predicting ph vibrations of gas phase molecules and surface-adsorbed species using bond...

Predicting PH Vibrations of Gas Phase Molecules

and Surface-Adsorbed Species Using Bond

Length-Frequency Correlations

UJJAL DAS, KRISHNAN RAGHAVACHARI

Department of Chemistry, Indiana University, Bloomington, Indiana 47405

Received 19 June 2008; Revised 9 October 2008; Accepted 10 November 2008DOI 10.1002/jcc.21187

Published online 29 December 2008 in Wiley InterScience (www.interscience.wiley.com).

Abstract: The high frequency XH (e.g., X 5 C, Si) stretching modes in small molecules are only slightly per-

turbed by other vibrational modes present in the system. The isolated frequencies, in these cases, exhibit a linear

relationship with the corresponding bond lengths. Here, we study such a bond length-frequency correlation in the

case of PH stretching vibrations for molecules in the gas phase as well as for surface-adsorbed species. Although a

high degree of linear correlation is found, there is a small dependence on the local coordination around P, leading to

significant deviations in some cases. By a careful analysis, we show that such correlations can be used to predict

new surface frequencies without computing the Hessian matrix explicitly.

q 2008 Wiley Periodicals, Inc. J Comput Chem 30: 1872–1881, 2009

Key words: bond length; frequency; linear correlation; surface vibrations; DFT

Introduction

The high frequency XH (e.g., X 5 C, Si) stretching modes pro-

vide a convenient channel to probe the local chemical bonding

environment in molecules. An efficient way to obtain vibrations

free from complicated couplings is to measure the ‘‘isolated’’ XH

stretching frequencies where the molecule is completely deuter-

ated barring a single proton.1 In two separate studies, McKean

et al.2 and Bernstein3 have obtained such isolated CH stretching

frequencies for many hydrocarbon analogues, and have shown

that a linear correlation prevails between these frequencies and

the corresponding bond lengths. McKean and coworkers4 have

also established a similar relationship between the isolated SiH

stretching frequencies and the SiH bond lengths in silanes and

silyl halides. Besides experiments, computational studies investi-

gating the substituent effects on the CH stretching frequencies

have also seen similar correlations and have revealed that the

inclusion of the electron correlation effects significantly improves

the accuracy of the predicted frequency shifts.5–8 In addition to

the case of strong covalent bonding discussed earlier, correlation

between the IR frequency shifts and the changes in equilibrium

bond lengths are also observed in systems containing weak inter-

actions such as hydrogen bonding.9,10 Although the relationship

between bond length and the corresponding stretching frequency

in such molecular systems are very well studied,11–13 a similar

analysis have not been attempted for molecules that are either

weakly or covalently attached onto a solid surface, and is the

subject of the present work.

Surface infrared spectra are often used to characterize the na-

ture of the chemical species formed by surface-molecule interac-

tions resulting in a functionalized surface.14–16 However, it is of-

ten very difficult to assign the individual surface frequencies

purely from the recorded IR spectra. Electronic structure calcula-

tions in such cases have proven to be very effective as a com-

plementary tool needed to provide definitive assignments of the

experimental infrared frequencies for surface-adsorbed mole-

cules. The surface is frequently modeled using a small cluster of

atoms. However, an accurate description of the surface elec-

tronic structure demands much larger cluster models.17 Despite

the cutting-edge computational facilities in these days, there is

an optimal point where a large cluster can only be energetically

optimized but calculations of the force constants to get the fre-

quencies may be prohibitively expensive using an accurate level

of model chemistry. In this work, we discuss the scope of apply-

ing the concept of bond length-frequency correlations as an al-

ternative approach to obtain frequencies of the surface adsorbed

species bypassing the costly task of computing the second order

energy derivatives.

Contract/grant sponsor: The Petroleum Research Fund; contract/grant

number: PRF 43465-AC10

Contract/grant sponsor: The National Science Foundation; contract/grant

number: CHE-0616737

Correspondence to: K. Ragavachari; e-mail: [email protected]

q 2008 Wiley Periodicals, Inc.

This work has been presented in three different sections. (1)

First, we discuss the PH stretching frequencies in gas phase mo-

lecular systems. Similar to the CH and SiH vibrations,2–4 PH

stretches also appear very high (above 2000 cm21) and are usu-

ally free from any contamination coming from coupling to other

vibrational modes. The calculated isolated PH frequencies show

a linear correlation with the associated bond lengths. (2) A simi-

lar analysis is then performed for different PH bonds produced

upon adsorption and dissociation of phosphine on In-rich or P-

rich indium phosphide (InP) surfaces. One of the reasons for

selecting this particular surface is that our group is currently

exploring the surface chemistry of this compound semiconduc-

tor. Here again, we see a linear relationship between the com-

puted isolated PH frequencies and the corresponding bond

lengths. (3) Finally, we discuss how such correlations can be

applied to predict new surface vibrations without analytical or

numerical evaluation of the force constant matrix.

