Available online at www.sciencedirect.com

www.elsevier.com/locate/chemphys

Chemical Physics 346 (2008) 1–7

Electronic states of BP, BP+, BP�, B2P2, B2P�2 and B2Pþ2

Roberto Linguerri a,*, Najia Komiha b, Rainer Oswald c, Alexander Mitrushchenkov a,Pavel Rosmus a

a Laboratoire de Chimie Theorique, Universite de Marne la Vallee, F 77454 – Champs sur Marne, Franceb Laboratoire de Chimie Theorique, Universite Mohamed V – Agdal, Faculte des Sciences, Rabat, Morocco

c Institut fur Theoretische Chemie, Universitat Gottingen D-37077 Gottingen, Germany

Received 13 November 2007; accepted 7 January 2008Available online 12 January 2008

Dedicated to P. Botschwina

Abstract

Using augmented sextuple zeta basis sets and internally contracted multireference configuration interaction (MRCI) wavefunctions,potential energy, electric dipole and transition moments have been computed for the X3P, a1R+, b1P and A3R� states of BP, X2R+ andA2P states of BP� and X4R� and A4P states of BP+. From these data spectroscopic constants, radiative transition probabilities andphotoelectron spectra of BP� and BP have been evaluated. The non-vanishing spin–orbit coupling elements between the four low lyingtriplet and singlet states of the neutral BP have also been calculated from MRCI wavefunctions. The treatment of the correspondingperturbations in the manifold of dense rovibrational states in the three lowest states would require a precise knowledge of the electronicexcitation energies. Our best singlet–triplet separations (X–a) are calculated to be 2412 cm�1 (MRCI) and 2482 cm�1 (restricted coupledcluster with perturbative triples (RCCSD(T))) with an estimated error bound of about ±200 cm�1. All three states have long radiativelifetimes with cascading among the rovibrational levels of different states. The ionization energy IEe of BP is calculated to be 9.22 eV(MRCI) and 9.48 eV (RCCSD(T)), the electron affinity EAe 2.51 eV (MRCI) and 2.74 eV (RCCSD(T)). The photoelectron spectra ofBP and BP� have been obtained from the Franck–Condon factors of the MRCI potentials. For the UV spectroscopy the dipole allowedradiative transition probabilities are given for A3R�M X3P, b1P M a1R+ of BP, A2P M X2R+ of BP� and A4P M X4R� of BP+. Theionization energy IEe of B2P2 of 8.71 eV and the electron affinity EAe of 2.34 eV have been calculated by the RCCSD(T)/aVQZapproach. Also the harmonic vibrational wavenumbers for the electronic ground states of the ions B2Pþ2 and B2P�2 are given.� 2008 Elsevier B.V. All rights reserved.

Keywords: PB; P2B2; Spectroscopic data; Ionization potential; Electron affinity; Photoelectron spectra

1. Introduction

The compounds of the IIIA–VA groups of the periodicsystem such as BN or BP are of considerable interest asrefractory semiconductors and in solid state physics in gen-eral. For instance, Kumashiro [1] described Schottkydiodes consisting of n-BP and Sb or n-BP and Au showingexcellent characteristics. For the chemical vapor deposition(CVD) technique commonly used to obtain desired materi-

0301-0104/$ - see front matter � 2008 Elsevier B.V. All rights reserved.

doi:10.1016/j.chemphys.2008.01.012

* Corresponding author. Tel.: +33 1 60 95 73 01; fax: +33 1 60 95 73 20.E-mail address: linguerr@univ-mlv.fr (R. Linguerri).

als it is of importance to identify the major components ofthe chemical vapor and to characterize their electronicstructure. In this study we focus on the BP monomer,dimer and their anions and cations.

