

applicable to large geometric changes in an electronic tran-

sition, and well suited to coding as a computer program.

3. Computational details

Geometry optimizations and harmonic vibrational

frequency calculations were carried out on the ~X2A0 state of

the neutral molecule P2H, and the ~X1A0 state of the negative

ion P2HK at the MP2, B3LYP, CCSD and QCISD levels with

the 6-311CG(2d,p), 6-311G(2d,p) and 6-311G(3df) basis sets.

The MP2, B3LYP, CCSD and QCISD calculations were

performed employing the GAUSSIAN 03 suite of programs [34].

FCFs calculations on the ~X2A0K ~X

1A0 photodetachment

were carried out, employing the ab initio force constants and

geometries initially (see later text) for the two electronic states

involved in the transition. The harmonic oscillator model was

employed and Duschinsky rotation was included in the FCFs

calculations as described in Section 2. The computed FCFs

were then used to simulate the vibrational structure of the ~X2

A0K ~X1A0 photodetachment spectrum of P2H

K, employing a

Gaussian line-shape and a full-width-at-half- maximum

(FWHM) of 200 cmK1 for the ~X2A0K ~X

1A0 detachment.

In order to obtain a reasonable match between the simulated

and observed spectra, the iterative FC analysis procedure [31]

nal frequencies (cmK1) of the ~X2A0state of P2H obtained at different levels of

) (8) u1(P–H) u2(bend) u3(P–P)

7 2396.9076 689.2049 632.3058

6 2259.9395 669.4214 608.4181

7 2247.1663 672.5565 615.2673

0 2257.7477 671.5956 609.9948

6 2350.4443 690.8280 609.6002

2 2346.5508 684.7185 609.9722

2160G30 630G20

W. Jun et al. / Journal of Molecular Structure: THEOCHEM 767 (2006) 149–153 151

was also carried out, where the ground state geometric

parameters of the P2H molecules were fixed to the

recommended values in Ref. [9] for the ~X2A0K ~X

1A0 photo-

detachment processes, while the ground state geometrical

parameters of the anion P2HK were varied systematically

until a best match between the simulated and observed

spectra was obtained.

4. Results and discussions

4.1. Geometry optimization and frequency calculations

The optimized geometric parameters and computed

vibrational frequencies for the ~X2A0 state of P2H and ~X

2A0

state of P2HK as obtained in this work are listed in Tables 1

and 2, respectively. The theoretical and/or experimental values

available in the literatures are also included for comparison.

The bending vibration is denoted as u2, according to the

convention for triatomic molecules. The other vibrational

modes, which designates the P–H stretch as u1 and the P–P

stretch as u3, are listed in decreasing order of size.

From Table 1, for the ~X2A0 state of P2H, the computed bond

lengths and angles obtained at different levels of theory are

highly consistent. The estimated values based on DFT at the

B3LYP/6-311CG(2p,d) level, are 0.20085 nm, 0.14325 nm

and 97.9588. The differences between calculated and rec-

ommended values given in Ref. [9] are only 0.00015,

0.00025 nm and 0.0428 for R(PP), R(PH) and :(PPH),

respectively. Both the optimized geometric parameters and

the vibrational frequencies calculated at B3LYP/6-311CG(2p,d) level gave the best agreement with the available

values, and were therefore utilized in subsequent Franck–

Condon analyses and spectral simulations.

From Table 2, for the ~X1A0state of P2H

K, the computed

bond lengths and angles at the different levels of theory are also

very consistent. Because no experimental geometric par-

ameters were obtained for comparison, it is expected that the

geometrical parameters and vibrational frequencies obtained at

the higher levels of calculation should be more reliable.

However, the optimized geometric parameters calculated at

the B3LYP/6-311CG(2d,p) level gave the best agreement with

the corresponding values given in Ref. [9], and were therefore

utilized in subsequent calculations.

Table 2

Summary of some computed and experimental geometrical parameters and vibration

calculation

Method R(PP) (nm) R(PH) (nm) :(PPH

MP2/6-311CG(2d,p) 0.20400 0.14436 106.07

B3LYP/6-311G(2d,p) 0.20381 0.14642 105.73

B3LYP/6-311G(3df) 0.20233 0.14684 105.93

B3LYP/6-311CG(2d,p) 0.20326 0.14633 106.01

CCSD/6-311CG(2d,p) 0.20449 0.14458 105.63

QCISD/6-311CG(2d,p) 0.20474 0.14466 105.66

From Ref. [9] 0.2030 0.1503 106

IFCA (this work) 0.1503G0.001 106.3G

From Tables 1 and 2, it can be seen that the computed bond

lengths R(PP) converge toward bigger values, bond lengths

R(PH) and bond angles :(PPH) converge toward smaller ones

when the level of calculation is improved from B3LYP to

QCISD or CCSD. This shows the effects of higher-order

electron correlation on the computed bond lengths and bond

angles of the ~X2A0 state of P2H and ~X

2A0 state of P2H

K. All

the calculated geometries of P2H and P2HK remain to be

tested, since there is no complete experimental information

available on the structures of this system.