Computational Methods

In this study, the isolated P-H stretching frequencies are com-

puted by deuterating all the hydrogens in the system except the

one of interest. This helps to avoid complex coupling interac-

tions (e.g., Fermi resonance)18 between the different modes that

complicate the analysis of the observed vibrational frequencies.

For the gas phase molecules, the calculations use the B3LYP

hybrid density functional method in conjunction with the polar-

ized Dunning-Huzinaga double-f type basis sets (D95 1 d func-

tions on the heavy atoms and p functions on H, denoted as

D95**).19–23 Because D95 basis sets are available only for the

first and second row elements, gas phase molecules containing

In atoms are treated with a similar all electronic valence double-

f type basis set (vide infra). Tight convergence criteria and

ultrafine integration grids have been used for the computation of

the structures and force constants of the stationary points to

increase the precision of the computed frequencies. In all cases,

only the harmonic vibrational frequencies are computed. In the

case of the isolated PH frequencies, the anharmonic effects may

be expected to be nearly the same in all the molecules. The

good agreement between theory and experiment indicates that

this is indeed a reasonable assumption.

The indium phosphide (001) surfaces can be either In-rich or

P-rich depending on the method of preparation.24,25 We consider

both of these surfaces in this study. (1) The In-rich d(2 3 4)

surface provides a platform to study vibrations of the PHx (x 51–3) species produced by adsorption and subsequent dissociation

of phosphine on this surface. This relatively complex surface is

terminated mostly with In-In dimers. In addition, there is an In-

P adatom dimer in each unit cell to provide additional stability

to this particular reconstruction.26 A cluster model representing

this surface is shown in Figure 1. The empty dangling bonds on

the surface indium atoms are available during PH3 adsorption

and subsequent reactions. (2) We also study the P-rich (2 3 1)

surface that is terminated with a complete monolayer of phos-

phorus dimers. This surface, when dosed with atomic hydrogen,

produces different PH vibrations.27 The cluster model of the

hydrogen stabilized buckled (2 3 1) surface is displayed in

Figure 2. The termination of the cluster back-bonds in these

systems has been achieved by considering the proper balance

between both covalent and dative bonds, a general characteristic

of III-V compound semiconductors. While the covalent bonds

are truncated with hydrogen atoms, the dative bonds at indium

are replaced with PH3 groups to provide an appropriate local

bonding environment. Additional information on the electronic

distributions of the surfaces and details of the surface modeling

can be found in our earlier publications.26–30

The surface calculations are also performed at the DFT level

using the B3LYP hybrid functional. The surface indium atoms

in the In-rich surface and the second-layer indium atoms in the

P-rich surface (and the indium atoms in the gas phase molecules

Figure 1. An optimized cluster model of the In-rich indium phos-

phide surface. Color scheme: black (In) and grey (P).

Figure 2. An optimized cluster model of the H-stabilized P-rich in-

dium phosphide surface. The inset shows three hydrogen atoms

adsorbed per dimer.

1873Predicting PH Vibrations of Gas Phase Molecules and Surface-Adsorbed Species

Journal of Computational Chemistry DOI 10.1002/jcc

mentioned earlier) are treated with an all-electron (18s/14p/9d)/[6s/5p/3d] contracted basis set while the rest of the bulk In

atoms are treated with the Stuttgart-Dresden pseudopotential

(SDD) and the associated double-zeta basis set to simplify the

calculations.31,32 To be consistent with the gas phase studies, the

same D95** basis set is applied to the P and surface H atoms.

For hydrogen atoms used in cluster backbond termination, the

extra polarization functions are removed from the above basis

set. The development version of the Gaussian 03 software pro-

gram is used to perform all these calculations.33

Results and Discussion

Gas Phase Molecules

The isolated harmonic PH stretching frequencies for 32 different

test molecules are listed in Table 1 along with the corresponding

PH bond distances. Among these, there are 27 molecules con-

taining a single phosphorus atom that can be considered as

mono- or di-substituted phosphines and their datively bonded

complexes. Gas phase experimental data on PH stretching fre-

quencies are available for 14 of these molecules (Table 2) and

solid state vibrational data is available for some of the dative-

bonded systems. In addition, we have considered five other more

complex molecules. These molecules contain multiple phospho-

rus atoms in cage-like structures that more closely resemble sur-

face-adsorbed species (Fig. 3). These molecules are assembled

to simulate a more complex environment, and there is no avail-

able experimental data for these systems.

