Study of the excited states of HPO and its emission spectrum in hydrogen-based flames

Analytica Chimica Acta, 226 (1989) 305-313 Elsevier Science Publishers B.V., Amsterdam -

305 Printed in The Netherlands

STUDY OF THE EXCITED STATES OF HP0 AND ITS EMISSION SPECTRUM IN HYDROGEN-BASED FLAMES I.H. EL-HAG and I. JAN0 Chemistry Department, U.A.E. Uniuerstty, P.O. Box 15551, Al-Ain (United Arab Emirates) (Received 20th February 1989)

SUMMARY INDO and configuration interaction calculations for the electronic excited states of the HP0 molecule are reported. The calculated energies of n-r II* and x + n* transitions are compared with ab initio results. The bands in the green emission spectrum of HP0 resulting from the lowest excited electronic state are identified as originating from O-+0 pure electronic, and 0-r 1, and l-10 transitions involving P=O stretching and HP0 bending modes of vibration. The calculation also indicates the existence of an electronic state close to the lowest excited state with similar symmetry (A”).

The green emission of phosphorus in cool flames has been reported extensively. In 1841, Wohler [ 1] reported a flame test for phosphorus when he noticed that phosphine burns with a white flame. The whitish flame spread out into a ring of green light when a porcelain surface was held in the flame. Merz [ 21 noticed that phosphorus colours the cool core of a hydrogen diffusion flame green. The most significant early work on the green phosphorus emission was by Salet [ 3,4], who noticed an intensified green colour from phosphorus when he directed a hydrogen flame against a curtain of falling water to chill the flame. The first spectra of the green phosphorus flame emission were reported in 1907 by Geuter [ 51. He reported diffuse headless bands from the ultraviolet region to 480 nm and a band system at longer wavelengths. Much confusion surrounded the identification of the nature of the green emitting species. In 1962, the emission was studied by Lam Thanh and Peyron [ 61. They obtained the spectrum as a result of a direct reaction between atomic hydrogen and phosphorus vapour. This vapour was entrained in argon which contained traces of oxygen. These workers convincingly attributed the green emission to HP0 [ 7,8]. Tracings of the spectrum by Brody and Chaney [ 91 and Dagnall et al. [lo] showed that the green emission has a banded structure with a strong maximum between 526 and 528 nm and weaker maxima at 510 and 560 nm. A more recent study of the green emission using a silicon-intensified target vidicon camera

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306

as a detector showed a banded spectrum with a strong maximum at 527 nm and two weaker maxima at 512 and 562 nm [ 111. The green emission from phosphorus has been used extensively for the determination of phosphorus in both organic and inorganic compounds, including gas chromatographic detection. The first important application was the flame photometric detector for gas chromatography [ 9,121. All volatile phosphorus compounds can be determined by this method after silylation. Recently, molecular emission cavity analysis (MECA) has been applied successfully to the determination of phosphorus using the HP0 emission. An automated MECA instrument was used for the determination of phosphorus in detergents after a rapid batch ion-exchange process to overcome the cationic depressive effects with a relative standard deviation of 0.9% and a detection limit of 2.5 ng of phosphorus [ 131. It is commonly believed that the emitting species is HPO. However, the identification of the spectral bands in the visible region has received little attention. This work was aimed at establishing whether one or more electronic excited states may be involved in the green emission from HP0 and to identify the origin of the strong maxima. Several workers have studied the structure of HP0 and its electronic states using ab initio calculations with different Gaussian basis sets [ 14-161. Some of these calculations included configuration interaction (CI) and Moller-Plesset perturbation corrections. However, only n+ rr*and z-+ rc*transitions were described for HPO. Other possible excited states have not been characterized. Reported here are the results of a study of a few lower excited states of HPO, using the INDO method with configuration interaction. The energies of the n+ r* and z-+ R” transitions are found to be fairly close to the ab initio results. The study also indicates that the lowest singlet excited electronic state of HP0 is responsible for the green emission in cool flames and that the stronger maxima originate mainly from an O+O electronic transition, accompanied by O+ 1 and l+O vibrational transitions involving P=O stretching and HP0 bending modes of vibration. METHOD OF CALCULATION

The ground and some excited states of HP0 were studied using the INDO method [ 171 with configuration interaction. In addition to the ground state, 36 spin-adapted configurations are considered, consisting of 9 singles and 27 doubles. These configurations are obtained from promoting one or two electrons in all possible ways from the three highest occupied to the three lowest unoccupied molecular orbitals of the ground state. Proper combinations of the resulting Slater determinants are formed to obtain singlet wave functions. A computer program was developed and carefully checked for carrying out configuration interaction calculations based on the INDO method.