4.2. Franck–Condon analyses and spectral simulations

In the present study, geometrical parameters obtained at

near state-of-the-art ab initio levels have been compared to the

values obtained by reasonable empirical adjustment of the

geometrical parameters of the anionic state in the IFCA

procedure, which lead to a good fit with an experimental

envelope.

Simulated photoelectron spectrum of the P2Hð ~X2A0ÞKP2

HKð ~X1A0Þ photodetachment using data obtained from the

B3LYP/6-311G(2p,d) is shown in Fig. 1(b) and the experi-

mental observed photoelectron spectrum is shown in Fig. 1(a).

Vibrational assignments for the symmetric u1 and bending u2

modes of the neutral molecule P2H are also provided, with the

labels (0,n,0–0,0,0), (1,n,0–0,0,0) corresponding to the

(u1,u2,0–0,0,0) transition. From the harmonic calculation, it

was found that the FCFs for transitions involving the asym-

metric stretching mode u3 are negligibly small and therefore

the u3 mode are not included in the assignment. At first glance,

the differences between the two spectra are significant,

although the major feature due to the two progressions of the

bending and symmetric stretching modes can be identified in

both. Based on the above comparisons, it could be concluded

that the computed vibrational frequencies obtained from the

present investigation largely support the vibrational assign-

ments given in Ref. [9]. In addition, since the vibrational

intensity distributions are very sensitive to the geometric

parameters, the variation of the geometries between the two

electronic states based on ab initio calculation is difference

from the true one. So, further slight adjustments in the

geometrical parameters of the anion state using the IFCA

method may give a better match between the simulated and

al frequencies (cmK1) of the ~X1A0state of P2H

K obtained at different levels of

)(o) u1(P–H) u2(bend) u3(P–P)

86 2153.2961 835.9190 597.0181

89 1994.4548 828.7623 587.6546

35 1969.1974 828.9003 601.5079

53 1986.8229 820.5299 591.9610

41 2126.1493 842.7155 592.2933

92 2118.2326 840.5251 586.0602

0.2

Fig. 1. (a) The experimental spectrum of the P2Hð ~X2A0ÞKP2H

Kð ~X1A0Þ

photodetachment process (from Ref. [9]). (b) The simulated spectrum using

the B3LYP/6-311G(2d,p) geometries for the two combining states. (c) The

simulated spectrum invoking the recommended geometry given in Ref. [9] for

the ~X2A0 state of P2H and the IFCA one for the ~X

1A0 state of P2H

K with

vibrational assignments provided for the ~X2A0K ~X

1A0 detachment process. The

FWHM used for the components of the simulated spectrum is 200 cmK1.

W. Jun et al. / Journal of Molecular Structure: THEOCHEM 767 (2006) 149–153152

observed spectra than that obtained with the ab initio

structures.

Based on the geometric parameters of the ~X2A0 state of

P2H in Ref. [9], the IFCA method was used to refine the

geometry of the ~X1A0 state of P2H. The simulated spectrum

that matches best is shown in Fig. 1(c). It was found that the

computed photoelectron spectrum of P2H for ~X2A0K ~X

1A0

detachment is almost identical to the experiment spectrum.

This suggests that the computed geometry changes upon

detachment by IFCA method are highly accurate and the

harmonic model seems to be adequate. The best IFCA

variation of geometry is 0.0026 nm for bond lengths R(PP),

0.0068 nm for bond lengths R(PH), and 8.38 for bond angles

:(PPH) from ~X2A0 state of P2H to ~X

1A0 state of P2H

K.

This result is very consistent with the result obtained by

Ervin and Lineberger.

The used FCFs were only computed for a vibrationally cold

molecule [30–32]. The peak ‘a’ at 1.42 eV in the Fig. 1(a) is

hot band, which is not analyzed in our spectral simulations.

From the ab initio results of vibrational frequency of the ~X1A0

state of P2HK, this peak can be assigned as 20

1.

It should be noted that since no P–P stretching structure is

observed in the experiment, the computed R(PP) bond length

change from the B3LYP/6-311CG(2d,p) calculations was

assumed in the IFCA procedure. In addition, because R(PH)

value change between the two states is so small, only

0.0031 nm at the B3LYP/6-311CG(2p,d) level(IFCA values

is 0.0068 nm), so the structure in the P–H stretching pro-

gression are relatively very weak.

5. Conclusions

In the present study, attempts have been made to

simulate the observed P2Hð ~X2A0ÞKP2H

Kð ~X1A0Þ detach-

ment photoelectron spectrum, using harmonic model and

including Duschinsky effects. By combining ab initio

calculations with Franck–Condon analyses, the assignment

of spectrum observed by Ervin and Lineberger is firmly

established to the ~X2A0K ~X

1A0 photodetachment process of

the P2HK radical.