Roughly, one third of the molecules listed in Table 1 have

only one PH bond. The remaining molecules have two or more

PH bonds. However, even in those molecules, the PH bonds are

all exactly equivalent because of symmetry (for the conformers

listed). Thus, all of these molecules show only one distinct

isolated PH stretching frequency. The molecules C2H5PH2,

CH3SiH2PH2, and C2H3PH2 have multiple conformers with simi-

lar energies. The listed frequencies correspond to the most stable

isomer for each species (trans isomers for C2H5PH2 and

CH3SiH2PH2, and the syn isomer for C2H3PH2, respectively).

Comparison of the calculated frequencies with the available ex-

perimental values (Table 2) indicates that all of them are overes-

timated at the level of theory considered in this study. This over-

estimation is mostly due to the neglect of anharmonicity, though

other intrinsic deficiencies of the theoretical model also contrib-

ute to the observed deviations.

Before trying to correlate the individual stretching frequen-

cies with the corresponding bond lengths, we give an estimation

of the quality of the computed results. The frequency shifts,

defined as the difference between the isolated PH stretching fre-

quency in a test molecule and that in a reference molecule (in

this case PH3), are presented in Table 2. The overall range of

this frequency shift is about 200 cm21. The shifts are mostly

negative except for the dative bonded compounds where they

are significantly positive. The most negative frequency shift is

observed in PHF2, clearly because of the strong electronegative

effect of the directly attached fluorine atoms. The most positive

shifts are seen for the dative bonded complexes. This is due to

the larger s character in the PH bonds in such complexes result-

ing in shorter bond lengths and higher vibrational frequencies.

Finally, for alkyl and silyl substituted phosphines, the frequency

shifts become slightly more negative as the side-chain length

increases.

Table 2 also includes the observed PH frequencies for some

of the species and the corresponding experimentally derived fre-

quency shifts. Although the isolated frequencies have been

directly observed in few cases, they have been derived in several

other cases as the (weighted) average of the measured symmetric

and asymmetric frequencies (for molecules containing PH2 or

PH3 groups). The computed frequency shifts are in very good

agreement with the available experimental information for most

of the species.34–45 The largest deviations between theory and

experiment are seen for the compounds containing multiple fluo-

rines, though the deviations are still reasonable. In addition to

the frequency shifts that have been measured in the gas phase,

the frequency shifts for several of the dative bonded complexes

Table 1. Computed Bond Lengths (A) and Isolated PH Stretching

Frequencies (cm21) for Different Gas Phase Molecules.

Molecule r(P–H)

Isolated frequency

Diff.Calculated Predicted

PH3 1.4270 2394 2382 12

PH3��BH3 1.4152 2461 2459 3

PH3��BCl3 1.4111 2491 2486 5

PH3��InH3 1.4177 2449 2442 7

PHCl�

1.4344 2342 2333 8

HP¼¼CF2 1.4272 2391 2380 11

H2P��CF3 1.4250 2407 2395 12

H2P��SiH3 1.4279 2381 2376 5

H2P��Cl 1.4290 2372 2369 3

H2P��CH3 1.4283 2375 2373 2

H2P��SiH2��CH3 1.4286 2375 2371 4

H2P��CH2��CH3 1.4294 2367 2366 1

H2P��CH¼¼CH2 1.4300 2363 2362 1

H2P��CBCH 1.4273 2379 2380 21

H2P��OH 1.4308 2353 2357 24

H2P��InH2 1.4273 2380 2380 0

F��PH2��BH3 1.4147 2460 2462 22

C2H5��PH2��BH3 1.4175 2439 2444 25

Al4P4O2H12 1.4167 2443 2449 25

In2P2H8 1.4152 2450 2459 29

F��PH��F 1.4398 2297 2298 22

F��PH��Cl 1.4344 2329 2334 25

Cl��PH��Cl 1.4295 2358 2365 27

CH3��PH��CH3 1.4295 2357 2365 28

CH3��PH��SiH3 1.4289 2365 2369 24

SiH3��PH��SiH3 1.4285 2370 2372 22

InH2��PH��InH2 1.4256 2384 2391 27

(CH3)2��PH��BCl3 1.4122 2473 2478 25

(CH3)2��PH��BH3 1.4175 2433 2443 210

Al4P4H8 1.4129 2447 2474 226

B4P4H8 1.4213 2382 2419 237

In4P4H8 1.4166 2422 2449 227

The predicted frequencies (cm21) are from the linear correlation in

Figure 4 (see text).

