Franck-Condon simulation of the single-vibronic-level emission spectra of HPCl/DPCl and the chemiluminescence spectrum of HPCl, including anharmonicity.

Abstract

Restricted-spin coupled-cluster single-double plus perturbative triple excitation [RCCSD(T)] potential energy functions (PEFs) were calculated for the X (2)A" and A (2)A' states of HPCl employing the augmented correlation-consistent polarized-valence-quadruple-zeta (aug-cc-pVQZ) basis set. Further geometry optimization calculations were carried out on both electronic states of HPCl at the RCCSD(T) level with all electron and quasirelativistic effective core potential basis sets of better than the aug-cc-pVQZ quality, and also including some core electrons, in order to obtain more reliable geometrical parameters and relative electronic energy of the two states. Anharmonic vibrational wave functions of the two states of HPCl and DPCl, and Franck-Condon (FC) factors of the A (2)A'-X (2)A" transition were computed employing the RCCSD(T)/aug-cc-pVQZ PEFs. Calculated FC factors with allowance for Duschinsky rotation and anharmonicity were used to simulate the single-vibronic-level (SVL) emission spectra of HPCl and DPCl reported by Brandon et al. [J. Chem. Phys. 119, 2037 (2003)] and the chemiluminescence spectrum reported by Bramwell et al. [Chem. Phys. Lett. 331, 483 (2000)]. Comparison between simulated and observed SVL emission spectra gives the experimentally derived equilibrium geometry of the A (2)A' state of HPCl of r(e)(PCl) = 2.0035 +/- 0.0015 A, theta(e) = 116.08 +/- 0.60 degrees, and r(e)(HP) = 1.4063+/-0.0015 A via the iterative Franck-Condon analysis procedure. Comparison between simulated and observed chemiluminescence spectra confirms that the vibrational population distribution of the A (2)A' state of HPCl is non-Boltzmann, as proposed by Baraille et al. [Chem. Phys. 289, 263 (2003)].

Full text

Page 1

Franck-Condon simulation of the single-vibronic-level emission spectra
of HPClÕDPCl and the chemiluminescence spectrum of HPCl,
including anharmonicity
Foo-tim Chau,a)Daniel K. W. Mok, and Edmond P. F. Leea),b),c)
Department of Applied Biology and Chemical Technology, Hong Kong Polytechnic University, Hung Hom,
Hong Kong
John M. Dyke
School of Chemistry, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom
?Received 29 January 2004; accepted 4 May 2004?
Restricted-spin coupled-cluster single-double plus perturbative triple excitation ?RCCSD?T??
potential energy functions ?PEFs? were calculated for the X˜ 2A? and A˜ 2A? states of HPCl
employing the augmented correlation-consistent polarized-valence-quadruple-? ?aug-cc-pVQZ?
basis set. Further geometry optimization calculations were carried out on both electronic states of
HPCl at the RCCSD?T? level with all electron and quasirelativistic effective core potential basis sets
of better than the aug-cc-pVQZ quality, and also including some core electrons, in order to obtain
more reliable geometrical parameters and relative electronic energy of the two states. Anharmonic
vibrational wave functions of the two states of HPCl and DPCl, and Franck-Condon ?FC? factors of
the A˜ 2A?-X˜ 2A? transition were computed employing the RCCSD?T?/aug-cc-pVQZ PEFs.
Calculated FC factors with allowance for Duschinsky rotation and anharmonicity were used to
simulate the single-vibronic-level ?SVL? emission spectra of HPCl and DPCl reported by Brandon
et al. ?J. Chem. Phys. 119, 2037 ?2003?? and the chemiluminescence spectrum reported by Bramwell
et al. ?Chem. Phys. Lett. 331, 483 ?2000??. Comparison between simulated and observed SVL
emission spectra gives the experimentally derived equilibrium geometry of the A˜ 2A? state of HPCl
of re(PCl)?2.0035?0.0015Å, ?e?116.08?0.60°, and re(HP)?1.4063?0.0015Å via the
iterative Franck-Condon analysis procedure. Comparison between simulated and observed
chemiluminescence spectra confirms that the vibrational population distribution of the A˜ 2A? state of
HPCl is non-Boltzmann, as proposed by Baraille et al. ?Chem. Phys. 289, 263 ?2003??. © 2004
American Institute of Physics. ?DOI: 10.1063/1.1765654?