The only experimental investigation of gaseous boronmonophosphide, BP, has been the Knudsen mass spectro-metric determination of the dissociation energy and theupper limit of the ionization energy by Gingerich [2]. Sev-eral theoretical studies of BP have been reported. Boldyrevand Simons [3,4] performed Moller–Plesset and QCISD(T)calculations for the low lying electronic states. The proper-ties of the lowest electronic states of BP were studied byGan et al. [5]. In the systematic DFT study by Chan and

2 R. Linguerri et al. / Chemical Physics 346 (2008) 1–7

Handy [6] the BP monomer has been also included. Brunaand Grein calculated the electron-spin g-shifts, ground stateequilibrium geometry and vertical excitation energies ofBP� [7]. Burrill and Grein investigated the geometries andelectronic states of B2P2 [8]. Calculations of the stabilityand the structure of BP clusters have been published byQu et al. [9].

The refractory solids such as boron nitride or boronphosphide can only be vaporized at very high tempera-tures, but conveniently produced using pulsed lasers asdemonstrated by Lorenz et al. [10], who performed Fou-rier-transform absorption and laser-induced fluorescencestudy of the BN monomer in solid neon. Asmis et al. [11]applied anion photoelectron spectroscopy to BN� andobtained information about four electronic states of BNand its electron affinity. Both experimental works showedthat the X3P and a1R+ states are energetically almostdegenerate, in agreement with the theoretical calculationsof Martin et al. [12] and Peterson [13].

2. Computational approach

The potential energy surfaces, electric dipole momentand transition moment functions have been calculated bythe full-valence state-averaged complete active space (SA-CASSCF) [14,15] and subsequent internally contractedmulti-reference configuration interaction (MRCI) [16,17]techniques. Most of the computations were carried outusing the large augmented cc-pV6Z set of basis functions[18–20]. For diatomic molecules the computational timewith such a large basis set and 8 valence electrons in 8 activemolecular orbitals is short and the results close to the AObasis set limit. The core-valence correlation contributionshave not been considered. The calculation of the spin–orbitcoupling matrix elements was carried out with an approachbased on the Breit-Pauli operator and MRCI wavefunc-tions. For the geometry optimization and harmonicfrequency calculation of the dimers the partially spin-restricted open-shell coupled-cluster theory with perturba-tive triple excitation corrections method (RHF-RCCSD(T))[21,22] has been used, employing the Dunning’s augmentedcorrelation-consistent basis set aug-cc-pVQZ [23,24]. Allelectronic calculations have been performed with the MOL-PRO quantum chemistry package [25]. The spectroscopicconstants have been obtained from the solutions of theradial Schrodinger equation for nuclear motion using themethod of Cooley [26]. The vibrational wavefunctions havebeen used to calculate the Franck–Condon factors and thedipole matrix elements for radiative transition probabilities.

3. Results and discussion

In Fig. 1a–c the potentials of the low lying electronicstates of BP, BP+ and BP� calculated with the augmentedaVTZ basis set and a full valence SA-CASSCF approachprovide information about the relative positions of elec-tronic states and can help to choose suitable spectroscopic

techniques for the observation of the boron phosphidemonomer and its ions. For the neutral BP we have focusedon the four lowest X3P, a1R+, b1P and A3R� states forwhich the potentials have been obtained in separate fullvalence CASSCF/MRCI/aV6Z computations. The spec-troscopic constants are given in Table 1. The RCCSD(T)/cc-pVTZ equilibrium distances of the recent study byGan et al. [5] for the X3P, a1R+, and A3R� states are alllonger by about 0.01 A than our MRCI values. Also theQCSID(T) distances of Boldyrev and Simons [3,4] arelonger, and their MP2 frequencies are higher. For theX2R+ state of BP� we found Re that differs by 0.04 A fromthe distance of Bruna and Grein [7]. From the single statefull valence CASSCF/MRCI/aV6Z calculations the disso-ciation energy D0 of the X3P state estimated as the energydifference at 1.7477 A and 10 A amounts to 76 kcal/mol, inreasonable agreement with the experimental D0 value of82 ± 4 kcal/mol [2]. Gan et al. [5] obtained 71 kcal/mol,Boldyrev and Simons 70 kcal/mol [3,4]. In Fig. 2 the vibra-tional levels at their classical turning points are shown forthe four lowest potentials of BP. Considering that 10B israther abundant in nature (19.9 percent) and, for instance,the shift Dxe in the X3P state amounts to +34 cm�1 thedensity of the vibrational states is higher than in Fig. 2which shows only the levels for 11B31P.