1874 Das and Raghavachari • Vol. 30, No. 12 • Journal of Computational Chemistry


of phosphines with boranes have been measured in the solid

state (not listed).46–49 The large positive values of the computed

frequency shifts are consistent with the values derived from such

solid state measurements.

Figure 4 illustrates the linear correlation between the calcu-

lated PH bond lengths and the associated isolated stretching fre-

quencies. When these data were analyzed initially, we found that

three of the molecules that resemble 3-dimensional cage struc-

tures (see Figure 3a) did not fit the linear correlation. Thus, we

have excluded these three molecules from the linear fit shown in

Figure 4. As mentioned earlier, a similar linear relationship was

also obtained by other research groups for the CH and SiH iso-

lated frequencies. This linear relationship can be used to predict

the isolated frequencies of the 29 molcules included in the fit

with an average absolute error of 5.2 cm21 and a maximum devi-

ation of 12 cm21. This suggests that such correlations can be

useful to predict new isolated PH frequencies.

The three molecules that do not fit the linear correlation are

the near-cubic systems B4P4H8 (deviation of 37 cm21), Al4P4H8

(deviation of 26 cm21), and In4P4H8 (deviation of 27 cm21).

These have Td symmetries and have two interpenetrating P4 and

X4 (X 5 B, Al, In) tetrahedra (nearly cubic) with a hydrogen

atom at each vertex. They have an environment significantly dif-

ferent from the other systems. They have a PH unit with the P

atom attached to three heavy (nonhydrogen) atoms where the

bonding is neither covalent nor dative but is a mixture of the

two. Alternatively, they can be considered as a linear combina-

tion of different resonance structures. The bond angles around

the P are also significantly larger than the typical values (90–

1008) seen for other systems. It is apparent that in such cases

the simple correlation between the bond length and the isolated

frequency is no longer valid. Interestingly, the other ‘‘cage’’

molecules containing PH2 groups (see Figs. 3b and 3c) show

smaller deviations. Also note from Table 1 that the predicted

frequencies are in general lower than the computed values in the

case of molecules with a terminal PH2 group. In contrast, the

predicted PH frequencies are generally higher than the directly

computed values when the P atoms are attached two or three

nonhydrogen atoms. We will analyze this further in the discus-

sion of similar surface-bound species.

Although isolated frequencies as considered above are a use-

ful measure of the local bonding environment, they give no

Table 2. Comparison of the Calculated and Experimental Isolated P��H

Stretching Frequencies (cm21) for Gas Phase Molecules.

Molecules Sym

Isolated

frequency Frequency shift

Calc. Expt.a Calc. Expt.

PH3 C3v 2394 2324 0 0

PH3��BH3 C3v 2461 67

PH3��BCl3 C3v 2491 97

PH3��InH3 C3v 2449 55

PHCl�

Cs 2342 2278 252 246

HP¼¼CF2 Cs 2391 2327 23 3

H2P��CF3 Cs 2407 2328 13 4

H2P��SiH3 Cs 2381 2311 213 213

H2P��Cl Cs 2372 2307 222 217

H2P��CH3 Cs 2375 2307 219 217

H2P��SiH2��CH3 Cs 2375 2299 219 225

H2P��CH2��CH3 Cs 2367 2301 227 223

H2P��CH¼¼CH2 Cs 2363 2297 231 227

H2P��CBCH Cs 2379 2316 215 28

H2P��OH Cs 2353 241

H2P��InH2 Cs 2380 214

F��PH2��BH3 Cs 2460 66

C2H5��PH2��BH3 Cs 2439 45

Al4P4O2H12 D2d 2443 49

In2P2H8 D2h 2450 56

F��PH��F Cs 2297 2242 297 282

F��PH��Cl C1 2329 265

Cl��PH��Cl Cs 2358 236

CH3��PH��CH3 Cs 2357 2288 237 236

CH3��PH��SiH3 C1 2365 2293 229 231

SiH3��PH��SiH3 Cs 2370 224

InH2��PH��InH2 Cs 2384 210

(CH3)2��PH��BCl3 Cs 2473 79

(CH3)2��PH��BH3 Cs 2433 39

Al4P4H8 Td 2447 53

B4P4H8 Td 2382 212

In4P4H8 Td 2422 28

Frequency Shift with Respect to PH3.aRef. 34–45.

