Force Field and Assignment of the Vibrational Spectrum of Anthracene


A complete set of force constants and their corresponding scale factors were obtained by fitting the experimental frequencies of naphthalene-d0 and -d...
0 downloads 4 Views 362KB Size


J. Phys. Chem. 1996, 100, 13963-13970

13963

Force Field and Assignment of the Vibrational Spectrum of Anthracene: Theoretical Prediction D. Chakraborty, R. Ambashta, and S. Manogaran* Department of Chemistry, Indian Institute of Technology, Kanpur 208016, India ReceiVed: December 13, 1995; In Final Form: April 10, 1996X

A complete set of force constants and their corresponding scale factors were obtained by fitting the experimental frequencies of naphthalene-d0 and -d8 to the ab initio force field obtained at the HF/4-21G level. A recently developed fitting procedure is used for this purpose with a modification. The fitting is extremely successful in producing a force field which reproduces the frequencies within an average deviation of 5.7 cm-1 for naphthalene-d0 and 4.0 cm-1 for naphthalene-d8 from the experimentally observed fundamentals. The ab initio force constants of anthracene were obtained using the same level of theory and scaled using the scale factors of naphthalene. The earlier assignments were either confirmed or reassigned utilizing the frequencies and potential energy distributions derived from the scaled force field. The agreement between the experimental and predicted fundamentals were excellent for this molecule containing 24 atoms, giving an average deviation of 8.2 cm-1.

Introduction The vibrational spectra of polyaromatic hydrocarbons and their cations received much attention recently due to their importance as the origin of infrared emission bands in the intersteller radiation from many gallactic sources.1 Naphthalene is the smallest member in the family and was studied by severals authors.2-18 Pulay et al. reported for the first time a complete theoretical force field of naphthalene obtained by using the scale factors from their benzene work.3 However, benzene and naphthalene are not really structurally related (naphthalene is a coupled ring system), and the direct transfer of scale factors from benzene leads to poor predicted numbers. A geometry refinement which includes the approximate cubic force constants was needed to obtain a good fit between experimental and predicted frequencies of naphthalene. Also, the number of force constants listed for naphthalene (208) is more than the number of symmetric force constants (189). More recently the vibrational spectra of naphthalene and its radical cation were studied using matrix isolation spectroscopy by Szczepanski et al.2 The second simplest member, anthracene, is also studied by several theoretical and experimental methods.19-28 The early work of Bruhn and Mecke21 and Califano22 identified many of the fundamental frequencies of anthracene and anthracene-d10 on the basis of their polarization measurements. The IR spectra of anthracene and anthracene-d10 crystals were analyzed by Bree and Kydd.23 Bakke et al. using a five parameter approximation analyzed all the in-plane fundamentals of anthracene and proposed their probable assignments.20 More recently, Szczepanski et al. analyzed the vibrational spectra of anthracene and its radical cation using matrix isolation spectroscopy.19 On the theoretical side, a detailed calculation of the normal modes of anthracene and anthracene-d10 was reported by Krainov using the complete system of induction coefficients from naphthalene.25 A simplified valence force field calculation for benzene, naphthalene, and anthracene was reported by Neto et al.9 Evans and Scully26 reported a theoretical calculation for the out-ofplane vibrations of anthracene, anthracene-d2, and anthracened10 by transferring the benzene force constants. Although a number of vibrational spectral studies have been reported for X

Abstract published in AdVance ACS Abstracts, July 1, 1996.

S0022-3654(95)03694-X CCC: $12.00

anthracene, some of the assignments still remain uncertain and the complete force field is not yet available. In this paper we report the ab initio force field of naphthalene and anthracene at the HF/4-21G level. We explicitly show that the benzene molecule is not structurally related to anthracene, whereas naphthalene and anthracene are structurally related. Using the newly developed fitting procedure,29 we report a set of 189 nonredundant local force constants which reproduces the naphthalene fundamental frequencies with an average error of 5.7 cm-1. The scale factors obtained from naphthalene force constants were used to obtain the complete anthracene force field which simulates the vibrational spectra of anthracene with remarkable accuracy. It is to be noted that no experimental data are used in the prediction of anthracene frequencies. Methodology The ab initio force constants and frequencies of naphthalene and anthracene were calculated by the numerical differentiation of analytically determined first derivatives of the energy with respect to the nuclear displacements using the 4-21G basis set30 available in the GAMESS program package.31 The Cartesian force constant matrix was then transformed to the nonredundant local coordinate space following the recommendation of Pulay et al.30 The nonredundant local coordinates of naphthalene and anthracene are shown in Table 1 and Figure 1. The ab initio force constants in nonredundant internal coordinates were then scaled using the scale factors obtained from our new scaling procedure described in detail elsewhere.29 The number of force constants getting adjusted due to the change in frequencies is smaller when the fitting is done in symmetry blocks compared to local coordinates. Hence, the fitting is done in symmetry coordinates by adjusting the scale factors in local coordinates. The fitting procedure involves a small perturbation in each step of the iteration. As in any perturbation, the effect is the mixing of eigenvectors of the unperturbed system. Using first order perturbation theory

L ) i

Li0

(Lj0)t∆F(Li0) +∑ Lj0 λi - λj i*j

(1)

When the eigenvalues are far off, the mixing is very small. When © 1996 American Chemical Society

13964 J. Phys. Chem., Vol. 100, No. 33, 1996

Chakraborty et al.