The singlet–triplet separation between the ground andfirst excited states of the IIIA–VA group diatomics has beenthe subject of several theoretical investigations. Peterson[13] performed an accurate study for BN which is of partic-ular interest for the present work using similar electronicstructure calculations. He found that the cc-pV5Z basis setyields results close to the basis set limit and that there is alarge difference in the calculated excitation energies whenone-state or state-averaged orbitals are used in the MRCIcalculations. The MRCI + Q correction overestimates theBN splitting. The Te (at MRCI equilibrium distances) exci-tation energies for the lowest separately optimized states ofBP are given in Table 2. At the Hartree-Fock level the loweststate is the 1R+ state followed by the 3P. The CASSCF val-ues differ from MRCI by several hundred wave numbers.The singlet–triplet splitting calculated by MRCI andRCCSD(T) methods lie between 2400 and 2500 cm�1 withorbitals from four averaged states at 2727 cm�1 (MRCI).The Gan et al. [5] value of 2787 cm�1 is higher, and the6709 cm�1 for the A3R� state lower than our MRCI valuesin Table 2 which are considered to be more accurate, witherror bounds estimated to lie between 100 and 200 cm�1.

In Fig. 3 the electric dipole moment functions and theclassical turning points of v = 0 for the electronic groundstates of BP and its ions (relative to the center of mass of11B31P) and for the four lowest states of BP are shown.The dipole moments l0 decrease from BP+ to BP� andBP. The slope of the functions determines the infraredabsorption oscillator strength f 1

0 and the radiative lifetimesof the vibrational levels. From the four lowest states of BPonly the 1P dipole moment is strongly dependent on thedistance and has a large l0 (cf. Table 1). The three lowest

BP BP +

BP -

Fig. 1. State-averaged valence SA-CASSCF/aVTZ potentials of the electronic states of BP (a), BP+ (b) and BP� (c).

Table 1Spectroscopic constants of BP, BP+ and BP� av6z/CASSCF/IC-MRCI

re Be ae xe xexe lo f10 s1

BP X3P 1.7520 0.6762 0.0059 941.39 6.41 �0.0598 4.9–7 3.55a1R+ 1.6808 0.7346 0.0054 1039.81 6.52 �0.2718 4.4–10 3.22+3b1P 1.7616 0.6688 0.0055 934.24 5.57 1.0499 3.1–5 5.61–2A3R� 1.9690 0.5353 0.0055 633.75 4.81 �0.2142 1.8–7 21.9

BP+ X4R� 1.8612 0.5991 0.0081 725.36 8.67 �0.6119 4.7–6 0.630BP� X2R+ 1.7061 0.7130 0.0054 1018.17 5.37 0.3933 1.8–7 8.20

f is the oscillator strength; s1 is the radiative lifetime of the first vibrational level in seconds; l0 is the electric dipole moment in v = 0 in a.u.; re is inangstrom; all other constants are in cm�1.

R. Linguerri et al. / Chemical Physics 346 (2008) 1–7 3

states have small dipole moments and very small radiativetransition probabilities within the electronic states. Due tothe very small slopes of these functions the numerical accu-racy of the oscillator strengths and lifetimes is limited and

the values in Table 1 are only indicative. Apart from the 1Pstate the lifetimes of the v = 1 levels lie on the second timescale. From the transition moments (cf. Fig. 4) for thedipole- and spin-allowed transitions between the X3P,

BP

Fig. 2. Valence CASSCF/MRCI/aV6Z potentials of the four lowest statesof 11B31P with their vibrational levels.