I. INTRODUCTION
Recently, we reported ab initio calculations on the A˜ 2A?
and X˜ 2A? states, and simulations of the A˜ 2A?→X˜ 2A? emis-
sion spectrum, of HPCl employing Franck-Condon ?FC? fac-
tors computed within the harmonic oscillator model.1In this
study, our ab initio results and spectral simulations con-
firmed the assignments of the emitter of, and the electronic
states involved in, the first observed chemiluminescence
spectrum of HPCl reported by Bramwell et al.2Also some of
the vibrational assignments and the T0 position of the
A˜ 2A?→X˜ 2A? transition of Bramwell et al. were revised.
However, it was noted in Ref. 1 that the experimentally de-
rived equilibrium bond angle ?e(HPCl) of the A˜ 2A? state of
HPCl, with a value of 112.6° obtained from the iterative
Franck-Condon analysis ?IFCA? ?see the following section
and Ref. 1, and references therein for detail?, was signifi-
cantly smaller than the ab initio value of ca. 116.8° obtained
at the restricted-spin coupled-cluster single-double plus per-
turbative triple excitation/correlation-consistent polarized-
valence-quadruple ? ?RCCSD?T?/cc-pVQZ? ?no g? level of
calculation. It was suggested that such a large difference of
over 4° between the calculated and experimentally derived
IFCA bond angle was possibly due to the inadequacy of the
harmonic oscillator model employed in the FC factor calcu-
lations. In the present study, effects of including anharmonic-
ity on the simulated emission spectra of HPCl, and, in par-
ticular, on the IFCA bond angle of the A˜ 2A? state of HPCl,
are investigated. In the following sections, we report com-
puted ab initio potential energy functions ?PEFs? of the
A˜ 2A? and X˜ 2A? states of HPCl, anharmonic vibrational
wave functions, FC factors, and spectral simulation of the
A˜ 2A?→X˜ 2A? emission of HPCl which include anharmonic-
ity.
During the preparation of the manuscript of the present
investigation, a theoretical study3on the A˜ 2A?→X˜ 2A?
emission of HPCl and HNCl, and a laser induced fluores-
cence ?LIF? and single-vibronic-level ?SVL? emission study4
on HPCl and DPCl have appeared. The former3reported
B3LYP, CCSD?T?, and CASPT2 calculations on the A˜ 2A?
and X˜ 2A? states of HPCl, using the cc-pVTZ basis set, and
also FC spectral simulations beyond the harmonic oscillator
a?Author to whom correspondence should be addressed. Electronic mail:
bcftchau@polyu.edu.hk
b?Electronic mail: epl@soton.ac.uk
c?Also at University of Southampton.
JOURNAL OF CHEMICAL PHYSICSVOLUME 121, NUMBER 422 JULY 2004
18100021-9606/2004/121(4)/1810/14/$22.00 © 2004 American Institute of Physics
Downloaded 10 Nov 2009 to 152.78.208.72. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

Page 2

model, based on a variation-perturbation approach. In gen-
eral, the ab initio results obtained in, and the conclusions
drawn from the theoretical investigation of Ref. 3 agree
mostly with those of Ref. 1, except that in the comparison
between their simulated spectra3and the observed chemilu-
minescence spectrum of Ref. 2, a non-Boltzmann distribu-
tion of the populations of the vibrational levels in the upper
electronic state of HPCl was proposed. This is in contrast to
the conclusion reached in Ref. 1 of a Boltzmann distribution
in the low-lying vibrational levels of the upper electronic
state with a vibrational temperature of 1000 K. These differ-
ent conclusions of Refs. 1 and 3 regarding the population
distribution of the low-lying vibrational levels of the upper
state are also investigated in the present study.