Although no experimental geometrical parameters are

available for the two states of interest prior to the present

study, the B3LYP/6-311CG(2p,d) geometry reported here for

the ground state of P2H should be reasonable reliable, as the

computed geometry parameter for this state obtained at

different levels of calculation are highly consistent. In this

connection, using the IFCA procedure, the reliable geometry

changes between the ~X2A0 state of P2H and ~X

1A0 state of

P2HK have been derived, and the equilibrium geometry

parameters, R(PH)Z0.1503G0.0010 nm, :(PPH)Z106.3G0.28,of the ~X

1A0 state of P2H

K are derived.

Acknowledgements

This work was supported by the Key Subject Foundation for

Atomic and Molecular Physics of Anhui Province, the Natural

Science Foundation of Anhui educational committee (Grant

No. 2005kj230) and Foundation of College Teacher of Anhui

Province (Grant No. 2004jq117).

References

[1] L. Margules, E. Herbst, V. Ahrens, F. Lewen, G. Winnewisser,

S.P. Muller, J. Mol. Spectrosc. 211 (2002) 211.

W. Jun et al. / Journal of Molecular Structure: THEOCHEM 767 (2006) 149–153 153

[2] R.J. Morton, R.I. Kaiser, Planet. Space Sci. 51 (2003) 365.

[3] O. Korobeinichev, T. Bolshova, V. Shvartsberg, A. Chernov, Combust.

Flame 125 (2001) 744.

[4] N.L. Haworth, G.B. Bacskay, J. Chem. Phys. 117 (2002) 11175.

[5] Y. Hirota, T. Kobayashi, J. Appl. Phys. 53 (1982) 5037.

[6] A. Robertson, A.S. Jordan, J. Vac. Sci. Technol. B 11 (1993) 1041.

[7] T. Sugino, M. Maeda, K. Kawarai, J. Shirafuji, J. Cryst. Growth 166

(1996) 628.

[8] M. Baudler, K. Glinka, Chem. Rev. 94 (1994) 1273.

[9] K.M. Ervin, W.C. Lineberger, J. Chem. Phys. 122 (2005) 194303.

[10] J.B. Coon, R.E. Dewames, C.M. Loyd, J. Mol. Spectrosc. 8 (1962) 285.

[11] T.E. Sharp, H.M. Rosenstock, J. Chem. Phys. 41 (1964) 3453.

[12] H. Kupka, P.H. Cribb, J. Chem. Phys. 85 (1986) 1303.

[13] E.V. Doktorov, I.A. Malkin, V.I. Manko, J. Mol. Spectrosc. 56 (1975) 1.

[14] E.V. Doktorov, I.A. Malkin, V.I. Manko, J. Mol. Spectrosc. 64 (1977) 302.

[15] T.R. Faulkner, F.S. Richardson, J. Chem. Phys. 70 (1979) 1201.

[16] K.M. Chen, C.C. Pei, Chem. Phys. Lett. 165 (1990) 532.

[17] N.J.D. Lucas, J. Phys. B: Atom. Mol. Phys. 6 (1973) 155.

[18] P. Malmqvist, N. Forsberg, Chem. Phys. 228 (1998) 227.

[19] T. Muller, P. Dupre, P.H. Vaccaro, F. Perez-Bernal, M. Ibrahim,

F. Iachello, Chem. Phys. Lett. 292 (1998) 243.

[20] R. Islampour, M. Dehestani, S.H. Lin, J. Mol. Spectrosc. 194 (1999) 179.

[21] G. Gangopadhyay, J. Phys. A: Math. Gen. 31 (1998) L771.

[22] J. Liang, X.L. Kong, X.Y. Zhang, H.Y. Li, Chem. Phys. 294 (2003) 85.

[23] J. Liang, H.Y. Li, Chem. Phys. 314 (2005) 317.

[24] F.T. Chau, J.M. Dyke, E.P.F. Lee, D.C. Wang, J. Electron Spectrosc.

Relat. Phenom. 97 (1998) 33.

[25] F. Duschinsky, Acta Physicochim URSS 7 (1937) 551.

[26] A. Warshel, J. Chem. Phys. 62 (1975) 214.

[27] A. Warshel, M. Karplus, Chem. Phys. Lett. (1990) 165532.

[28] A. Warshel, M. Karplus, J. Am. Chem. Soc. 96 (1974) 5677.

[29] I. Ozkan, J. Mol. Spectrosc. 139 (1990) 147.

[30] Yaron, D. PhD Dissertation, Harvard University, 1991.

[31] D.W. Kohn, E.S.J. Robles, C.F. Logan, P. Chen, J. Phys. Chem. 97 (1993)

4936.

[32] P. Chen, Photoelectron spectroscopy of reactive intermediates, in:

C.Y. Ng, T. Baer, I. Powis (Eds.), Unimolecular and Bimolecular

Reaction Dynamics, Wiley, New York, 1994, p. 371.

[33] J. Liang, X.L. Kong, X.Y. Zhang, H.Y. Li, J. Mol. Struct. (Thochem) 672

(2004) 133.

[34] M.J. Frisch, G.W. Truchs, H.B. Schlegel, G.E. Scuseria, et al., GAUS-

SIAN03, Gaussian, Inc., Pittsburgh, PA, 2003.