Table 2Excitation energies Te (in cm�1) of the low lying states of BP

3P 1R+ 1P 3R�

Re (A)a 1.7478 1.6770 1.7573 1.9616RHF 0b �1452 261 7612CASSCF 0 2159 3879 6822MRCI 0 2412 3272 7469MRCI + Q 0 2548 3145 7412RCCSD(T) 0 2482

a MRCI equilibrium distances.b Total energies (aV6Z basis set):�365.236626 (RHF),�365.387429 (full

valence CASSCF), �365.544317 (MRCI), �365.556780 (MRCI + Q),�365.554129 (RCCSD(T)) (all values in a.u.).

BP

Fig. 3. MRCI/aV6Z dipole moment functions of the electronic groundstates of BP, BP+ and BP� (a) and electronically excited states of BP (b)including the classical turning points of v = 0.

4 R. Linguerri et al. / Chemical Physics 346 (2008) 1–7

a1R+, b1P and A3R� state only the A3R�- X3P lifetimesare calculated to lie on the ls time-scale. The slow radiativecascading within and between X3P, a1R+, b1P states willbe influenced by the spin–orbit coupling. This coupling willalso perturb the rotational-vibrational states.

For the four lowest electronic states of BP X3P, a1R+,b1P and A3R� there are 12 spin states, with X = ± 2 (1state each), X = ± 1 (3 states each) and X = 0 (4 states).All non-vanishing spin–orbit matrix elements have beencalculated from MRCI wavefunctions as a function ofinternuclear distance. The reference wavefunction com-prised all valence CASSCF configurations obtained fromstate-averaged calculations and aV6Z basis set.

Following phase convention has been used

IhPxjLzjPyi ¼ �1: ð1ÞThe non-vanishing coupling elements are:

X�X ¼ hX3Pþ1;MS ¼ 1j bH LS jX3Pþ1;MS ¼ 1i ð2ÞX� a ¼ hX3Pþ1;MS ¼ �1j bH LS ja1Rþ;MS ¼ 0i ð3ÞX� b ¼ hX3Pþ1;MS ¼ 0j bH LS jb1Pþ1;MS ¼ 0i ð4ÞX�A ¼ hX3Pþ1;MS ¼ 0j bH LS jA3R�;MS ¼ 1i ð5Þa�A ¼ ha1Rþ;MS ¼ 0j bH LS jA3R�;MS ¼ 0i ð6Þb�A ¼ hb1Pþ1;MS ¼ 0j bH LS jA3R�;MS ¼ 1i: ð7Þ

Their values are plotted in Fig. 5. Providing that theexcitation energies between the four electronic states areprecisely known from experiment, these functions couldbe used to calculate the spin–orbit perturbations of therotational-vibrational levels and changes of the radiativetransition probabilities within and between those fourstates of BP, which have very long radiative lifetimes.The largest value of about �75 to �80 cm�1 has beenobtained for the X–X coupling element followed by X–a(�75 cm�1) and X–b (+75 cm�1). Considering the rela-tively small xe’s and rotational constants in precise analysisof the gas phase emission or absorption spectra of 10BP and11BP the spin–orbit perturbations are not negligible.

The radiative probabilities calculated from the transi-tion moment functions using the SA-CASSCF reference

Fig. 4. MRCI/aV6Z transition moments for several electronic transitionsin BP and its ions.

–100

–80

–60

–40

–20

0

20

40

60

80

1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1

Spin

orb

it co

uplin

g [c

m– 1

]

R [Å]

X–X

X–a

X–b

X–A

a–A

b–A

Fig. 5. Non-vanishing spin–orbit MRCI/aV6Z coupling elements of thefour lowest electronic states of BP.