TABLE 1: Nonredundant Local Coordinates (a) Of Naphthalenea In Plane S1-11 ) R(CC stretch)(Ri) S12-19 ) r(CH stretch)(ri) S20-27 ) 2-1/2(φ1 - φ2); 2-1/2(φ3 - φ4); ... (CH-deform)(βi) S28,31 ) 6-1/2(R1 - R2 + R3 - R4 + R5 - R6)(ring deform)(δ1,δ4) S29,32 ) 12-1/2(2R1 - R2 - R3 + 2R4 - R5 - R6)(ring deform)(δ2,δ5) S30,33 ) 2-1/2(R2 - R3 + R5 - R6)(ring deform)(δ3,δ6) Out of Plane S1-8 ) γ(CH wag)(γi) S9,12 ) 6-1/2(τ1 -τ2 + τ3 - τ4 + τ5 - τ6)(ring torsion)(τ1,τ4) S10,13 ) 12-1/2(τ1 - 2τ2 + τ3 + τ4 - 2τ5 + τ6)(ring torsion)(τ2,τ5) S11,14 ) 2-1/2(τ1 - τ3 + τ4 - τ6)(ring torsion)(τ3,τ6) S15 ) τ3126 - τ4215(τ) (b) Of Anthraceneb In Plane S1-16 ) R(CC stretch)(Ri) S17-26 ) r(CH stretch)(ri) S27-36 ) 2-1/2(φ1 - φ2); 2-1/2(φ3 - φ4); ... (CH deform)(βi) S37,40,43 ) 6-1/2(R1 - R2 + R3 - R4 + R5 - R6)(ring deform)(δ1,δ4,δ7) S38,41,44 ) 12-1/2(2R1 - R2 - R3 + 2R4 - R5 - R6)(ring deform)(δ2,δ5,δ8) S39,42,45 ) 2-1/2(R2 - R3 + R5 - R6)(ring deform)(δ3,δ6,δ9) Out of Plane S1-10 ) γ(CH wag)(γi) S11,14,17 ) 6-1/2 (τ1 - τ2 + τ3 - τ4 + τ5 - τ6)(ring torsion)(τ1,τ4,τ7) S12,15,18 ) 12-1/2(τ1 - 2τ2 + τ3 + τ4 - 2τ5 + τ6)(ring torsion)(τ2,τ5,τ8) S13,16,19 ) 2-1/2(τ1 - τ3 + τ4 - τ6)(ring torsion)(τ3,τ6,τ9) S20 ) τ7342 - τ1348(τ′) S21 ) τ15610 - τ9562(τ′′) a All internal coordinates are according to Figure 1a. b All internal coordinates are according to Figure 1b.

Figure 1. Internal coordinates of (a, top) naphthalene and (b, bottom) anthracene.

they are close, the mixing could be substantial. Since the isolated molecule (ab initio) gets perturbed by the environment in the real system, when the experimental frequencies are used in the fitting, this effect is more realistic and acceptable. A brief description of the modified procedure is given as a flow chart in Figure 2.

clearly that the benzene force field is very different from that of naphthalene. For naphthalene our fitted force field shows a good agreement with the earlier SQM predicted force field in both in-plane and out-of-plane diagonal force constants. Obviously such good agreement is not expected in the case of the coupling constants because of the oversimplification involved in the evaluation of the coupling force constants in the SQM procedure. The fitted force field produced frequencies for both naphthalene and naphthalene-d8 better than the earlier SQM prediction, so it can be considered as an improvement over the earlier force field. A representative set of force constants of naphthalene and anthracene is listed in Table 2, and the complete force field is available as Supporting Information from which we can draw the following conclusions. (1) C-H diagonal force constants of naphthalene and anthracene are almost identical except for a minor deviation of the anthracene central ring. Interactions involving C-H bonds (σ bond) are small, and only the first neighbors contribute significantly. (2) C-C force constants exhibit similar trends, although the absolute values are different because of π-π interaction. The trend and the accuracy of the predicted C-C frequencies indicate the transferability of the scale factors. The diagonal force constants are in accordance with the Huckel π bond order.32 Interactions involving C-C bonds (σ and π bonds) are much stronger and extend over the entire ring in both systems, confirming the earlier preliminary conclusion based on only naphthalene.33 (3) Diagonal fβis are almost the same for the naphthalene and anthracene. CHi-βi interactions are less than 0.01 and negligible in most cases. CCi-βi interactions are substantial only for the connecting bonds. For outer rings of naphthalene and