The rotationally resolved LIF and vibrationally resolved
SVL emission study of Ref. 4 reported experimentally de-
rived r0and estimated re
HP and PCl bond lengths, and the HPCl bond angle? of the
A˜ 2A? and X˜ 2A? states of HPCl, and the fundamental and
harmonic vibrational frequencies of these two electronic
states of HPCl and DPCl. In addition, CCSD?T?/augmented-
coupled-cluster-polarized-valence-triple-? aug-cc-pVTZ cal-
culations were carried out on both states of HPCl. One major
difference between the chemiluminescence spectrum re-
ported in Ref. 2 and the SVL emission spectra reported in
Ref. 4 is that the latter spectra are free from overlapping
bands, which arise from emissions from low-lying vibra-
tional levels of the upper electronic state, as observed in the
chemiluminescence spectrum. In this connection, the simpler
SVL emission spectra will be considered first in the section
dealing with the comparison between the simulated and ob-
served spectra, before the chemiluminescene spectrum is
discussed.
zstructures ?i.e., the corresponding
II. THEORETICAL CONSIDERATIONS AND
COMPUTATIONAL DETAILS
A. Ab initio calculations, potential energy functions,
and Franck-Condon factor calculations
Restricted-spin coupled-cluster single-double5plus per-
turbative triple6excitation ?RCCSD?T?? calculations were
carried out on the A˜ 2A? and X˜ 2A? states of HPCl, employ-
ing the aug-cc-pVQZ basis set.7The 1s22s22p6core elec-
trons of P and Cl were frozen in these RCCSD?T? calcula-
tions. 171 RCCSD?T?/aug-cc-pVQZ energy points were
scanned on the electronic energy surface of the X˜ 2A? state of
HPCl in the geometrical ranges of 1.21?r(HP)?1.77Å,
1.84?r(PCl)?2.40Å, and 55.0???HPCl??135.0°, and 163
energy points were scanned on the A˜ 2A? surface in the geo-
metrical ranges of 1.198?r(HP)?1.758Å, 1.810?r(PCl)
?2.370Å, and 84.0???HPCl??148.0°. Polynomial func-
tions of the following form were fitted to the corresponding
computed ab initio total energies to give the potential energy
functions ?PEFs? of the X˜ 2A? and A˜ 2A? states of HPCl.
V??
ijk
Cijk?S1?i?S2?j?S3?k?Veqm.
?1?
The bending coordinate suggested by Carter and Handy,8
S2???????2????3,
has been employed for S2, where ?? is the displacement of
the bond angle from the equilibrium value, (???e), while
S1and S3are the displacements of the HP and PCl bond
lengths from the equilibrium values, (r?re), respectively.
The fitting of the PEFs, the variational calculations of
the anharmonic vibrational wave functions and the FC factor
calculations were carried out as described previously.9,10In
brief, Watson’s Hamiltonian11,12for a nonlinear molecule
was used, and both anharmonicity and Duschinsky rotation
were included in the FC factor calculations. Here, only some
technical details specific to the present study are given and
these are as follows: Anharmonic vibrational wave functions
were expressed as linear combinations of harmonic oscillator
functions, h(v1,v2,v3), where v1, v2, and v3denote the
quantum numbers of the harmonic basis functions for the HP
stretching, bending, and PCl stretching modes, respectively.
Harmonic basis functions with vibrational quantum numbers
of up to h(6,20,10) and a restriction of v1?v2?v3?20
were included in the variational calculations of the X˜ 2A?
state. For the A˜ 1A? state, harmonic basis functions of up to
h(6,10,10), with a restriction of v1?v2?v3?10 were
considered.
The IFCA procedure was carried out ?see Refs. 9 and 10
for details? with the geometry of the X˜ 2A? state fixed to the
experimentally derived, estimated equilibrium (re
of Ref. 4, while the geometrical parameters of the A˜ 2A? state
were varied systematically, until the best match between
simulated and observed SVL emission spectra was obtained
?see also the following section for a more detailed descrip-
tion, which includes the ab initio calculations?. Vibronic
components in the SVL A˜ 2A?→X˜ 2A? emission spectra of
HPCl/DPCl were simulated using Gaussian functions with a
full width at half maximum ?FWHM? of 15 cm?1, which is a
spectral resolution slightly better than that of the observed
SVL emission spectra of Ref. 4. For simulated chemilumi-
nescence spectra, a FWHM of 1 nm ??30 cm?1in the visible
region of 400–600 nm? was used ?cf. an experimental reso-
lution of 0.32 nm quoted in Ref. 2 for the wavelength region
of 400–600 nm?. The relative intensity of each vibrational
component in a simulated spectrum is given by the product
of the corresponding computed anharmonic FC factor and a
frequency factor of power 4.