Figure 3. Molecules containing multiple phosphorous atoms.



account of the inter-bond coupling present in such molecules

that can lead to frequency splitting. As a result, though they are

relatively ‘‘pure’’, they can deviate from the measured frequen-

cies of the associated split modes. We have shown previously

that this splitting is usually quite significant for molecules con-

taining CH bonds.6 The isolated and the actual frequencies will

be close to each other only when the extent of bond-bond inter-

actions is less significant and some of these examples are

discussed below.

The PH stretching frequencies in molecules like PHF2,

(CH3)2PH, PHCl�, and PHCF2 containing a single PH bond are

free from any contamination coming from the inter-bond interac-

tions. In contrast, such interactions are prevalent in molecules

like CH3PH2 or CF3PH2 containing two equivalent PH bonds.

We can estimate the extent of such interactions by computing

the splitting, resulting from the coupling of two equivalent PH

bonds. Here, the splitting is obtained from the difference

between the asymmetric and the symmetric PH vibrations.

They are shown in Table 3 for several test molecules. The com-

puted splittings are in good agreement with the experimental

values.40–42,50–52 The small splitting, on average 7 cm21, for

these molecules indicates that the extent of coupling between

the pairs of modes is indeed fairly small. The change in such

splitting induced by the deuterium substitution (i.e., interaction

of two P��D bonds) gives a sensitive measure of the effect of

the local geometry and is also known for most of these mole-

cules. Interestingly, these changes are also not very significant

(as can be seen from Table 3, the computed splitting of 7 cm21

in PH2CH3 becomes 10 cm21 in PD2CH3 giving a net change of

only 3 cm21). Overall, we see that unlike the CH bonds, the

splitting between the two PH (or PD) frequencies is quite small.

In addition, there are relatively small changes in splitting on

going from PH2 to PD2 groups. These observations are consist-

ent with the HPH bond angle being close to 908 for most of

these systems.

In a similar manner, there is a splitting between the symmet-

ric (nondegenerate, a) and asymmetric (degenerate, e) stretchingfrequencies in the case of PH3 or in dative bonded systems such

as PH3BCl3 containing three equivalent PH bonds. The HPH

bond angle in dative bonded systems opens out to about 99 or

1008, and the splitting between the modes is correspondingly

larger (about 10–20 cm21).

Surface-Adsorbed Molecules

First, we consider the In-rich InP surface. There are three chemi-

cally distinct indium sites that can interact with PH3 molecules

on this surface. They are marked as atoms 1, 3, and 5 in Figure

1 (the other two indium atoms labeled 4 and 6 are already tetra-

coordinate and do not interact with PH3). We have considered

phosphine adsorption and dissociation on each of these atoms.

In general, we have computed three different binding states for

phosphine. (1) The dative-bonded phosphine (In��PH3), similar to

some of the complexes considered in the case of gas-phase mole-

cules, (2) the covalently attached phosphorus dihydrogen species

(In��PH2), similar to many of the substituted phosphines consid-

ered earlier, and (3) the bridged phosphides (In��PH1,2��In). In

these examples, ‘‘In’’ represents a surface indium atom. In addi-

tion, there is a PH bond formed between a surface phosphorus

atom (labeled 2 in Fig. 1) and hydrogen. Unlike the gas phase

molecules, the PH bonds are not all equivalent in the surface

adsorbed PH3 and PH2 units. This change is due to the effect of

the local geometric and electronic structure of the surface atoms

resulting from their asymmetric environment. As in the case of

Figure 4. The correlation plot of the computed PH bond length (A)

versus the corresponding isolated PH frequency (cm21) for different

gas phase molecules. The filled symbols correspond to the five cage

molecules that are excluded from the linear fit (see text).

Table 3. Frequency Splitting Between Asymmetric and Symmetric PH

(or PD) Vibrations (cm21).

Molecules Bond

masym—msym

Theo. Expt.

H2PCH3 P��H 7 4a

D2PCH3 P��D 10 7a

H2PCF3 P��H 8 8a

D2PCF3 P��D 11 10a

PH2SiH3 P��H 9 14a

PD2SiH3 P��D 11 10a

H2P��CH2��CH3 P��H 7 6b

D2P��CH2��CH3 P��D 10 5b

H2P��CH¼¼CH2 P��H 21 1b

D2P��CH¼¼CH2 P��D 4 3b

H2P��SiH2��CH3 P��H 9 9b

D2P��SiH2��CH3 P��D 11 na.

aref. 50–52bref. 40–42



the gas phase molecules considered earlier, in the dative-bonded

complexes (In��PH3) where the P atom is fourfold-coordinated,

the average P��H bond length (�1.418 A) is shorter than in

comparable In��PH2 species (�1.430 A). As a result, the PH

stretching frequency in the latter goes down by �80 cm21. The

P��H bond lengths and the isolated stretching frequencies in dif-

ferent surface adsorbed species are listed in the first three col-

umns of Table 4. Unfortunately, there is not enough information

available to directly compare these computed isolated surface

PH frequencies with experiment.

The direct adsorption of hydrogens on the P-rich InP surface

also produces PH bonds. The surface structure for one hydrogen

atom adsorbed per P��P dimer has been shown in Figure 2. In

this case, the surface dimer bond remains intact. Alternatively,

the surface may be completely saturated with hydrogens, in

which case, the P��P bond breaks and the PH2 and PH species

are formed on the surface (inset, Fig. 2). The PH bond distances

and the computed frequencies on the P-rich surface are reported

at the end of Table 4.

Similar to the gas phase molecules, we have plotted the sur-

face PH frequencies against the corresponding bond lengths and

obtained a linear correlation. Here also, two of the surface fre-

quencies deviate significantly from the fitted trendline (videinfra). Thus, we have excluded these two frequencies and plot-

ted the remaining 20 isolated frequencies versus the correspond-

ing bond lengths (see Fig. 5). Using this linear correlation, the

different surface PH frequencies can be reproduced with a mean

absolute error of 6.4 cm21 and a maximum deviation of 10

cm21. The two excluded species (shown in dark in Fig. 5) have

deviations larger than 20 cm21. Both of these have a P atom

bound to three other heavy (nonhydrogen) atoms, as in the case

of the excluded species in the gas phase analysis.

Although we have investigated a simple bond length-fre-

quency correlation thus far, a closer examination of Table 4

(and Fig. 5) reveals that that the computed bond length-fre-

quency correlation depends slightly on the local coordination of

the phosphorous atoms. The schematic diagram of the different

surface units presented in Figure 6 shows that the P atoms in the

surface bound PH3 and PH2 species are attached to one heavy

atom (in this case indium). We call them ‘‘type 1’’ species and

their predicted frequencies (from the linear regression) are typi-

cally lower than the directly computed values. On the other

hand, in the bridged phosphides, the P atoms are sandwiched

between two indium atoms. In such ‘‘type 2’’ species, the pre-

dicted frequencies are typically slightly higher than the directly

computed values. Finally, in the ‘‘type 3’’ species, the P atoms

are attached to three other surface heavy atoms and these are the

two previously identified species with deviations larger than 20

cm21. Although we could fit three different lines through the

points, we have chosen to fit only one line after excluding the

two species with the largest deviations. Finally, with a cluster

model half of the size of the model shown in Figure 1, we were

able to reproduce similar heavy-atom effects on the surface fre-

quencies. This suggests that the observed trend is independent of

the size of the surface models.

Thus far, we have treated the gas phase species and surface

species separately. However, as the entire surface calculations

Table 4. Bond Distances (A) Calculated and the Predicted (from the

Linear Correlation in Figure 5) Isolated PH Frequencies (cm21) for

Different Surface Adsorbed Species on the In and P-rich InP Surfaces.

Species r(P–H) Calculated freq. Predicted freq. Diff.

In-rich surface

1–PH3 1.4193 2438 2430 8

1.4179 2444 2440 4

3–PH3 1.4187 2439 2434 6

1.4172 2449 2445 4

5–PH3 1.4203 2429 2422 6

1.4172 2451 2445 6

1–PH2 1.4303 2353 2351 2

3–PH2 1.4300 2361 2353 8

1.4297 2362 2356 7

5–PH2 1.4294 2364 2358 7

1.4298 2362 2355 7

3–PH2–4 1.4200 2416 2424 29

1.4185 2430 2435 25

5–PH2–6 1.4198 2417 2426 29

1.4191 2423 2431 28

3–PH–4 1.4326 2333 2335 23

5–PH–6 1.4316 2339 2342 24

P(2)–H 1.4220 2389 2410 221

P-rich surface

3–PH2–4 1.4200 2414 2425 210

1.4145 2456 2463 27

5–PH–6 1.4285 2354 2364 210

P(1)–H 1.4183 2411 2437 226


versus the corresponding isolated PH frequency (cm21) for different

surface species. The filled symbols correspond to surface species

that are excluded from the linear fit (see text).