R. Linguerri et al. / Chemical Physics 346 (2008) 1–7 5

wavefunctions for a given transition and MRCI/aV6Zapproach are shown for two transitions of BP in Table 3.The functions with the classical turning points are shownin Fig. 4. The spontaneous emission rates depend stronglyon the size of the transition energies. This is why the vibra-tional radiative lifetimes of the a1R+–b1P transition are inthe range of milliseconds and for the A3R�–X3P on themicrosecond time scale. Both transition moments are rela-tively large and depend strongly on the distance. For BP�

and BP+ we have calculated in a similar way the radiativeprobabilities for the A2P–X2R+ and A4P–X4R� transi-tions. As shown in Fig. 4 the transition moment functionfor BP+ weakly depends on the distance in the region oflow lying vibrational states in both electronic states, i.e.the Franck–Condon approximation can be used to inter-pret the emission or absorption UV spectra. The lifetimesof the upper state are just a few microseconds. In theBP� ion the lifetimes are about ten times longer. In all con-sidered transitions they decrease with increasing v0 (seeTable 4).

Experimental electron affinities amount to 2256 ±20 cm�1 for boron [27] and to 6010 cm�1 for phosphorus[28], hence the dissociation asymptote P�(3P) + B(2P) lieslower by about 3800 cm�1 than the B�(3P) + P(4S) asymp-tote. The X2R+ state correlates with the lowest asymptote.The RCCSD(T)/aV6Z electron affinity EAe of BP is calcu-lated to be 2.74 eV, and the MRCI/aV6Z (X2R+ and A2Paveraged CASSCF reference) 2.54 eV. Based on the calcu-lated vibrational wavefunctions of BP� and BP theFranck–Condon factors have been used to model the anionphotoelectron spectrum of BP� which is shown in Fig. 6.Similar to the BN� spectrum it yields the informationabout the energetic positions of the four lowest states ofBP and would allow radiative decay calculations includingthe spin–orbit couplings. The Franck–Condon factors forthe hot bands observed in the BN� spectrum can be calcu-lated within the harmonic approximation from the spectro-scopic constants in Table 1. The MRCI radiative lifetimesfor the first excited bound 2P state are calculated to lie inthe range of ls (cf. Table 3). The MRCI/aV6Z T0 excita-tion energy of 7170 cm�1 is much lower than the Tv valueof 9597 cm�1 of Bruna and Grein [7].

The experimental ionization energies of boron andphosphorus are 8.298 and 10.486 eV, respectively [28].Hence the ground state of BP+ correlates with theB+(1S) + P(4S) asymptote. The first RCCSD(T)/aV6ZIEe ionization energy of BP (BP(X3P)–BP+(X4R�)) hasbeen calculated to be 9.48 eV, the MRCI/aV6Z 9.22 eV.The experimental estimate [2] of the upper limit,13 ± 2 eV, is far too high. In Fig. 7 the first band of thephotoelectron spectrum of BP based on the calculatedFranck–Condon factors is shown, which could prove help-ful in the identification of BP in the gas phase. The transi-tion moment for the A4P � X4R� (Fig. 4) is almostconstant in the region between the classical turning points,i.e. the Franck–Condon approximation works very wellfor this transition. The radiative lifetimes lie in the rangeof a few ls. This intense transition is suitable for the detec-tion of the BP ion by its UV spectrum, for instance in acold matrix.

The planar rhombic form is the most stable structure ofthe boron phosphide dimer [8,9]. In Table 5 we giveRCCSD(T)/aVQZ optimized geometries for the neutralmolecule and its ions. The equilibrium distance and angleof the neutral species are in good agreement with theDFT results of Qu et al. [9] and Burrill and Grein [8].