z) geometry
B. Further geometry optimization calculations
In order to obtain more reliable computed equilibrium
geometrical parameters of the A˜ 2A? and X˜ 2A? states of
HPCl, and transition energies (Teand T0) between the two
states, further geometry optimization calculations employing
basis sets of better quality than the aug-cc-pVQZ basis set
were carried out at the RCCSD?T? level of theory. First, the
aug-cc-p(d?Q?Z basis sets,13which contain an extra tight d
function added to the original aug-cc-pVQZ basis sets for the
second row elements, were used for P and Cl. This is because
tight d polarization functions have been found to be impor-
1811 J. Chem. Phys., Vol. 121, No. 4, 22 July 2004 Emission spectra of HPCl
Downloaded 10 Nov 2009 to 152.78.208.72. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

Page 3

tant in the basis set at the Hartree-Fock level of theory for
second row elements ?see Refs. 13 and 14, and references
therein?.
Second, in addition to the valence electrons, the 2s22p6
core electrons of P and Cl were correlated in the RCCSD?T?
calculations ?i.e., only the 1s2electrons of P and Cl are
frozen?
and theenergy-weighed
pwCVQZ basis sets15were used for P and Cl. This is to
investigate the effects of core-core and core-valence correla-
tion on the minimum-energy geometries of the two states of
HPCl, which contains the second row elements, P and Cl
?see, for examples, Ref. 14, and references therein?. It should
be noted that these calculations including the core electrons
were extremely, computationally demanding ?in terms of
both memory and CPU time?.
Third, the cc-pV5Z basis set was employed to examine
the effects of better valence description than the valence QZ
quality. The augmented ?or diffuse? part of the aug-cc-pV5Z
basis set has been excluded, because its inclusion would lead
to unmanageably demanding calculations. Nevertheless, ba-
sis sets, which make use of effective core potentials ?ECPs?
to account for core electrons, and are of the augmented po-
larized valence 5Z quality, were considered for P and Cl. The
following contracted ?6s6p5d4f3g2h? valence basis sets of
the aug-cc-pV5Z quality, which coupled with the respective
quasirelativisticenergy-consistent
?ECP10MWB? of the Stuttgart/Koeln group,16were designed
to describe the valence 3s and 3p shells of the P and Cl
atoms.
?a? P: 15 even-tempered s primitives ?ratio?1.75; center
exponent?1.5? and 13 even-tempered p primitives ?1.75;
0.8? were contracted to ?1s1p?, with the contraction coeffi-
cients obtained from a restricted open shell Hartree Fock
?ROHF? calculation of the neutral atom employing the
15s13p primitives uncontracted, plus the following uncon-
tracted functions: 5s(2.5; 0.25?, 5p(2.4; 0.18?, 5d(2.5; 2.0?,
4f ?exponents; 0.76832, 0.2744, 0.098, 0.035?, 3g(0.49,
0.14, 0.04?, and 2h(0.24, 0.06?.
?b? Cl: 15 even-tempered s primitives ?ratio?1.8; center
exponent?2.0? and 13 even-tempered p primitives ?1.75;
0.8? were contracted to ?1s1p?, with the contraction coeffi-
cients obtained from an ROHF calculation of the neutral
atom employing the 15s13p primitives uncontracted, plus
the following uncontracted functions: 5s(2.5; 0.45?, 5p(2.6;
0.3?, 5d(2.6; 0.3?, 4f ?exponents; 1.8, 0.6, 0.2, 0.066667?,
3g(1.75, 0.38889, 0.0864197?, and 2h(0.35, 0.077778?.
The above ECP10MWB ?6s6p5d4f3g2h? basis sets
for P and Cl ?ECP-AV5Z in short? were used together with
the aug-cc-pV5Z basis set for H. Calculations using these 5Z
quality basis sets of cc-pV5Z and ECP-AV5Z explore the
effects of basis set extension towards the complete basis set
?CBS? limit on the minimum-energy geometries of the two
states of HPCl and their relative electronic energies. In addi-
tion, the quasirelativistic ECPs employed for P and Cl in the
ECP-AV5Z basis sets described above also account for a
certain amount of relativistic contribution. Summing up,
various effects, arising from basis size extension towards the
CBS limit, electron correlation of core electrons, and relativ-
istic contributions of the second row elements, P and Cl, on
core-valenceaug-cc-
pseudopotentials
the computed equilibrium geometrical parameters of, and
transition energies between, the A˜ 2A? and X˜ 2A? states of
HPCl were investigated by carrying out RCCSD?T? geom-
etry optimization calculations employing various basis sets
described above.