are done using cluster models by treating them as molecules, we

may expect to see similar bond length-frequency correlation for

both gas phase molecules and surface-bound species. All the

molecules are plotted together in Figure 7 showing a single lin-

ear correlation. Again the filled symbols indicate the frequencies

where the P atoms are attached to multiple heavy atoms. The

quality of the linear fit obtained here (the maximum and mean

absolute deviations are 15 and 6 cm21, respectively) is compara-

ble to the individual gas phase and surface correlations shown in

Figures 4 and 5, respectively. Note that the linear behavior of

the plot indicates that the gas phase and the surface isolated

frequencies can be treated together as far as the theoretical fre-

quencies are concerned. This is particularly important as this

suggests that, if necessary, the surface frequencies can be esti-

mated based purely on the computed gas phase structure-fre-

quency correlations.

Predicting New Vibrations

In the previous section, we have seen that the bond length-fre-

quency relationship can be used to predict the isolated frequen-

cies from the computed bond lengths. However, we would also

like to correct for the systematic errors in the computed frequen-

cies to predict the observed frequencies in the gas phase as well

as for surface-adsorbed species.

We know that the frequencies computed within the harmonic

approximation usually overestimate the corresponding experi-

mental frequencies. The extent of such overestimation typically

depends on the type of the vibration. In our case, if we look

back at Table 2, the mean deviation between the computed har-

monic frequencies and the corresponding experimentally

observed PH frequencies for gas phase species is approximately

65 cm21. As discussed earlier, this is due to the neglect of

anharmonicity as well as the inherent deficiencies of the theoret-

ical model used. Interestingly, this difference between the com-

puted and the observed frequencies is substantially larger for

surface-adsorbed species. The most well-characterized InP sur-

face frequency is for the P-rich surface containing a single

hydrogen, observed at 2308 cm21 (denoted as P(1)–H in Table

3). If we compare it with the computed harmonic frequency

(2411 cm21), the overestimation is 103 cm21. The rough magni-

tude of this value is consistent with several previous studies27–30

where a uniform shift of 110 cm21 has been used to correct the

computed PH vibrations on indium phosphide surfaces. Thus, it

appears that the computed surface frequencies are overestimated

significantly more (by about 40 cm21) than their gas phase

counterparts. The reason for this difference between the gas

phase and the surface is not clear though; it could be an artifact

of the adopted cluster models and has been discussed in more

detail in the last section. However, we can now use this piece of

information and the bond length-frequency linear relationship to

predict observable surface frequencies.

Figure 6. Different types of PH bonds on the In-rich and P-rich

indium phosphide surfaces.


versus the corresponding isolated PH frequency (cm21) for both gas

phase molecules as well as surface species. The filled symbols cor-

respond to molecules and surface species that are excluded from the

linear fit (see text).



To derive reliable predictions of the observable PH frequen-

cies on surfaces, we can use the following steps. First, using the

optimized surface PH bond lengths, we can derive the corre-

sponding isolated frequencies from the linear correlation as dis-

cussed earlier. In addition, because the surface frequencies show

some dependence on the local coordination of the phosphorous

atoms, the frequencies need to be shifted down by 20 cm21 if

the PH unit is attached to three other surface heavy atoms. From

our earlier analysis, the predicted isolated frequencies derived

using such a procedure are likely to be reliable to within a few

wavenumbers. The PH frequencies can then be uniformly shifted

down by 105 cm21 to correct for the known overestimation of

surface frequencies. A similar procedure can be followed for

predictions involving gas phase molecules except for applying a

smaller correction factor of 65 cm21. Alternatively, the pre-

dicted isolated frequencies can be scaled down by an appropriate

amount to take into account the known overestimations. Obvi-

ously, the scaling factor would vary depending on the type of

vibrations. Note that the use of a uniform scale factor to correct

for the systematic errors in the computed frequencies is a com-

mon practice in the computational chemistry community.53

The predicted frequencies discussed so far yield the isolated

PH modes that may be different from the experimentally

observed surface PH vibrations. The experimental frequencies

are typically obtained without any deuterium substitution. Never-

theless, because we know that the intra-mode coupling in PH3

and PH2 species are comparatively weak, the predicted isolated

frequencies should be within the range of the corresponding

vibrations observed in the experiments. As a rough guide, we

can guess that the splitting of a terminal PH2 group is around 5–

10 cm21 and the splitting in a bridging PH2 group will be larger

(10–20 cm21). The splitting in the case of a dative-bonded phos-

phine is also similar, though there can be further symmetry low-

ering on the surface. In addition, in cases where the inter-mode

coupling between the neighboring surface species is important,

they need to be taken into account.

Although many PH frequencies have been experimentally

observed on InP, most of their assignments are from our own

previous papers.27–30 Thus to avoid circular arguments, we have

not included a more detailed comparison between the predicted

frequencies and the experimental frequencies in this article.

However, the close agreement between the predicted isolated

frequencies and directly computed frequencies is very encourag-

ing and demonstrates that this simple approach can be used to

make similar assignments.

We now discuss the applicability of bond length-frequency

correlations shown in Figure 5 to predict isolated PH vibrations

on other surfaces. For this, we consider phosphine adsorption

and dissociation on the Si(100)–2 3 1 surface that has a similar

surface architecture as the P-rich InP surface. The surface has

been modeled using a Si9H12 cluster successfully used in many

previous surface calculations.54 Structures A and B shown in

Figure 8 resemble type 1 species because the P atoms here are

attached to one surface Si atom. On the other hand, species C

and D, in which cases the P atoms are attached to two Si atoms,

are similar to type 2 species. The computed bond lengths, the

corresponding isolated PH frequencies, as well as the predicted

frequencies for these species (using the linear regression from

Fig. 5) are listed in Table 5. The very good agreement between

the predicted and the computed results supports the usefulness

of such an approach in calculating the isolated surface vibra-

tions.

Finally, we discuss the possible reasons for the gas phase fre-

quencies being overestimated by 65 cm21 whereas similar sur-

face frequencies are overestimated by 105 cm21. What causes

this additional 40 cm21 difference? This may be partly due to

the inherent differences in the measurements because of solid

state perturbations. For example, the PH vibrational frequency

for dimethylphosphine has been measured to be 2288 cm21 in

the gas phase and 2269 cm21 in the solid.55 In addition, it may

be partly due to the deficiency of treating surfaces using small

cluster models. While a surface is an infinitely extended system,

representing it using clusters of a few atoms may not be suffi-

cient to include the contribution of the surface dielectric to the

calculated vibrational properties. To investigate this further, we

have computed the PH vibration in species D (see Fig. 7) using

one, three, five, and seven dimer cluster models of the Si(100)-

(2 3 1) surface. We have noticed that as the size of the cluster

increases, there is a simultaneous small increase in the PH bond

length. On going from a single dimer model to a seven-dimer

Figure 8. Different types of PH bonds on the Si(100)-(2 3 1) sur-

face.

Table 5. Bond Lengths, (A) Calculated and Predicted (from the Linear

Correlation in Figure 5) Isolated Surface PH Frequencies (cm21)

on the Si(100)-(2 3 1) surface.

Species Bond length Calculated freq. Predicted freq. Diff

Si��PH3 1.4179 2435 2439 24

1.4122 2482 2480 2

Si��PH2 1.4275 2378 2371 7

Si��PH2��Si 1.4174 2439 2443 24

Si��PH��Si 1.4284 2359 2365 26



model, the increase in the PH bond length is �0.0016 A. This is

equivalent to a drop of nearly 11 cm21 in the computed fre-

quency (from the correlation seen earlier). Considering the infi-

nite nature of the surface, a seven-dimer cluster model is still

quite small in size. Moreover, we have not included the contri-

bution of deeper layers to the computed frequency. An alterna-

tive possibility is to perform solid state calculations using

Periodic Boundary Conditions (PBC) to ensure that the surface

species feel the effects of the entire extended system. However,

efficient second derivative techniques for the computation of the

vibrational frequencies for extended systems are not yet widely

available. It will be interesting to perform such PBC calculations

involving many layers to investigate this more thoroughly in the

future.

We should also note that although the density functional

methods considered in this article are inexpensive enough to

compute the vibrational frequencies explicitly, the ideas pre-

sented in this article will be very useful for other methods such

as MP2 where there is a larger mismatch between the computa-

tional expense involved in a structure determination relative to

that for the computation of the force constants and the harmonic

frequencies.

Conclusions

We have studied the relationship between PH bond lengths and

isolated frequencies for gas phase molecules as well as for sur-

face-adsorbed species. In all cases, we observe a good correla-

tion between the bond length and the corresponding isolated

vibrational frequency with a small dependence on the local coor-

dination of the P atoms. By a careful analysis, we can use such

correlations to predict new isolated vibrational frequencies for

gas phase molecules as well as for those adsorbed on surfaces

without computing the force constant matrix explicitly.

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predicting ph vibrations of gas phase molecules and surface-adsorbed species using bond...

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