Results As pointed out by Pulay et al.3 in their SQM study of naphthalene, the naphthalene force field is quite different from that of benzene and hence simple transfer of the benzene force field would poorly reproduce the naphthalene fundamental vibrational frequencies. So, our present method also fails to achieve a better fit for naphthalene by simple transfer of benzene scale factors, largely because of the absence of interring CCCC couplings in benzene. However, it is possible to predict the vibrational frequencies of anthracene from naphthalene as naphthalene and anthracene resemble each other even in CCCC couplings. Because the prediction requires a complete set of scale factors, we fitted the experimental frequencies of naphthalene-d0 and -d8 to the theoretically calculated ab initio HF/4-21G force field. The fitting produced an excellent agreement between the experimental and the calculated frequencies. The average deviation is 5.7 cm-1 (4.0 cm-1 in C10D8) including C-H frequencies and 3.6 cm-1 (2.4 cm-1 in C10D8), excluding C-H frequencies. Force Field of Naphthalene and Anthracene. The force constant values obtained for benzene are 6.716 for C-C stretch, 5.181 for C-H stretch, 0.510 for C-H deformation, 1.271 and 1.236 for ring deformation, and 0.318 and 0.386,0.304 are for out of plane C-H wagging and ring bending, respectively. These, when compared to naphthalene force constants, indicate

Vibrational Spectrum of Anthracene

J. Phys. Chem., Vol. 100, No. 33, 1996 13965

Figure 2. Flow chart for the fitting algorithm. Note: Rewind (1) should be shifted to the next box, after nm=0 in Step 3. (Uortho and symf matrices are available as Supporting Information).

anthracene they are almost the same, while the central ring has slightly higher values. (4) Diagonal ring deformation force constants are similar for naphthalene and the outer rings of anthracene and somewhat higher for the central ring. These conclusions clearly indicate that the force field of the outer rings of anthracene is almost identical with that of naphthalene and the central rings differ to some extent. As a result, the prediction is excellent for the outer ring modes of anthracene, and the deviation is slightly more from the experimental frequencies for the central ring. Vibrational Spectra of Naphthalene. The 48 normal modes of naphthalene in D2h symmetry factorize in 8 symmetry blocks

as 9Ag, 8B3g, 8B1u, 8B2u, 4Au, 4B3u, 3B1g, and 4B2g. The calculated fundamentals from the fitting procedure of naphthalened0 and -d8 are given in Table 3, along with their assignments. The assignments agree well with that of Pulay et al. in almost all of the modes. However, there is a controversy regarding one of the B2u fundamentals. It could be at 1144 or 1163 cm-1. In the SQM method, the predicted number 1158 cm-1 was closer to 1163 cm-1. We tried fitting both frequencies separately. The frequency 1163 cm-1 gave the C-C force constants in agreement with the expected bond orders. As a result we assigned it at 1163 cm-1. In B1u, the band at 810 9,11-12 and 748 cm-1 6 were suggested as possible alternatives for the δ1 + δ3 mode.

13966 J. Phys. Chem., Vol. 100, No. 33, 1996

Chakraborty et al.

TABLE 2: Selected Scaled Force Constants of Naphthalene and Anthracenea naphthalene

anthracene

local coordinates

force constants

π bond order

local coordinates

force constants

π bond order

(R1,R3,R7,R11) (R4,R6,R8,R10) (R5,R9) (R2) (R1,r1) (R6,r1) (r1,r1) (R4,r3) (R5,r3) (r3,r3)

6.076 7.513 6.112 5.607 0.060 0.076 5.113 0.075 0.096 5.153

0.554 0.725 0.603 0.518

(R1,R3,R12,R16) (R4,R6,R13,R15) (R5,R14) (R2,R9) (R1,r1) (R6,r1) (r1,r1) (R4,r3) (R5,r3) (r3,r3) (R7,r5) (R8,r5) (r5,r5)

5.695 7.988 5.703 5.242 0.057 0.077 5.115 0.076 0.093 5.155 0.092 0.092 5.085

0.535 0.738 0.586 0.485

C-C Coupling R1(nap) R1(anth) r1(nap) r1(anth) β1(nap) β1(anth) R1(nap) R1(anth) r1(nap) r1(anth) β1(nap) β1(anth)

R1

R2

R3

R4

R5

R6

R7

R8

6.076 5.695 0.060 0.057 -0.183 -0.183

0.586 0.442 -0.015 -0.015 0.001 0.005

-0.332 -0.241 -0.020 -0.019 0.017 0.016

0.301 0.217 -0.016 -0.016 -0.019 -0.017

-0.438 -0.363 0.002 0.001 0.005 0.003

0.608 0.529 0.076 0.077 0.164 0.167

0.705 0.769 0.003 0.004 0.018 0.018

-0.169 -0.253 0.004 0.007 0.001 0.000

R12

R13

R14

R15

R16

R9

R10

r11

0.073 0.025 0.005 0.005 -0.006 -0.006

-0.251 -0.193 0.013 0.008 0.000 0.000

0.135 0.141 -0.001 -0.002 -0.004 -0.003

0.103

-0.047

0.053

-0.051

0.042

0.000

0.002

-0.002

0.001

-0.001

-0.001

0.000

0.000

0.000

0.000

C-H Coupling r1(nap) r1(anth)

r1

r2

r3

r4

r5

r6

r7

r8

5.113 5.115

0.002 0.002

0.004 0.004

0.011 0.011

0.013 0.011

0.001 0.002

0.000 0.000

0.002 0.000

r1(anth) a

r9

r10

0.000

0.000

Stretch, bend, and stretch-bend constants are in mdyn/Å, (mdyn Å)/rad, and mdyn/rad, respectively.