Table 3Radiative transition probabilities and Franck–Condon factors for some electronic transitions of BP

Transition T0 (cm�1) v0 v00 FC-factors fv0v00 v0 s (s)

BP A3R�–X3P 7504 0 0 0.01 0.20–4 0 0.873–40 1 0.06 0.84–40 2 0.15 0.16–30 3 0.22 0.18–30 4 0.22 0.14–30 5 0.16 0.79–41 0 0.05 0.80–4 1 0.579–41 1 0.14 0.20–31 2 0.15 0.18–31 3 0.05 0.52–42 0 0.09 0.17–3 2 0.442–42 1 0.14 0.23–32 2 0.03 0.51–4

BP b1P–a1R+ 574 0 0 0.02 0.52–5 0 0.8661 0 0.06 0.43–4 1 0.144–11 1 0.17 0.35–42 0 0.11 0.12–3 2 0.172–22 1 0.14 0.86–42 2 0.01 0.17–5

Table 4Radiative transition probabilities and Franck–Condon factors for some electronic transitions of BP� and BP+

Transition T0 (cm�1) v0 v00 FC-factors fv0v00 v0 s (s)

BP� A2P–X2R� 7170 0 0 0.21 0.62–3 0 0.184–40 1 0.35 0.85–30 2 0.27 0.51–30 3 0.12 0.18–31 0 0.30 0.18–2 1 0.159–41 1 0.07 0.19–31 2 0.05 0.11–31 3 0.23 0.42–32 0 0.24 0.92–3 2 0.141–42 1 0.02 0.55–42 2 0.17 0.46–3

BP+A4P–X4R� 22532 0 0 0.38 0.50–3 0 0.254–50 1 0.30 0.37–30 2 0.17 0.21–30 3 0.22 0.18–31 0 0.47 0.64–3 1 0.240–51 1 0.01 0.11–41 2 0.12 0.15–31 3 0.15 0.19–32 0 0.15 0.21–3 2 0.229–52 1 0.45 0.62–32 2 0.01 0.14–43 0 0.00 0.55–5 3 0.227–53 1 0.24 0.35–33 2 0.43 0.60–33 3 0.01 0.19–4

6 R. Linguerri et al. / Chemical Physics 346 (2008) 1–7

The ionization is hardly changing the planar rhombicgeometry and only small changes are calculated for thenegative ion. Both ions have totally symmetric electronicground state, since the electron is either removed fromthe non-bonding b2g orbital to form the 2Ag state or addedto the same orbital leading again to a totally symmetricstate. The first ionization potential IEe is calculated to be8.71 eV. Also the negative ion remains planar and the BP

distance is longer by about 0.02 A relative to the neutralmolecule. The electron affinity EAe is calculated to be2.34 eV. Both the ionization energy and the electron affin-ity of the dimer are smaller than those of boron monophos-phide. For the neutral dimer the harmonic wavenumbershave been reported by Qu et al. [8]. The harmonic wave-numbers of the normal modes for the ions (Table 5) couldbe useful for spectroscopic experiments. To our knowledge,

1-0 2-0 3-0 4-0 5-0 6-0 7-0 8-0 9-03

1-0 2-0a 1

1-0 2-0 3-0b1

1-0 2-0

X 3

0-0

0-0

0-0

0-0

A ∑-

∑

ΠΠ

+

Fig. 6. Photoelectron spectrum of BP� using Franck–Condon factorsfrom the MRCI/aV6Z potentials.

1-0 2-0 3-0X 4 - 0-0 4-0 5-0 6-0 7-0 8-0 9-0∑

Fig. 7. Photoelectron spectrum of BP electronic ground state usingFranck–Condon factors from the MRCI/aV6Z potentials.

Table 5RCCSD(T)/aug-cc-pVQZ energies, optimized geometries and harmonicwave numbers for the ground state of the most stable rhombic form (D2h)of (BP)2, ðBPÞþ2 and ðBPÞ�2

(BP)23B2g ðBPÞþ2

2Ag ðBPÞ�22Ag

RB � P (A) 1.845 1.845 1.860h

BbPB(�) 55.37 56.89 54.06

DEea (eV) 0.00 8.71 �2.34

Modesb (cm�1) x1(ag) 498 508x2(ag) 838 936x3(b3g) 874 576x4(b1u) 981 943x5(b2u) 802 582x6(b3u) 132 333

a The calculated energy for the X 3B2g state of (BP)2 is �731.33434886a.u.

b Relative atomic masses of 10.810000 and 30.973760 were used for Band P, respectively.

R. Linguerri et al. / Chemical Physics 346 (2008) 1–7 7

neither theoretical nor experimental works have beenreported about the ionic dimers, to date.

4. Conclusions

Large scale ab initio calculations have been used to cal-culate spectroscopic constants, dipole moments, infraredand UV radiative transition probabilities, and the photo-electron spectra of boron monophosphide and its negativeion. The ionization energies and electron affinities arereported also for the most stable planar rhombic structureof the dimer. The data can help to detect these molecules,for instance, in the chemical vapor deposition (CVD) pro-cess used for coating solid surfaces required for electronicdevices.

References

[1] Y. Kumashiro, J. Mater. Res. 5 (1990) 2933.[2] K.A. Gingerich, J. Chem. Phys. 56 (1972) 4239.[3] A.I. Boldyrev, J. Simons, J. Phys. Chem. 97 (1993) 6149.[4] A.I. Boldyrev, N. Gonzales, J. Simons, J. Phys. Chem. 98 (1994) 9931.[5] Z. Gan, D.J. Grant, R.J. Harrisson, D.A. Dixon, J. Chem. Phys. 125

(2006) 124311.[6] G.K-L. Chan, N.C. Handy, J. Chem. Phys. 112 (2000) 5639.[7] P.J. Bruna, F. Grein, J. Phys. Chem. A 105 (2001) 3328.[8] S. Burrill, F. Grein, J. Mol. Struct. (THEOCHEM) 757 (2005) 137.[9] Y. Qu, W. Ma, X. Bian, H. Tang, W. Tian, Int. J. Quantum Chem.

106 (2006) 960.[10] M. Lorenz, J. Agreiter, A.M. Smith, V.E. Bondybey, J. Chem. Phys.

104 (1996) 3143, and references therein.[11] K.R. Asmis, T.R. Taylor, D.M. Neumark, Chem. Phys. Lett. 295

(1998) 75, and references therein.[12] J.M.L. Martin, T. Lee, G. Scuseria, P.R. Taylor, J. Chem. Phys. 97

(1992) 6549.[13] K.A. Peterson, J. Chem. Phys. 102 (1995) 262.[14] H.-J. Werner, P.J. Knowles, J. Chem. Phys. 82 (1985) 5053.[15] H.-J. Werner, P.J. Knowles, J. Chem. Phys. 115 (1985) 259.[16] H.-J. Werner, P.J. Knowles, J. Chem. Phys. 89 (1988) 5803.[17] P.J. Knowles, H.-J. Werner, Chem. Phys. Lett. 145 (1988) 514.[18] A.K. Wilson, T. van Mourik, T.H. Dunning Jr., J. Mol. Struct.

(THEOCHEM) 388 (1966) 339.[19] T. van Mourik, A.K. Wilson, T.H. Dunning Jr., Mol. Phys. 99 (1999)

529.[20] T. van Mourik, T.H. Dunning Jr., Int. J. Quantum Chem. 76 (2000)

205.[21] P.J. Knowles, C. Hampel, H.-J. Werner, J. Chem. Phys. 99 (1993)

5219.[22] P.J. Knowles, C. Hampel, H.-J. Werner, J. Chem. Phys. 112 (2000)

3106 (Erratum).[23] R.A. Kendall, T.H. Dunning Jr., R.J. Harrison, Chem. Phys. 96

(1992) 6796.[24] D.E. Woon, T.H. Dunning Jr., J. Chem. Phys. 98 (1993) 1358.[25] MOLPRO is a package of ab initio programs, H.-J. Werner, P.J.

Knowles, see http://www.molpro.net.[26] J.W. Cooley, Math. Comput. 15 (1961) 363.[27] M. Scheer, R.C. Bilodeau, H.K. Haugen, Phys. Rev. Lett. 80 (1992)

2562.[28] Atomic data base, NIST; www.nist.gov.