All the RCCSD?T? calculations carried out in the present
study were performed using the MOLPRO suite of programs.17
III. RESULTS AND DISCUSSION
The RCCSD?T?/aug-cc-pVQZ PEFs of the X˜ 2A? and
A˜ 2A? states of HPCl, and some of the computed anharmonic
vibrational energies and wave functions of the two states are
given in Tables I and II respectively. The calculated equilib-
rium geometrical parameters, harmonic and fundamental vi-
brational frequencies of, and transition energies (T0/Te) be-
tween, the X˜ 2A? and A˜ 2A? states of HPCl ?DPCl? are
summarized in Tables III to VI, together with previously cal-
culated and experimentally measured/derived values for
comparison. Simulated spectra are shown in Figs. 1–6 to-
gether with the corresponding experimental spectra for
comparison.
TABLE I. The RCCSD?T?/aug-cc-pVQZ PEFs of the X˜ 2A? and A˜ 2A?
states of HPCl ?see text and Eq. ?1??.
C(I,j,k)
X˜ 2A?
A˜ 2A?
002
200
020
101
011
110
003
300
030
102
012
201
210
021
120
111
004
400
040
103
013
301
310
031
130
202
022
220
112
211
121
0.3269
0.3785
0.1051
0.0038
0.0558
?0.0120
?0.5186
?0.6485
?0.0307
?0.0225
?0.0937
0.0272
?0.0016
?0.1286
?0.0187
?0.0201
0.4136
0.5343
0.0074
0.0352
0.0505
0.0025
0.0136
0.0672
?0.0097
?0.0343
0.0645
?0.0380
0.0555
?0.0214
0.0176
2.0511
1.4209
95.1664
4.7?10?5(10.3)
0.3652
0.3768
0.0561
?0.0125
0.0162
0.0086
?0.6241
?0.7243
0.0016
?0.0230
?0.0347
0.0037
0.0147
?0.0537
?0.0410
?0.0220
0.4795
0.5914
?0.0129
0.0356
0.0060
0.0068
?0.0351
0.0194
0.0252
?0.0726
0.0030
?0.0358
0.0077
?0.0117
0.0160
2.0142
1.4101
116.9346
6.4?10?5(14.0)
Re?P-Cl?/Å
Re?H-P?/Å
?(HPCl?e/°
rms/hartree ?cm?1?
1812J. Chem. Phys., Vol. 121, No. 4, 22 July 2004Chau et al.
Downloaded 10 Nov 2009 to 152.78.208.72. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

Page 4

A. The ab initio potential energy functions and the
anharmonic vibrational wave functions of the
A˜ 2A? and X˜ 2A? states of HPCl
The RCCSD?T?/aug-cc-pVQZ PEFs of the A˜ 2A? and
X˜ 2A? states of HPCl are given in Table I. The root mean
square ?rms? deviations of the fitted potentials from the com-
puted single point energies are 14.0 and 10.3 cm?1for the
A˜ 2A? and X˜ 2A? states, respectively.
Table II shows the computed energies and anharmonic
wave functions of some low-lying vibrational levels of the
A˜ 2A? and X˜ 2A? states of HPCl expressed as linear combi-
nations of harmonic basis functions ?five largest harmonic
terms are shown?. First, based on the computed anharmonic
wave functions, the normal modes correspond largely to the
HP stretching, bending, and PCl stretching modes, respec-
tively, and the vibrational designations of the anharmonic
vibrational wave functions follow closely with those of the
leading harmonic basis functions at least for most of the
low-lying vibrational levels shown in Table II. Second, other
than the HP stretching mode, which is expected to be
strongly anharmonic, the PCl stretching mode is also signifi-
cantly anharmonic in both the A˜ 2A? and X˜ 2A? states of
HPCl. This anharmonic effect in the PCl stretching mode is
reflected in the calculated anharmonic vibrational wave func-
tions with leading harmonic basis functions of h(0,0,v3),
where v3?3. It can be seen that, for these higher vibrational
levels of the PCl stretching mode, the coefficients of the
leading harmonic terms become significantly smaller than
unity as v3increases, and contributions from other harmonic
terms become significant. Nevertheless, these computed an-
harmonic wave functions suggest a purely PCl stretching
mode with negligibly small coupling with the bending and/or
HP stretching modes. Third, anharmonic effects are also
found to be significant in combination levels involving the
PCl stretch. For example, the anharmonic wave function of
the X˜ 2A? state with h(0,1,3) as its leading harmonic term
has significant contribution also from h(0,1,4) ?with a cal-
culated coefficient of 0.44; see Table II?. Fourth, anharmonic
vibrational wave functions of very close calculated energies
show some ‘‘mode mixing,’’ as expected. For example, for
the vibrational levels of the X˜ 2A? state with h(1,0,0) and
h(0,2,1) as the leading harmonic terms in their anharmonic
wave functions, which are calculated to be only 12.6 cm?1
apart in energy, the anharmonic wave functions show signifi-
cant mixing ?see Table II?. Finally, in general, the computed
anharmonic vibrational wave functions for both states of
DPCl behave in similar ways as those of HPCl discussed,
though the magnitudes of anharmonic effect and mode mix-
ing in DPCl are slightly smaller than in HPCl.