The fitting using 810 cm-1 produced 805 cm-1 as the calculated fundamental, while 748 cm-1 produced 765 cm-1 as the calculated frequency. This clearly indicates that the 810 cm-1 band is more likely to be the correct one, and this is in agreement with the earlier SQM assignment. C-H Stretching Vibrations. Due to anharmonicity and the perturbations because of Fermi resonance, the C-H fundamentals are difficult to assign. However, we used the following strategy to address the effect of anharmonicity on the naphthalene frequencies. We started with the assumption that the anharmonicity of the C-H and C-D bonds are the same for benzene and naphthalene because the C-H force constants are nearly the same (5.181, C6H6; 5.113, R-C10H8; 5.153 (β-C10H8) and the C-H and C-D stretching frequencies appear in the same narrow range of frequencies. The harmonic frequencies could be estimated from the equation

wi ) νi + ∆i

(2)

where ∆i represents the total anharmonic corrections to the fundamental frequency. Following Goodman et al.34 we adopted a 117 cm-1 anharmonic correction for C-H fundamentals and 59 cm-1 for C-D ones. The second assumption we made is that the deuterated fundamentals are not perturbed by Fermi resonance because there is no frequency in the 1100-1150 cm-1 range whose overtone can interact with the C-D fundamentals

(2200-2300 cm-1). (However, it is possible to have a combination band of the right frequency. We neglect such a possibility because without further experimental data this problem could not be addressed.) The best fitted C-D fundamentals are converted to harmonic frequencies based on eq 2 and fitted to get the harmonic force constants. During the fitting all C10H8 and C10D8 frequencies other than C-H stretching ones are used. The computed harmonic force constants are in good agreement with the benzene value obtained by Goodman et al.34 (5.567, C6H6; 5.459, R-C10H8; 5.486, β-C10H8). These harmonic force constants are used to predict the harmonic C-H frequencies which in turn are used to calculate the corresponding anharmonic frequencies using eq 2. The predicted anharmonic frequencies agree well with the observed fundamentals except for one of the B3g modes (3031 cm-1), as shown in Table 4, indicating that this particular frequency is a likely candidate for Fermi resonance. The computed mean amplitudes of vibration (Figure 3) are in good agreement with the reported values,35,36 indicating that the final force field is reliable. Vibrational Spectra of Anthracene. Anthracene is planar with D2h symmetry and is characterized by 66 vibrational degrees of freedom. The 45 in-plane and 21 out-of-plane normal vibrations span the irreducible representations as 12Ag + 11B3g + 11B1u + 11B2u + 4b1g + 6b2g + 5a1u + 6b3u. The

Vibrational Spectrum of Anthracene

J. Phys. Chem., Vol. 100, No. 33, 1996 13967

TABLE 3: Fitted ab Initio (4-21G) Frequencies of Naphthalene symmetry blocks A1g

B3g

B1u

B2u

A1u

B3u

B1g B2g

av error av error a

SQMa

present work d0

d8

3079 3053 1579 1461 1384 1166 1023 762 513 3063 3046 1632 1455 1245 1153 940 508 3066 3050 1594 1395 1271 1129 805 358 3077 3048 1509 1354 1208 1154 1008 620 975 837 591 190 962 781 476 166 954 712 392 992 887 772 472 [5.7] [3.6]

2285 2253 1554 1292 1381 837 861 691 494 2270 2249 1602 1355 828 1024 882 491 2274 2252 1546 1254 1044 887 740 327 2284 2250 1446 1294 1090 839 827 593 816 657 501 171 790 629 401 153 762 538 345 871 758 635 417 [4.0] [2.4]

d0

d8

3085 2289 3056 2257 1590 1563 1458 1287 1385 1385 1170 838 1023 860 757 689 505 486 3067 2273 3047 2246 1644 1617 1458 1359 1255 833 1156 1030 940 879 512 495 3070 2275 3049 2249 1595 1546 1391 1248 1272 1049 1137 882 792 737 354 323 3083 2288 3052 2253 1515 1446 1341 1288 1204 1081 1158 840 1002 826 626 600 981 815 825 647 622 531 188 169 969 797 777 627 480 404 172 159 952 761 705 532 387 341 987 857 879 766 773 634 471 413 incl C-H excl C-H

experimenta

HF/6-31G*b scaled (d0)

d0

d8

PED

3085 3056 1645 1453 1355 1134 1043 780 517 3069 3046 1673 1461 1219 1149 917 491 3071 3047 1654 1364 1261 1130 781 364 3083 3052 1539 1321 1165 1091 988 596 970 824 606 184 977 791 485 172 968 708 397 985 880 785 478

3060 3031 1578 1460 1380 1163 1020 761 514 3055 (3055)c 1624 1458 1240 1158 939 508 3056 3029 1595 1389 1265 1125 810 359 3056 3029 1509 1361 1209 1163 1008 619 970 841 581 195 958 780 476 166 951 717 386 983 876 772 470

2291 2257 1553 1298 1386 835 863 692 493 2276 2257 1605 1353 828 1027 883 491 2295 2278 1545 1260 1045 885 734 326 2295 2258 1445 1290 1089 840 828 594

r3 + r1 r1 + r3 R4 + R5 + δ2 β1 + β2 + R5 r2 + R1 + R4 β2 + β1 R5 + β1 + R4 R1 + R2 + δ2 δ2 + R1 r3 + r1 r1 + r3 R4 + R1 + β1 β2 + R1 + R4 β1 + R1 + δ1 β2 + β1 + R4 δ1 δ3 R3 + R1 r1 + r3 R4 + β2 β2 + β1 + R1 β1 + R1 + δ1 δ1 + β2 + R4 + β1 δ1 + δ3 + R1 δ3 + R1 r3 + r1 r1 + r3 R5 + β2 + R1 + β1 R4 + β1 R1 + β2 β1 + R1 + β2 + R4 R5 + R4 + β1 δ2 γ3 + γ1 γ1 + γ3 τ1 + γ1 τ2 + τ1 γ1 + τ3 + γ3 γ3 + γ1 τ3 + τ + γ3 τ + τ3 γ1 + γ3 γ3 + γ1 τ3 + γ3 γ3 + γ1 + τ1 + τ2 γ1 + γ3 τ1 + τ2 τ2 + γ1 + γ3

791 629 401 153 766 541 350 875 761 646 413

Reference 3. b Reference 2. c Number in the parantheses is not used in fitting.

fundamental frequencies of anthracene are predicted separately by transferring scale factors of benzene and naphthalene, respectively. Table 5 shows the predicted frequencies obtained from the scale factors of benzene and naphthalene along with their assignments. The table clearly indicates that transferring the diagonal force constants and taking their geometric mean for the off-diagonal elements give poor agreement compared to transferring all of the scale factors. When the molecules are structurally related, the assumption that each force constant is associated with its own scale factor works well rather than the geometric mean of diagonal force constants for the off-diagonal elements because the characteristics of each force constant are retained. The average devations for the 66 frequencies are 15.0, 13.5, and 9.2 cm-1 (13.6, 13.2, and 8.2 cm-1 excluding the CH stretch) for the different predictions, as shown in Table 5. As expected, the predicted anthracene frequencies from naphthalene scale factors are better than those predicted from benzene, even in geometric mean approximation. In the prediction, corrections

for basis set error, correlation and anharmonicity were transferred through scale factors from naphthalene to anthracene. In-Plane Frequencies. C-H Stretching Vibrations. The ν(C-H) frequencies appear as independent modes, and all of the C-H stretching fundamentals appear in the region ν > 3000 cm-1. To address the problem of anharmonicity, the harmonic scale factors are transferred from naphthalene to anthracene to predict the harmonic frequencies. The harmonic frequencies are then corrected for anharmonicity as in the case of naphthalene. The final values are given in Table 4 along with the experimental numbers. The agreement is good for six frequencies, indicating the other four are possibly perturbed by Fermi resonance. Ag Modes. The frequencies in this block are only Raman active, and the earlier assignments proposed by several authors are quite consistent and agree within the experimental error. One of the RCC bands in the earlier assignment was doubtful, either at 1412 or 1400 cm-1,20 which was resolved later by

13968 J. Phys. Chem., Vol. 100, No. 33, 1996

Chakraborty et al. TABLE 5: Predicted Vibrational Frequencies of Anthracene symmetry benzene blocks GMa A1g

B3g

B1u Figure 3. Mean amplitudes of vibration of naphthalene and anthracene (Å). Numbers are obtained from our predicted force field. Numbers in the parentheses are observed values taken from ref 36.

TABLE 4: Anharmonic and Harmonic Frequencies and Force Constants of C-H and C-D Vibrations of Naphthalene and Anthracene Naphthalene anharmonic symmetry blocks A1g B3g B1u B2u fC-HR fC-Hβ

harmonic

C10D8

C10H8

expt3

C10D8

C10H8

2291 2257 2276 2257 2295 2278 2295 2258 5.113 5.153

3060 3034 3046 3031 3048 3034 3058 3030

3060 3031 3055 (3055) 3056 3029 3056 3029

2350 2315 2334 2315 2354 2336 2354 2316 5.459 5.486

3177 3150 3162 3146 3164 3150 3175 3145

B2u

A1u

Anthracene symmetry blocks A1g B3g B1u

B2u fC-HR fC-Hβ fC-H

C14H10

C14H10

expt19

3177 3150 3141 3164 3149 3165 3150 3150 3143 3176 3148 5.461 5.489 5.429

3079 3052 3040 3066 3049 3066 3050 3050 3042 3079 3051 5.115 5.155 5.085

3072 3048 3027 3054 3017 3084 3052 3052 3022 3067 3021

assignment at 1412 cm-1 to the A1g mode and 1400 cm-1 to the B2u fundamental.19 The predicted numbers 1408 and 1404 cm-1 agree very well with the later assignment. The prediction is poor only in the case of the 1264 cm-1 band with a deviation of 21 cm-1. This is clearly due to the differences between the naphthalene and anthracene force constants for the diagonal R1,

B3u

B1g

B2g

ave error ave error

-19 -15 -28 -28 3 -9 4 -15 13 1 3 8 -22 -39 -37 -24 -2 -13 -11 -1 -13 1 10 7 -5 -30 -44 -7 24 5 -12 1 7 5 -24 -40 -28 10 -7 35 -2 38 19 16 6 -11 17 -6 7 9 -18 -17 12 7 14 19 -14 16 11 22 -23 1 29 -9 6 29 [15.0] [13.6]

naphthalene GMa allb -8 -4 -17 -9 -10 6 -11 -11 1 9 0 3 -11 -28 -46 -22 -4 -13 -8 -6 -20 -2 7 18 6 -20 -30 -18 13 0 -7 -5 0 3 -12 -29 -23 8 13 38 1 31 5 18 4 -6 18 5 -9 3 -26 -20 14 8 4 19 -22 20 12 20 -19 7 36 24 21 22 [13.5] [13.2]

-7 -4 -13 -3 -4 4 -21 -8 8 5 -1 0 -12 -32 -2 0 -4 -20 0 -1 -13 -2 9 18 2 -20 -9 -7 6 1 -4 -4 7 2 -12 -30 -18 15 -4 33 0 -13 5 13 1 4 3 4 0 0 -12 -16 5 4 -1 19 -8 9 8 21 -9 0 21 16 29 24 [9.2] [8.2]

exptc

PED

3072 3048 3027 1561 1480 1412 1264 1164 1007 754 625 397 3054 3017 1632 1596 1384d 1433 1273 1187 1098 903 522 397 3084 3052 3022 1627 1450 1346 1272 1151 908 652 234 3067 3021 1542 1460 1400 1318 1167 1124 998 809 603 988 858 743 (491)f 126 958 879 726 469 380 106 956 760 479 244 977 916 852,e 896 773 580 287 incl CH excl CH

r3 + r1 r1 + r3 r5 R4 + R2 + R5 + R7 R5 + β3 + β1 + R7 R2 + R4 + R1 + R7 R1 + R7 + β1 β3 + β1 R5 + R4 + β1 R2 + δ2 + R7 + R1 δ2 δ2 + R7 + R1 r3 + r1 r1 + r3 R4 + R7 + R1 R7 + R4 β3 + β1 + R1 β5 + β1 β1 + β5 + R1 R1 + β3 + R4 δ1 δ3 δ2 r3 + r1 r1 + r3 + r5 r5 + r1 R4 + R1 β3 + R1 + R7 R7 + δ1 + β3 β1 + δ2 + R1 β3 + β1 + R4 δ1 δ3 + δ1 + R1 δ3 + R7 r3 + r1 r1 + r3 R4 + R5 + R7 β1 + β3 + R5 + R1 R2 + β5 + R1 + R4 R7 + β5 + β1 β3 + R1 + β5 R7 + β1 + R4 R5 + β1 R1 + R2 δ2 γ3 + γ1 γ1 + γ3 τ1 + τ2 τ2 + γ1 + τ1 τ2 + τ1 γ1 + γ3 + τ3 γ5 + τ3 + γ3 γ1 + γ3 + γ5 τ′′ + τ′ + τ3 τ3 τ′ + τ′′ + τ3 γ1 + γ3 + τ3 γ1 + γ3 τ′ + τ′′ + τ3 τ3 + τ′′ + τ′ γ3 + γ1 γ5 + γ3 γ1 + γ3 + γ5 τ1 τ1 + γ1 + τ2 τ2 + τ1

a Geometric mean of the respective diagonal scale factors are taken for the off-diagonal scale factors. b All (diagonal and off-diagonal) scale factors are taken. c Reference 19. d Reference 23. e Reference 26. f Number in the parentheses is our predicted frequency.

Vibrational Spectrum of Anthracene R7 and their interactions. B3g Modes. In this block a weak Raman band observed by Bakke et al.20 at 1574 cm-1 was assigned at 1596 cm-1 by Neto et al.9 and Colombo.24 Our predicted number 1596 cm-1 exactly matches with the latter assignment. So we confirm this mode at 1596 cm-1. With this modification all predicted frequencies match well with the earlier assignments except the one at 1433 cm-1. This band shows a deviation of 55 cm-1, the predicted one being at 1388 cm-1. It is unlikely that the force fields of naphthalene and anthracene are very different to cause this much error. It is likely that either this assignment is incorrect or something like Fermi interaction occurs for this mode. Bakke et al. observed a Raman band at 1384 cm-1,20 which agrees well the predicted value of 1388 cm-1. It is interesting to note that the earlier calculated values based on NCA also occur at 1389 9 and 1396 cm-1.25 B1u Modes. These IR and Raman active bands are available from the more recent work.19 The agreement with the earlier experimental numbers are within a few cm-1, except for the one at 1346 cm-1. The earlier workers assigned this band at around 1317 cm-1.9,20-24,28 The predicted frequency at 1340 cm-1 agrees well with the recent assignment. All of the other predicted numbers in this block agree very well with the experimental numbers. B2u Modes. This is probably the most controversial block in the anthracene spectra. Deviations of 100-150 cm-1 could be found in the existing assignments. The RCC band is assigned at different frequencies by different authors. Frequencies 1695,23 1720,24 1690,20 1533,9,22 and 1524 28 cm-1 are some of the available assignments. The most recent work19 assigned it at 1542 cm-1. The predicted number 1560 cm-1 confirms this assignment. The other controvertial bands were assigned at 1460, 1400, and 1318 cm-1 in the latest work.19 For the 1460 cm-1 fundamental earlier assignments were made at 1534,20 1533,23 1680,24 and 1462 cm-1.9,22 The predicted number that appears at 1445 cm-1 is in agreement with 1460 cm-1. The 1400 cm-1 band was assigned at 1494,20 1398,9,22 1495,23 1537,24 and 1350 28 cm-1. Our predicted frequency 1404 cm-1 confirms the assignment at 1400 cm-1. The predicted frequency corresponding to the experimental 1318 cm-1 band19 occurs at 1283 cm-1, off by 33 cm-1. This band corresponds to R7 + β5, which represents the central ring, and there is no exact counterpart of this in naphthalene. Hence, the deviation is higher than the expected one. Out-of-Plane Frequencies. A1u Modes. This class is inactive in both Raman and IR spectra of the free molecule, and hence comparison is made with the IR active crystal bands. Only three out of five fundamentals were reported.20,21,27 The highest frequency mode was assigned at 988 20 and 979 cm-1.27 The predicted value 984 cm-1 is closer to the first one. The other two bands agree between the different authors as well as with the predicted ones. For the two lower frequencies the predictions are at 491 and 126 cm-1. Early work of Chantry et al.27 gives the experimental frequency at 126 cm-1. B3u Modes. The highest frequency in this symmetry is assigned at around 956 2,20-24,27 and at 920 cm-1.28 The predicted frequency 970 cm-1 supports the higher number in agreement with most of the literature. The next higher band is assigned as 883 20 and 879 cm-1.19 These are within experimental error, and we took the most recent value of 879 cm-1 for the predicted value 895 cm-1. The other three numbers are in excellent agreement with the most recent paper.19 It is of interest to note that the torsional numbers > 300 cm-1 were predicted very well compared to the out-of-plane wagging fundamentals. Again this is a reflection of the differences in

J. Phys. Chem., Vol. 100, No. 33, 1996 13969 force fields between naphthalene and anthracene. It is known that the ab initio method gives a very low value for the torsions below 300 cm-1. B1g and B2g Modes. The earlier work of Evans and Scully26 do not agree with that of Bakke et al.20 It appears that the only reliable values are that of Bakke et al.20 for these modes. Although there is overall agreement between the predicted and the experimental frequencies, deviations are quite large in three of the fundamentals assigned at 896, 773, and 580 cm-1. The 896 cm-1 band, if assigned at 852 cm-1,26 gives better agreement with the predicted 831 cm-1. An experimental reinvestigation of these frequencies may give a better agreement with the prediction. Conclusion The fitting procedure to obtain the scaled force constants and scale factors from the ab initio force field has shown to be remarkably successful for naphthalene, giving an average deviation of 5.7 cm-1 between fundamental and experimental frequencies. When these scale factors were used to predict the frequencies of anthracene, the results were shown to be in excellent agreement with the experimental ones with an average deviation of 8.2 cm-1 for a molecule of 24 atoms. From the highly accurate predicted frequencies it is clear that the methodology could be used successfully for the prediction of unknown molecules. The earlier assignments of naphthalene were confirmed, and the anthracene assignments were confirmed or reassigned. A complete set of nonredundant force constants were obtained for both naphthalene and anthracene. Supporting Information Available: Tables of the symbolic force constant matrices in terms of symmetry unique local force constants and the orthogonal transformation matrices from local to symmetric coordinates for naphthalene and anthracene and the complete mean amplitudes of the vibration of naphthalene (9 pages). Ordering information is given on any current masthead page. References and Notes (1) Szczepanski, J.; Vala, M. Nature 1993, 363, 699. (2) (a) Szczepanski, J.; Roser, D.; Personette, W.; Eyring, M.; Pellow, R.; Vala, M. J. Phys. Chem. 1992, 96, 7876. (b) Pauzat, F.; Talbi, D.; Miller, M. D.; Defrees, D. J.; Ellinger, Y. J. Phys. Chem. 1992, 96, 7882. (3) Sellers, H.; Pulay, P.; Boggs, J. E. J. Am. Chem. Soc. 1985, 107, 6487. (4) (a) Hanson, D. M.; Gee, A. R. J. Chem. Phys. 1969, 51, 5052. (b) Hanson, D. M. J. Chem. Phys. 1969, 51, 5063. (5) Behlen, F. M.; Mcdonald, D. B.; Sethuraman, V.; Rice, S. A. J. Chem. Phys. 1981, 75, 5685. (6) Krainov, E. P. Opt. Spektrosk. 1964, 16, 415, 763. (7) Freeman, S. D. E.; Ross, I. G. Spectrochim. Acta 1960, 16, 1393. (8) Mitra, S. S.; Bernstein, H. J. Can. J. Chem. 1959, 37, 553. (9) Neto, N.; Scorocco, M.; Califano, S. Spectrochim. Acta 1966, 22, 1981. (10) Bree, A.; Kydd, R. A. Spectrochim. Acta 1970, 26A, 1791. (11) Scully, D. B.; Whiffen, D. H. Spectrochim. Acta 1960, 16, 1409. (12) Ohno, K. J. Mol. Spectrosc. 1978, 72, 238. (13) (a) Luther, H.; Feldmann, K.; Hampel, B. Z. Electrochem. 1955, 59, 1008. (b) Luther, H.; Brandes, G.; Guenzler, H.; Hampel, B. Z. Electrochem. 1955, 59, 1012. (14) Stenman, F. J. Chem. Phys. 1971, 54, 4217. (15) Lippincot, E. R.; O’Reilly, E. J. J. Chem. Phys. 1955, 23, 238. (16) Hollas, J. M. J. Mol. Spectrosc. 1962, 9, 138. (17) Rich, N.; Dows, D. Mol. Cryst. Liq. Cryst. 1968, 5, 111. (18) Pietila, L. O.; Stenmann, F. Commentat. Phys.-Math. Soc. Sci. Fenn, 1978, 48, 145. (19) Szczepanski, J.; Vala, M.; Talbi, D.; Parisel, O.; Ellinger, Y. J. Chem. Phys. 1993, 98, 4494. (20) Bakke, A.; Cyvin, V. N.; Whitmer, J. C.; Cyvin, S. J.; Gustavsen, J. E.; Klaeboe, P. Z. Naturforsch. 1979, 43, 579. (21) Bruhn, W.; Mecke, R. Z. Elektrochem. 1961, 65, 543.

13970 J. Phys. Chem., Vol. 100, No. 33, 1996 (22) Califano, S. J. Chem. Phys. 1962, 36, 903. (23) (a) Bree, A.; Kydd, R. A. J. Chem. Phys. 1968, 48, 5319. (b) Bree, A.; Kydd, R. A. J. Chem. Phys. 1969, 51, 989. (24) Colombo, L. Spectrochim. Acta 1964, 20, 547. (25) Krainov, E. P. Opt. Spektrosk. 1964, 16, 984. (26) Evans, D. J.; Scully, D. B. Spectrochim. Acta 1964, 20, 891. (27) Chantry, G. W.; Anderson, A.; Browning, D. J.; Gebbie, H. A. Spectrochim. Acta 1965, 21, 217. (28) Mecke, R.; Bruhn, W.; Chafik, A. Z. Naturforsch. A 1964, 19, 41. (29) Manogaran, S.; Chakraborty, D. J. Phys. Chem. submitted for publication. (30) Pulay, P.; Fogarasi, G.; Pang, F.; Boggs, J. E. J. Am. Chem. Soc. 1979, 101, 2550. (31) Schmidt, M. W.; Baldridge, K. K.; Boatz, J. A.; Elbert, S. T.; Gordon, M. S.; Jensen, J. J.; Koseki, S.; Matsunaga, N.; Nguyen, K. A.;

Chakraborty et al. Su, S.; Windus, T. L.; Dupuis, M.; Montgomery, J. A. J. Comput. Chem. 1993, 14, 1347. (32) Streitweiser, A., Jr. Molecular Orbital Theory for Organic Chemists; Wiley: New York, 1961; p 170. (33) Fogarasi, G.; Pulay, P. In Vibrational Spectra and Structure; Durig, J. R., Ed.; Elsevier: Amsterdam, 1985; Vol. 14, p 193. (34) Goodman, L.; Ozkabak, A. G.; Thakur, S. N. J. Phys. Chem. 1991, 95, 9044. (35) Cyvin, S. J.; Cyvin, B. N.; Brunvoll, J. Z. Naturforsch. A 1979, 34, 887. (36) Kethkar, S. N.; Fink, M. J. Mol. Struct. 1981, 77, 139.

JP953694K