307 TABLE 1 Parameters used m the calculations Atom

4,

H

1.000

0 P

2.2458 16000

rP

2.2660 1.6000

(atomic units )

Cd

- L’,

-Up

0 5333

0.5000 4 9570 2.4107

4 6520 2 0693

-cTd

I,

1,

0 7467

0.5000 12014 0 6250

0 3866

Li

0 6000 0 0490

In calculating the molecular orbitals of the ground state, the original INDO method [ 17 ] was used with slight modification in parametrization. The diagonal elements of the H matrix are given by

(1) where a and b are different atoms, ,Urepresents an atomic orbital and Zb is the core-charge of atom b. U; is considered as a parameter, and the integral in Eqn. 1 was computed with an s-type Slater orbital having the same exponent 5 and principal quantum number n as the orbital p. The off-diagonal elements HLbYbare given by

(2) where S,,, is the overlap integral and I, and I, are the ionization potentials corresponding to orbitals p and v on their respective atoms. Finally, two-centre coulomb integrals were calculated with s-type Slater orbitals having the proper 5 and n values. Everything else was as in the original INDO method. The modifications mentioned above make it easier, in practice, to extend the atomic orbital basis to include d orbitals, without impairing the basic characteristics of the INDO method. Table 1 shows the parameters adapted for HPO. These parameters produced the correct signs of the charges and led, after configuration interaction, to a first transition energy agreeing with the experimental value (see below ) . RESULTS OF CALCULATION

The ground state A Slater atomic orbital basis was used in the calculation. It contains the 1s orbital on H, 2s and 2p orbitals on 0, and 3s, 3p and 3d orbitals on P. Figure la shows the geometry utilized for HPO. The bond lengths were estimated from the atomic covalent radii, while the bond angle was optimized. It is known that the INDO method gives, in general, reasonable bond angles but underestimates bond lengths [ 18,191. These characteristics remained almost the same

308

s H

/

PSO

.

(00881) P----O

(-02433)

j,($ / H (01552) (a)

(b)

Fig. 1. (a) Geometry used in the calculation of transition energies; (b) INDO charge densities.

ev 11

-10

9

8 a(-J -

-2

(TT')LUMO 7

-3 t -4.

6

-5-6. -7. -6

a(+) a(-) a(*) cl(+) -

-1o-

5

4

-9 -

-11 .

HOMO ITT)

a(+)-

3

-12 2

-13 -14

1

-15 -16

t

a(*) 0,

i=-Lcc90

100 110 120 130 140

-+. oi

Fig. 2. Molecular orbital energy level diagram for HPO. The plus and minus signs mean symmetric and antisymmetric, respectively, with respect to the plane of the molecule and a.u. stands for atomic units. Fig. 3. Energy variations of the ground and lower excited states of HP0 as functions of the HP0 angle (c!).

309

after configuration interaction. The optimum bond angle of HP0 obtained in our calculation (103 o ) agrees fairly well with the angle calculated by ab initio methods, using the STO-2G* atomic orbital basis (104.5” ) [ 14,151, or combined with configuration interaction using the SD/6 31G** basis (105.3” ) [ 161. The molecular orbital energy diagram is depicted in Fig. 2. The HP0 molecule has one plane of symmetry (C, point group). The molecular orbitals are denoted as a’ ( + ) or a” ( - ) meaning, respectively, symmetric and antisymmetric with respect to the plane of symmetry. The highest occupied molecular orbital (HOMO) is of the a’ ( + ) type. It is an antiboncling combination of mainly p orbitals localized on oxygen and phosphorus atoms, with their axes lying in the plane of the molecule perpendicular to the P=O bond. This orbital has an n nature owing to the localization of its charge density on 0 and P atoms. The lowest unoccupied MO (LUMO) having a” ( - ) symmetry is a ti orbital localized on the P=O bond. The highest five MOs are mainly d orbitals localized, more or less, on the phosphorus atom. The percentage contribution of d orbitals of phosphorus to the different MOs may be expressed by: (3) where the Ci,s are the coefficients of the d atomic orbitals in the expansion of the ith MO. Table 2 contains the values of D for different MOs. The molecular orbitals in Table 2 are arranged in ascending order of energy, the top one being the lowest energy MO. Only the first six MOs are occupied in the ground state. The orbitals indicated by (7~) and (n*) are linear combinations of P, orbitals of phosphorus and oxygen atoms. It can also be noticed that the contributions of d atomic orbitals to the occupied MOs of the ground state of HP0 are negligible, whereas the three lowest unoccupied MOs have an appreciable contribution. TABLE 2 Molecular orbitals arranged in ascending order of energy contribution of the d orbitals No.

Symmetry

De(%)

No.

Symmetry

D* (%)

1 2 3 4 5 6 7

a’(+) a’(+) a’(+) a’(+) a” (- ), a’(+) a” (- )”

0.14 0.10 0.31 0.31 0.28 0.12 1.60

8 9 10 11 12 13 14

a’(+) a’(+) a”(--) a’(+) a”(-) a’(+) a’(+)

7.60 15.00 100.00 99.39 98.13 96.07 80.64

Cd) "D,=

100 1 C:,; for explanation, see text. /1

310 TABLE 3 Relative energes of the excited states State (symmetry)

Energy (eV)

State (symmetry)

Energy (eV)

GM’) &(A”) Ez(A”) &(A’) &(A’ ) &(A’) &(A 1 -%(A’)

0.000 2.408 (n, x*) 2.987 4.638 7.802 8.322 (71,n*) 9.225 9.375

&(A”) &(A’ 1

9.851 9.946 10.224 11.274 11.470 12.692 13.236 13.511

&,(A” 1 E,, (A ” 1 E,, (A’ ) 4, (A ” ) E,, (A ” ) E,, (A’ )

The excited states A configuration interaction calculation was carried out with 37 spin-adapted singlet configurations, including the ground state. The relative energies of the resulting excited states are given in Table 3 with their symmetry. These energies correspond to the geometry of the ground state. In an attempt to find which states are stable, the energies were also calculated as a function of the HP0 bond angle. Figure 3 shows the energy variation curves of the five lower excited electronic states. The curves indicate that the three lower states are bound. The lowest excited state corresponds to an n-t IT*transition with energy equal to 2.41 eV. Ab initio calculation gives 2.27 eV [ 161. The experimental value [20] is 2.3 eV. The second and third excited states also correspond to transitions from the a-framework to the x* orbital, whereas the x+x* transition leads to a state 8.32 eV above the ground state (highest curve in Fig. 3). The reported [ 161 ab initio value is 6.99 eV with an oscillator strength (f) of 0.130. Since we were interested mainly in the lower electronic states, no further analysis of the higher states was pursued. THE EMISSION SPECTRUM

It has become evident from the calculation that a green emission from HP0 could be due to a transition from the lowest excited electronic state E, (‘A ” ) (Fig. 3). Transitions from higher states to the ground state would emit light outside the observed wavelength range (570-490 nm). For example, a O-+0 transition from the E2 (‘A u ) state (Fig. 3) would give light at 415 nm. Such emission is not observed at cool flame temperature [ 111. Therefore, the bands in the green spectrum of HP0 must correspond to transitions from different vibrational levels of the first excited electronic state. Table 4 lists the observed emission maxima of HP0 in the visible region. The details of the spectrum have been published [ 111. To identify the strong bands in the spectrum, the theoretical transition energies have been derived from different vibrational

311 TABLE 4 Observed emission maxima in the visible region [ 111 Band

(nm)

Energy (cm-‘)

Relative strength*

Wl WZ

492 504

20 325.2 19 841.3

vw vw

521 512 545 562 569

19 18 531.3 975.3 18 348.6 17 793.6 17 574.7

; w3 C WA

vs 9 W S

vw

%=very; s=strong; w=weak. TABLE 5 Theoretical transition energy formulae Transition VI-+vN o-*0 041 l+O

Energy

Transition

Energy

(w,+de,)

0+2 z-+0 l-*2 2-l

w,--Zw(l-3x) w,+Zc~(l-3~) w,-0(1--4X) u,+o(l--4%)

00

w,-w(l-2x) 0,+0(1-2X)

levels of state E, (‘A” ) to those of the ground states. Table 5 shows the theoretical energies corresponding to 0 + 0,O + 1 and 1 -P0 transitions to the ground state. It is assumed that the vibrational energy of a given mode is given by (4) where w is the fundamental frequency (in cm -‘) of the corresponding mode, while w. in Table 5 is the energy (in cm- ’ ) of the O-+0 transition from E, (‘A” ) to the ground electronic state; x is the anharmonicity coefficient. The sum of the 0-t 1 and l+O transition energies, as can be seen from Table 5, is equal to 2wo, i.e. twice the O-+0 transition energy. This also implies that the O+l and 140 bands should be found on both sides of the O-+0 band. Based on this remark, three pairs of frequencies have been identified, in Table 4, whose sums are almost constant, namely: 18 348.6+ 19 531.3=37 879.9 cm-l-+~o= 19 841.3+17 793.6=37 634.9 cm-l-+wo=18 20 325.2 + 17 574.7= 37 899.9 cm-‘-+oo=

18 939.95 cm-’ 817.45 cm-’ 18 949.95 cm-’

The calculated values of m. from these pairs are of the same order as the fre-

312

quency of the strongest band of the spectrum (band b), that is, 18 975.3 cm-’ (Table 4). Therefore, it may be concluded that the strongest band b results from the 040 transition. The energy of this transition is equal to 2.35 eV, which compares favourably with the calculated energy of the El (‘Au ) electronic state (2.41 eV) of HPO. The fluctuation of the o. values found above could be due to different rotational energies. The pair of bands 19 531.3 and 18 348.6 cm-l may be identified with the l-+0 and O-1 transitions involving HP0 bending vibrational mode, respectively. Using the experimental fundamental frequency of this mode [ 161 (o=985 cm-‘), x=0.1998. The bands at 19 841.3 and 17 793.6 cm-’ may be 1 -SO and O-+1 transitions related to the P=O stretching mode. The experimental value of cr)of this mode [ 161 is 1188 cm-‘, which corresponds to x=0.0691. The last pair of bands at 20 325.2 and 17 574.7 cm-’ is more difficult to identify, since both intensities are very weak. It is not clear whether they arise from 2--+0 and O-+2 transitions, or from transitions involving combinations of vibrational modes, or perhaps from the pure H-P stretching mode. However, use of the above values of x leads to the conclusion that these bands are unlikely to be combination bands, nor do they correspond to transitions from higher vibrational levels. This leaves the possibility of pure H-P stretching bands. This would correspond to x=0.1725, assuming 0=2100 cm-’ [16]. Conclusion The absorption spectrum of HPO, due to n+n* or x+x* transitions, has not, to the authors’ knowledge, been reported. In addition, there is no mention in the literature of lower electronic states other than those arising from n-, n* and x+ n* transitions (including singlet and triplet states). The INDO and CI calculation indicates the existence of three other electronic states lying between the reported states (see Fig. 3). The probability of transition from the ground to one of these states, namely E2(lA” ) (Fig. 3), is not zero. Whether this result is an artefact of the INDO method with a limited CI calculation is not clear. It is worth mentioning, however, that the structured green emission spectrum of HP0 occurs only at low flame temperatures. The hot flame spectrum is perturbed, with no definite band structure. This could well be an indication of a perturbation resulting from vibronic interaction between closelying electronic states. If this is the case, then it follows that the interacting electronic states must both have similar (A")symmetry, because all the vibrational modes of HP0 have A ’ symmetry. This conclusion would support the existence of an A ' state close to the reported lower one, E, (A"). The authors are indebted to the Computer Centre of the U.A.E. University for free access and generous computer time.

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