B. The equilibrium geometrical parameters
of the A˜ 2A? and X˜ 2A? states of HPCl
Calculated minimum-energy geometrical parameters of
the two states of HPCl and the corresponding experimentally
derived values are summarized in Table III. We have only
included previous ab initio results of relatively higher levels
in Table III ?for earlier and lower level results from ab initio
and/or density functional calculations, see Refs. 3 and 4, and
references therein?. When the levels of theory employed to
obtain the calculated values as shown in Table III are con-
sidered, it is clear that the levels used in the present study are
superior to those reported previously. Therefore, we will fo-
cus on the results obtained in the present study from here
onward. For the X˜ 2A? state of HPCl, the ranges of the cal-
culated re(HP), ?e(HPCl), and re(PCl) values at the
RCCSD?T? level with basis sets of, or better than, the aug-
cc-pVQZ quality are between 1.4166 and 1.4213, 94.97 and
TABLE II. Calculated energies Evib(cm?1) and anharmonic vibrational
wave functions ?vibin terms of harmonic basis functions ?see text? of some
low-lying vibrational levels of the X˜ 2A? and A˜ 2A? states of HPCl.
Evib
?vibof the X˜ 2A? state
0.0000.9932h(0,0,0)?0.0808h(1,0,0)?0.0642h(0,0,1)
?0.0299h(3,0,0)?0.0293h(0,1,0)
?0.9793h(0,0,1)?0.1613h(0,0,2)?0.0790h(1,0,1)
?0.0644h(0,0,0)?0.0307h(0,1,1)
?0.9898h(0,1,0)?0.1006h(0,1,1)?0.0699h(0,2,0)
?0.0334h(1,3,0)?0.0300h(1,1,0)
0.9388h(0,0,2)?0.2767h(0,0,3)?0.1625h(0,0,1)
?0.0750h(1,0,2)?0.0534h(0,0,4)
0.9651h(0,1,1)?0.2106h(0,1,2)?0.1011h(0,1,0)
?0.0702h(0,2,1)?0.0360h(0,1,3)
0.8581h(0,0,3)?0.3945h(0,0,4)?0.2804h(0,0,2)
?0.1033h(0,0,5)?0.0803h(0,0,6)
0.9664h(0,2,0)?0.1458h(1,0,0)?0.1336h(0,2,1)
?0.1173h(0,3,0)?0.0709h(0,1,0)
?0.9065h(0,1,2)?0.3304h(0,1,3)?0.2131h(0,1,1)
?0.0783h(0,1,4)?0.0677h(0,2,2)
?0.7282h(0,0,4)?0.4967h(0,0,5)?0.4029h(0,0,3)
?0.1686h(0,0,6)?0.1171h(0,0,7)
?0.9036h(0,2,1)?0.2448h(0,2,2)?0.2446h(1,0,0)
?0.1239h(1,0,1)?0.1114h(0,3,1)
?0.9122h(1,0,0)?0.2450h(2,0,0)?0.2167h(0,2,1)
?0.1744h(0,2,0)?0.0821h(1,0,1)
0.8020h(0,1,3)?0.4434h(0,1,4)?0.3369h(0,1,2)
?0.1381h(0,1,5)?0.0920h(0,1,6)
0.5651h(0,0,6)?0.5514h(0,0,5)?0.5119h(0,0,4)
?0.2394h(0,0,7)?0.1566h(0,0,8)
?0.9214h(0,3,0)?0.2477h(1,1,0)?0.1665h(0,4,0)
?0.1610h(0,3,1)?0.1231h(0,2,0)
528.659
877.123
1051.932
1401.246
1570.048
1746.993
1919.965
2083.455
2265.935
2278.549
2433.532
2594.024
2609.757
Evib
?vibof the A˜ 2A? state
0.000 0.9921h(0,0,0)?0.0819h(1,0,0)?0.0697h(0,0,1)
?0.0345h(3,0,0)?0.0335h(1,2,0)
?0.9759h(0,0,1)?0.1713h(0,0,2)?0.0800h(1,0,1)
?0.0701h(0,0,0)?0.0340h(3,0,1)
?0.9902h(0,1,0)?0.0911h(0,1,1)?0.0574h(0,2,0)
?0.0571h(1,3,0)?0.0310h(3,1,0)
0.9302h(0,0,2)?0.2908h(0,0,3)?0.1737h(0,0,1)
?0.0756h(1,0,2)?0.0623h(0,0,4)
0.9669h(0,1,1)?0.2000h(0,1,2)?0.0922h(0,1,0)
?0.0667h(0,2,1)?0.0562h(1,3,1)
0.9702h(0,2,0)?0.1217h(1,0,0)?0.1098h(0,2,1)
?0.0926h(0,3,0)?0.0781h(1,4,0)
?0.8397h(0,0,3)?0.4103h(0,0,4)?0.2975h(0,0,2)
?0.1181h(0,0,5)?0.0887h(0,0,6)
0.9092h(0,1,2)?0.3212h(0,1,3)?0.2045h(0,1,1)
?0.0773h(0,1,4)?0.0741h(0,2,2)
?0.9382h(0,2,1)?0.2224h(0,2,2)?0.1179h(1,0,1)
?0.1149h(0,2,0)?0.1046h(0,3,1)
0.9305h(0,3,0)?0.2033h(1,1,0)?0.1392h(1,3,0)
?0.1308h(0,4,0)?0.1229h(0,3,1)
558.616
641.242
1110.287
1196.615
1270.096
1655.136
1745.006
1822.059
1885.977
1813 J. Chem. Phys., Vol. 121, No. 4, 22 July 2004Emission spectra of HPCl
Downloaded 10 Nov 2009 to 152.78.208.72. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

Page 5

95.23°, and 2.0397 and 2.0517 Å, respectively. The very nar-
row spreads of the computed geometrical parameters of
0.0047, 0.26° and 0.0120 Å, respectively, suggest a high de-
gree of consistency in these theoretical values. Therefore, it
is concluded that these ab initio results should be reasonably
reliable and any further improvements in the level of calcu-
lation would not lead to any significant changes of the opti-
mized geometrical parameters of the X˜ 2A? state of HPCl.
The averaged calculated values of re(HP), ?e(HPCl), and
re(PCl) are 1.4196?0.0030, 95.15?0.18°, and 2.0467
?0.0070 Å, which agree with the experimentally derived,
estimated re
retical and experimental uncertainties.
Comparing the calculated and experimentally derived
equilibrium geometrical parameters of the X˜ 2A? state of
HPCl in more detail, the computed equilibrium bond lengths
obtained using the aug-cc-pwCVQZ basis set ?correlating the
core 2s62p6electrons of P and Cl explicitly in the
RCCSD?T? calculations? agree best with the experimentally
derived re
the RCCSD?T?/ECP-AV5Z, value agrees best with the re
zvalues of Ref. 4 to within the combined theo-
zvalues4?to within 0.001 Å?. For the bond angle,
z
value ?to within 0.05°?. If the computed equilibrium geo-
metrical parameters, obtained using basis sets of better than
the aug-cc-pVQZ quality ?i.e., the aug-cc-pwCVQZ, cc-
pV5Z, and ECP-AV5Z basis sets? are considered, the aver-
aged calculated values of re(HP), ?e(HPCl), and re(PCl)
are 1.4184?0.0018, 95.14?0.17°, and 2.0437?0.0041 Å,
respectively. These values agree with the corresponding ex-
perimentally derived, estimated re
0.0026 Å, 0.12°, and 0.0049 Å. Such good agreement be-
tween theory and experiment confirms the reliability of these
equilibrium geometrical parameters of the X˜ 2A? state of
HPCl.
For the A˜ 2A? state of HPCl, the spreads of the calcu-
lated re(HP),
?e(HPCl),and re(PCl)
RCCSD?T? level with basis sets of, or better than, the aug-
cc-pVQZ quality are 0.0041, 0.23°, and 0.0076 Å, respec-
tively ?Table III?, which are even smaller than those of the
X˜ 2A? state, indicating that these ab initio geometrical pa-
rameters are highly consistent and hence should be reason-
ably reliable. The averaged calculated re(HP), ?e(HPCl),
zvalues of Ref. 4 to within
values at the
TABLE III. The computed and experimentally derived geometrical parameters ?Equilibrium geometrical pa-
rameters, unless otherwise stated; estimated uncertainties/errors given in parentheses ?see original works for
details?; for earlier works see Refs. 1, 3, and 4, and references therein.? of the X˜ 2A? and A˜ 2A? states of HPCl.
X˜ 2A?
Re(HP?/Å
?e(HPCl)/°
Re(PCl?/Å
Reference
RCCSD?T?/aug-cc-pVQZ?PEF?
RCCSD?T?/aug-cc-pVQZa
RCCSD?T?/aug-cc-pV(d?Q?Za
RCCSD?T?/aug-cc-pwCVQZa
RCCSD?T?/cc-pV5Za
RCCSD?T?/ECP-AV5Za
Averaged
CCSD?T?/aug-cc-pVTZ
CCSD?T?/cc-pVTZ
CASPT2/cc-pVTZ
RCCSD?T?/cc-pVQZ ?no g?
r0
rz
re
1.4209
1.4213
1.4200
1.4166
1.4195
1.4192
1.4196?30?
1.425
1.4239
1.4250
1.4188
1.4331?36?
1.4279?23?
1.4158?23?
95.17
95.11
95.23
95.22
95.22
94.97
95.15?18?
94.9
95.18
94.64
95.06
95.0?4?
95.02?27?
95.02?27?
2.0511
2.0517
2.0462
2.0397
2.0437
2.0478
2.0467?70?
2.067
2.0633
2.0628
2.0570
2.0418?6?
2.0433?4?
2.0388?23?
Present
Present
Present
Present
Present
Present
Present
4
3
3
1
4
4
4
z
A˜ 2A?
RCCSD?T?/aug-cc-pVQZ?PEF?
RCCSD?T?/aug-cc-pVQZa
RCCSD?T?/aug-cc-pV(d?Q?Za
RCCSD?T?/aug-cc-pwCVQZa
RCCSD?T?/cc-pV5Za
RCCSD?T?/ECP-AV5Za
Averaged
Ab initio changesb
CCSD?T?/aug-cc-pVTZ
CCSD?T?/cc-pVTZ
CASPT2/cc-pVTZ
RCCSD?T?/cc-pVQZ ?no g?
r0
rz
re
IFCA ?harmonic?
IFCA ?anharmonic?c
1.4102
1.4113
1.4100
1.4072
1.4095
1.4093
1.4096?24?
1.4058
1.414
1.4124
1.4111
1.4080
1.4231?38?
1.4168?20?
1.4067?20?
116.93
116.72
116.76
116.70
116.73
116.71
116.76?17?
116.63
116.6
116.54
116.96
116.76
115.4?2?
115.53?12?
115.53?12?
112.6
116.08?60?
2.0142
2.0150
2.0094
2.0029
2.0074
2.0104
2.0099?70?
2.0020
2.030
2.0294
2.0246
2.0205
2.0078?4?
2.0093?2?
2.0050?2?
2.013
2.0035?15?
Present
Present
Present
Present
Present
Present
Present
Present
4
3
3
1
4
4
4
1
Present
z
1.4063?15?
aOptimized geometry; see text.
bExperimental re
deexcitation; see text.
cSee text.
zvalues of the X˜ 2A? state of HPCl plus the averaged ab initio geometrical changes upon
1814 J. Chem. Phys., Vol. 121, No. 4, 22 July 2004Chau et al.
Downloaded 10 Nov 2009 to 152.78.208.72. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp