BIOINORGAiVIC CHEMISTRY 7,283-296

(1977)

283

CNDO Molecular Orbital CalcuIations on Porphyrins--I. Ground and Excited States of Porphyrin, Divinylporphyrin and Tetraphenylporphyrin

S. J. CHANTRELL, C. A. McAULIFFE, and R. F. WEAVER

R. W. MUNN, A. C. PRATT

Department of Chemistry. UMiST, Manchester 11160I QD, UK. ABSTRACT Semi-empirical CNDO/2 MO calculations are reported for the ground states of porphyrin, 2$-divinylporphyrin (DVP), and (r,B;T,&-tetraphenylporphyrin (TPP). Results for TPP refer to the conformation with all phenyl groups perpendicular to the porphyrin ring, c&x&ted to be 108 kJ mol-l more stable than the coplanar conformation_ The substituents withdraw electron density where they are attached to the porphyrin ring, increasing selected orbital energies_ The vinyl groups also modify the electron population at nitrogen_ CNDO/S calculations with extensive configuration interaction are reported for excited states. The lowest singlet states are closely similar in energy and composition for all three molecules, except for an extra state and more complex compositions in DVP above 3 eV. The lowest triplet states of porphyrin and DVP are very similar, while those of TPP are comparable in energy or composition but not both. Experimental data on the excited states are broadly consistent with the calculations, although comparisons for the excited triplets are tentative.

INTRODUCTiON

Porphyrins and their metal complexes have been the subject of numerous molecular orbital calculations, the most sophisticated of which until recently used the semi-empirical CNDO method [ 1] . In this paper we report CNDO calculations on the ground state and singlet and triplet excited states of porphyrin, q 0. y. Stetraphenylporphyrin (TPP) and 2,4_divinylporphyrin (DVP). The calculations on porphyrin are mainly for comparison with the others, but ours are the first CNDO calculations of the triplet excited states. TPP is readily synthisized, and is widely used as a “typical” porphyrin_ It has been the subject of a free-electron calculation [2] and a Hiickel calculation [33, and there have also been free-electron caIculations on its zinc(I1) complex [4], but ours are the first semi-empirical calculations_ DVP is the conjugated system of protoporphyrin IX, the porphyrin occurring in haem. 0 Elsevier North-Holland. Inc., 1977

284

R. W. MUNN ET AL.

The only calculations on DVP applied a modified Htickel method to its iron (II) complex [5], so that ours are again the first semi-empirical calculations. A preliminary report of our calculations on DVP appeared elsewhere [6] in reiation to energy transfer studies on protoporphyrin IX. Since the present work was begun, there have appeared the first ab initio calculations on porphyrins (with all integrals calculated explicitly)These include an LCAO calculation on porphyrin itself [7] and calculations using the molecular fragment method on ethyl chlorophyllide a [S, 91 and related simpler molecules including porphyrin itself [9] _ These calculations deal with different molecules from ours, in their ground states only, and hence do not supersede our calculations_ Moreover, the a6 irririo calculations on porphyrin [7] show that the earlier CND0/2 calculations [lo] give a good overall picture of the ground-state molecular orbitals, apart from some differences of ordering. We have performed two sorts of CNDO calculations_ The variant CNDOJ2, referred to above, has generally been found to be most suitable for groundstate calculations [l 1] _ These permit us to discuss the conformations of the substituted porphyrins, and to compare the ground-state molecular orbitals of the three porphyrins. The variant CNDO/S has been developed to give improved energies for excited states [12] . These calculations permit us to compare the excited-state energies and spectra of the three porphyrins. We have also performed CNDO/:! calculations on lithium and sodium porphyrin, as reported in the following paper. All the calculations have used standard methods and standard sets of parameters. CNDO/Z CALCULATIONS Geometries The orientations of the substituents on the porphyrin ring are not known for free DVP and TPP_ The porphyrin ring geometry was taken as that used by Zemer and Gouterman [ 131, in which the ring is treated as planar; possible small deviations from planarity have negligible effect. For DVP, the carbon-carbon distance in the vinyl groups was taken as 1.33 a and that from the ring to the vinyl carbon as 1.56 A, these representing average values of comparable distances in cvchlorohaemin [14J _ All vinyl carbonhydrogen distances were taken as 1.07 a, that in ethylene [15], and for simplicity all angles involving the vinyl groups were taken as 120°. The total electronic ener,7 was calculated for the four possible planar DVP structures, but the energies differed by at most 0.013 eV, or %kT at room temperature. This implies that all forms coexist, but for definiteness we adopt the lowest enerv structure, shown in Fig. 1. In this structure, both vinyl groups point away from their nearest methine bridge. Our choice of geometry corresponds to that used in the previous calculation [S] on iron(I1) DVI!.

CNDO MO CALCULATIONS

7 FIG. 1. Composite structure, three porphyrins.

ON PORPHYEUNS-I

Y conformation,

285

6 numbering scheme and axes for the

For TPP, the carbon-carbon distances in the phenyl rings were all taken as 1.385 a, and the distance between the porphyrin and phenyl carbons was taken as 1.514 A, as obtained by X-ray diffraction [ 16]_ The phenyl carbon-hydrogen distances were taken as 1.08 .%, that in benzene [ 161, and all angles were again taken as 120”. The X-ray studies [ 16- 181 show that in the crystal the phenyl planes are inclined at about 60” to the porphyrin ring. However, resonance energy calculations combined with a Lennard-Jones potential energy function suggest [ 191 that in solution this angle may be about 45” _We have calculated the total electronic energy for the two extreme modei structures having the phenyl groups ail coplanar with the porphyrin ring or all perpendicular to it. (The length of the calculations precluded study of intermediate structures.) It was found that the perpendicular structure is more stable by 1.12 eV (108 lcJ molB1), indicating a very strong repulsion between the pyrrole and phenyl hydrogens in the coplanar structure, more than sufficient to outweigh the advantageous resonance energy. Henceforth, all calculations on TPP reported

R. W. MUN?N ET

286

a::a

b*

b-I!3

w a8 \ a QI -51 G w' is

+3 _0

b --au -,---"" --

_q” a-c-

a,----

b

-lO-

AL.

l”

0’ -1S Porphyrin

TPP

DVP

FIG. 2. Calculated energies and symmetries of the four highest occupied and two lowest unoccupied molecular orbitals for the three porphyrins.

here (2,3]

refer to the perpendicular structure. the coplanar structure was used.

In

both previous calculations

Ground-State MO Structures Here we compare the ground state MO structures of the three porphyrins, showing the effect of the different substituents. The analysis also serves as a basis for the discussion of the excited states in the next section. Since porphyrin and DVP are planar, their orbitals can be classified as of o or il type; in the nonplanar TPP, the orbitals are of mixed type, but the predominance of o or B type may be noted. The numbering scheme for the carbon atoms is shown in Fig. 1 together with the choice of axes used in assignmg symmetry classifications to the orbitals. Cporphyrin and TPP have Dab Symmetry, DVp has C, symmetry-) We discuss the two lowest unoccupied MOs (LUMOs) and the four highest occupied MOs (HOMOs), which are the most important in constructing the excited states. The energies and symmetries of these six orbitals are shown in Fig. 2; for Porphyrin, the results for the HOMOs agree with the calculations of

00

MO CALCULATIONS

ON PORPHYRINS-I

287

Maggiora [IO], who did not quote results for the LUMOs. We discuss the orbitals in terms of the contributions to the electron population (EP) from individual atomic orbitals. The highest occupied orbital HOMO1 in porphyrin is of n type, and has 80% of the EP on the inner ring carbon atoms (9-16). Peripheral substitution should affect these populations only weakly, and indeed the corresponding orbitals HOMO1 in DVP and HOMO2 in TPP each have ‘ITsymmetry and 8% of the EP on the inner ring 4. The second highest porphyrin orbital HOM02, also of rr type, has 12% of its EP located at each of the meso carbon atoms (a, 0, y and S), the rest being distributed round the porphyrin ring- As a result, the corresponding orbital in TPP shouId be significantly changed owing to the substituent phenyl groups at the meso positions. In fact, the result is to destablilize this orbital to such an extent (0.76 eV) that it becomes the highest occupied one, HOMO 1 _ This retains the rr character, with 11% of the EP at each of the meso positions, but concentrates a further 11% on the imino nitrogen atoms. In DVP HOMO2 is scarcely changed from that in porphyrin as earlier found in the modified l-hickel study

PI -

A complementary effect is found in the n-orbital HOM03. In porphyrin, this orbital has 20% the EP at the imino nitrogens in rings II and IV and 13% at each of the carbon atoms 3,4,7 and 8 in the same rings, and HOMO3 in TPP is essentially the same. However, in DVP the vinyl substituents destabilize this orbital by 0.5 eV. The reduced symmetry also allows 90% of the EP to concentrate near ring II, including 30% on the nitrogen, 25% and 17% on carbon atoms 3 and 4, and 12% on carbon atom 1311in the vinyl group. The fourth highest occupied orbitals are of a type. In porphyrin 15% of the EP is located on each of the imino nitrogen atoms (their lone pairs) with 16% at each of the carbon atoms 3,4,7 and 8. The corresponding orbital in TPP is very similar, but is actually HOM05; this is a reversal of the porphyrin orbital order on substitution similar to those discussed above, and also reflects the increasing congestion in the TPP orbitals (there are six between -12 and -13 eV compared with three each for porphyrin and DVP). In DVP, HOMO4 shows an effect similar to that in HOM03, with 35% of the EP becoming concentrated on the imino nitrogen in ring II, the rest being distributed around the porphyrin ring. The effect of the vinyl substituents in encouraging EP to accumulate in both n and a orbitals on this atom seems likely to be of significance in metalloporphyrin formation. The two lowest unoccupied MOs turn out to have no particular concentration of EP (less than 1% on any one atom), and to be little different in porphyrin, TPP and DVP_ We also calculated the net atomic charges from the total EP in occupied orbitals on each atom. In porphyrin, the largest charges (as multiples of the pro-

288

R. W. MUNN ET AL.

ton charge) are -0.30 on the imino nitrogens, -0.10 on the imido nitrogens, +0.12 on the inner carbons (9-16) and +O_lS on the hydrogens attached to nitrogen. Phenyl and vinyl substituents withdraw negative charge from the carbons where they are attached (to the extent of about 0.03 in each case), with smaller opposing changes at adjacent carbon atoms. Changes at the nitrogen atoms are negligible. Overall, the effect on the vinyl and phenyl substituents is thus to remove electron density from the porphyrin ring at their sites of attachment. This withdrawal has little effect on many orbitals, but in some orbitals with large EP contributions at the substituent sites, significant increases of energy may result. Figure 2 illustrates this pattern. By being substituted on the heterocyclic rings, the vinyl groups can affect the EP on the nitrogen atoms (and hence bonding to metal atoms). These substituent effects appear to determine the symmetry of -the ground state in metalloporphyrin n-cation radicals [22]. Similarly, the effect of the substituents on the basicity of the nitrogens gives rise to the ciseffect in octahedral metalloporphyrins [23], whereby stronger bonding between the porphyrin and the metal leads to weaker bonding between the metal and axial ligands. CNDO/S CALCULATIONS Principles The calculations in this section used the CNDOlS parametrization [ 121 used by Maggiora and Weimann [24] for calculations on the singlet excited states of porphyrin and its dianion- These calculations serve as a check on our own. The geometries were taken to be the same as for the CNDO/2 ground-state calculations. The excited-state calculations incorporate substantial configuration interaction (CI): for porphyrin the 80 lowest singlyexcited configurations were mixed and for DVP the 100 lowest were mixed, in each case selected from all possible such configurations. For TPP and 150 lowest singly-excited configurations selected from excitations between orbitals in the range 60-160 were mixed. In discussing the results, a question of principle arises. The CNDO/S calculations give the best excited-state energies relative to the ground state and presumably the best excited-state orbital composition, but the CNDO/2 calculations give the best ground-state energy and presumably the best ground-state orbital composition. Should one therefore discuss the composition of the excited states in terms of the actual (but poor) CNDO/S ground-state orbit&, or in terms of the good (but not directly relevant) CNDO/2 orbitals? Fortunately, in the present case it transpires that there is negligible difference_ We therefore analyse the composition of each excited state in terms of configurations like

CNDO MO CALCULATIONS

ON PORPHYRINS--I

HOMO l+LUMO2, but interpret these orbitals as those. obtained calculations and discussed above.

Singlet Excited

289 by the CNDO/2

States

Table 1 shows our calculated energies for the singlet excited states, with the symmetries, oscillator strengths and polarizations. States with zero oscillator strength are omitted. For porphyrin the calculations reproduce the results of Magiora and Weimann [24]. Also shown in Table 1 are experimental energies, relative intensities (opt&I densities) and polarizations, obtained from measurements on porphyrin solutions [25] . In porphyrin and TPP the B and N states are separated by 0.5 eV, but in DVP there is no such obvious gap, making the grouping into 3 and N states appear rather arbitrary. However, the composition of the state at 3-5 1 eV (discussed below), as well as its large oscillator strength and predominantly _Y polarization, indicate clearly that it corresponds to the B, states of porphyrin and TPP. If one compares the calculated and observed values, it is apparent that there is reasonable agreement in the energies and intensities, with a similar pattern for each porphyrin, including the usual overestimate of the Q-B separation. However, the agreement is only semi-quantitative (as the theory is only semi-empirical), and detailed comparisons do not seem profitable. instead, we shall compare the calculations for the three porphyrins, examining how the substituents affect the excited states and hence the spectra_ Only the Q and B states will be analyzed_ We first examine the compositions of the states in terms of the singly-excited configurations listed in Table 2. These configurations are numbered according to their parentage rather than their energies, so that TPP requires separate specification owing to the reversal of energy order in the HOMOs derived from porphyrin’s HOMOs 1 and 2. Table 3 shows the compositions of the various states. States QX, Q, and B, have essentially the same composition for each porphyrin, although the relative proportions of the configurations differ in TPP because of their different energies_ With this reservation, states B, are essentially the same in porphyrin and TPP_ However, in DVP there are two B states with predominatly x polarization, containing large contributions from configurations 5 and 6 respectively_ These are the configurations originating from HOMO3 and HOM04, which are substantially changed from those in porphyrin, as discussed above. The contributions to these B states from configuration 4 also account for its reduced contribution to the B,, state. The classic four-orbital model [26] treats HOMOs 1 and 2 and LUMOs 1 and 2, and hence is restricted to the first four configurations. It can be seen that the model explains the composition of the states QX. Q,. and B, more or less completeIy for all three porphyrins_ For porphyrin and DVP the B, state has an

R.W.MUNNETAL_

290 TABLE

1

Singlet Excited States of Porphyrin, TPP and DVP: Calculated Energies E and Oscillator Strengths f with Polarization; Experimental Energies and Relative Intensities with Polarization Calculated State (a) Porpfryrin

E/eV

Symmetry

Observed [ 25 ] Solvent

f

(241

Qx

I-78

QY

2.09 3.34

BY

3.57

NX

4.03

NY

4.35

33,

% B3u %x B3u

%z

0.015x

2.02

0.03x

chloroform

0.09y

2.38

0.09~

chloroform

3.15

7.40

chloroform

0.007x

1.92

0. I Ox chloroform

2.25

0.15~

chloroform

2.94

8.30

chloroform

1.96

0.1 Ix

benzene

229

0.22y

benzene

1.44x 2.63~ 1

2.21x osoy

(b) TPP 0 -r

1.77

QU

2.09

8%

3.34

B3u

0.02 ly . I .80x

Be,

2_93y 1.

3.45

B3Ix

NX

3.95

B3ll

200x

NY

4.42

Bf&

0.34y

1.78

A’

(c) DVF O.OOly

Q

0.018x

0.1 ly

2.07

A’

1

0.004x

CNDO MO CALCULATIONS

ON PORPHYRINS-I

291

TABLE 1 (continued) Observed [ 25 1

Calculated State

EjeV

Sym-

metry

E/eV

f

‘ztg-

Solvent

(c) DVPO (continued) 0.13y

3

3.18

A’

I I I I I I 1 I

0.55x 0.07y

3.37

A’

benzene

0.9o.u 2.341,

3.51

A'

0.004x

0.17y

N

3.68

A’

0.08,

0.00 1y

3.79

A’

2.0 lx

0.23~

3-90

A’

0.007x

o.oooy

4.18

A’

0.09x

0.3oy

4.29

A’

0.00x

a Experimental results are for protophyrin

IX dixnethyl ester.

R.

292 TABLE

W.MUNNETAL.

2

Some Important Singly-excited Configurations Excitation TPP

Porphyrin and DVP Number

HOMO 1 2 I 2 3 4

I 2 3 4 5 6

+

LUMO

-+ --t 3 + + +

2 1 1 2 1 1

HOMO 2 1 2 1 3 4

TABLE Composition

EfeV

LUMO

+ + + + + 3

2 1 1 2 1 1

Type Tr+rr* ?r+Ti* n+n* R-+X* il+-rrTT* cr+TT*

3

of Singlet Excited States in Terms of Configurations Numbered as in Table 2

Porphyrin State

+

TPP

Composition

E/eV

DVP

Composition

E/eV

Composition

a

1.78

52% 1 45% 2

1.77

41% 1 57% 2

1.78

52% 1 45% 2

QY

2.09

66% 33%

2.09

57% 42%

2.07

66% 31%

3.18

16% I 13% 4 59% 5

3 4

3 4

&cp

3 4

&

3.34

32% 31% 32%

1 2 6

3.34

44% 26% 27%

1 2 6

3.37

14% 14% 16% 40%

2 4 5 6

BY

3.57

32% 64%

3 4

3-45

42% 56%

3 4

3.5 1

26% 3 55% 4

CNDO MO CALCULATIONS

ON PORPHYRINS-1 TABLE

293

4

Triplet Excited States of Porphyrin, TPP and DVP: Calculated Energies E and Symmetries, and Observed Energies Porphyrin

DVP

TPP

State

EIeV

Symmetry

E/eV

Symmetry

EIeV

2-1

1.02 1.41 1.61 1.71

8%

1.30

8%

1.05

A’

B3ll

1.39

B3u

1.40

A’

%

1.51 1.68

%

1.61 1.71

A’

T2 T3 T4

B3ll

B3u

Symmetry

A’

Observed 1251 1.58 a Protoporphyrin

l-45

1.56”

IX dimethyl ester.

important contribution from the o + II* configuration 6 not treated on the fourorbital model, while for DVP configuration 5 is also required. The excited-state energies are calculated to be very close for states Q,. QY and B, _ Apart from the extra B, * state for DVP, the only noticeable differences in ener,7 are in the B, states, where the trend follows that observed in the solution measurements for the B band (see Table 1). However, the measurements also indicate similar but smaller variations for the Q bands, not suggested by our calculations. Altogether, the calculations show how r&-coplanar phenyl group substitution has little effect on the composition of the lower singlet excited states but minor effects on their energies. Vinyl group substitution produces more states in the same energy range, with more complicated compositions. Ti@Iet Excited States. Table 4 shows our calculated energies for the triplet excited states_ Also shown are experimental energies derived [25] from the phosphorescence maxima in rigid glasses at 77 K. The pattern of states is similar for the three porphyrins, except that in TPP the Tl state lies si8nificantly higher and the T2 state lower than in the other two. Several factors make the comparison of theory with experiment more difficult for the triplet states than for singlets. The experimental results will include solvent shifts. These could be particularly marked for TPP if the preferred conformation of the phenyl rings relative to the porphyrin plane alters significantly on excitation, although in restraining such changes the glass matrix makes the energy differences closer to those for a fifed geometry (as used in the calculation) than for free TPP. The triplet energies are also more sensitive to the

R. W. MUNN ET AL.

294

TABLE Composition

5

of Triplet Excited States in Terms of Configurations Numbered as in Table 2 DVP

TPP

Porphyrin State

E:eV

Composition

E/eV

TI

I.02

80% 3 15% 4

I.30

7-2

1.41

98%

1

T3

1.61

T4

I.17

Composition

E/eV

Composition

76% 3 22% 4

1.05

82% 3 12% 4

1.39

98% 2

1.40

97%

17% 3 81% 4

1.51

73% 3 76% 4

l-61

15% 3 82% 4

98% 2

1.68

98%

1.71

97% 2

1

1

number of configurations mixed than the singlets. For example, in CNDO/S calcdations on acridine [27], which has 65 MOs, increasing the number of singly exczted configurations mixed from 50- 100 reduced the energy of the two lowest singlet states by o&y I%, the next singlet by 370, and all other singlets by less than 5%; on the other hand, the energy of the lowest triplet state was reduced by 15%. and other triplets by typically 5%. However, these shortcomings of the calculations serve to make the triplet energies in Table 4 too high, whereas the experimental energies are already the higher (as for the singlets). One further piece of experimental information comes from ESR measurements on the triplet state of porphyrin in a Shpol’ski matrix (frozen n-octane) [X3] _ Comparison with Pariser-Parr-Pople spin-density calculations including CI indicates that this tripiet is of B2 symmetry_ This assignment fits not only the r, state but also the T3 stak Our calculated energies for T3 agree very well with the observed energies, notably in reproducing the lower value for TPP, in contrast to the much higher value of the Tl energy, and it is tempting to suggest that the observed phosphorscence originates from T3_ This, though, would place too much trust in the calculations, which could agree with experiment so well only by a fortuitous cancellation of the errors outlined above and the inherent weaknesses of the CNDO method_ We now examine the compositions of the caicuIated triplet states, given in Table 5 in terms of the singly-excited configurations from Tabie 2. All four Iowest triplets contain a contribution of at least 75% from one of the first four configttrations, and admixtures of higher configurations are very smaB so that the four-oribtal model 1261 is justified for these states. The main difference

CNDO MO CALCULATIONS

ON PORPHY-RINS-I

295

from the singlets is that here the compositions for TPP are not all directly comparable with those for porphyrin and DVP, T2 and T4 for TPP corresponding in composition to T4 and T2 for porphyrin and DVP. It will be recalled that in Table 2 the configurations are labelled by parentage rather than energy, a procedure justified by the similar compositions obtained for the singlets and for Tl and T3_ It appears that T2 and T4 are sensitive-to excitation configurations which both for 7.87 7.92 eV DVP, 8.35 7.21 eV TPP. the and T4 nearly configurations, it is the energy and departure degeneracy of 1 and in which the composition. triplet-state show marked between and others the state do. differences the could the between ESR observed TPP in glass and porphyrin in n-octane _ For DVP. on the other hand, the lowest triplet states are much closer to those of porphyrin than the Iowest singlets (though differences do occur in the higher triplets). The pattern of observed phosphorescence energies departs markedly from that of the calculated T, energies, but as noted above various uncertainties hamper the comparison, leading to no clear conclusion. CONCLUSIONS

CNDO calculations are useful for providing detailed information about-theground and excited states of free base porphyrin molecules, subject to the usual proviso that the relative results for similar molecules should be more reliable than the absolute results for an individual molecule. Here we find that the phenyl and vinyl substituents modify the energies of different selected porphyrin molecular orbitals. Substitution on the methine bridges affects the nitrogen atoms little, but vinyl substitution in the nitrogen-containing rings has a substantial effect on the electron population at nitrogen. This implies a corresponding effect on metal complexation by divinylporphyrins, and is presumably related to their biological functions. For the excited states, the calculations broadly confirm the utility of the four-orbital model. The principal exceptions-are the participation of a a-orbital involving nitrogen in the B, state for all three porphyrins, and participation of a lower occupied n-orbital in DVP , giving an extra B state. For the excited singlets, the calculations can be correlated with the observed fluorescence, but diftlculties arise in comparing the triplet energies with the phosphorescence_ In particular there seems to be scope for further investigation of the relationship between the lowest triplet states of TPP and porphyrin_ Wethank the SRC for a Research Studenship

@.fC)_

R. W. MUNN ET AL. REFERENCES 1. S. J_ C’hamt-eJl,C. A. McAuliffe, R. W. Munn and A. C. Pratt, Coord. them Revs. 16, 252 (1975). H. Takeda-and K. Oki, Kagaku 20,186 (1950). S. Basu, prOc_ NatI. Inst. Sci. India21A, 259 (1955)4_ H. Kuhn aud W_ Huber, HeZv_Chim Acta 42,363 (1959). 5. C. Spanjaard and G. Berthier, J. Chim Phys. 58,169 (1961)6_ S. J. ChantreB, C_ A_ McAuliffe, R. W. Munn, A. C. Pratt and E. J. Land, J. Lumine2. 3_

scence 12113,887 (1976). J. AlmlGf, ht. J. Quantum Chem. 8,915 (1974). 8. L. L. Shipman, T. R. Janson, G. J. Ray and J. J. Katz, P~oc. Ni.tl. .kUd. SCi IX?. 72, 2873 (1975) 9. D. Spangler, R. McKinney, R. E. Christoffersen, G. M. Maggiora and L. L. Shipman, C&em. Phys. Letters 36,427 (1975). 10. G. M. Maggiora,.I Amer. Chem. Sot. 95,6555 (1973) 11. J. A. Pople and D. L. Beveridge, Approximate Molecular Orbital Theory. McGrawHill, New York (1970X 12. R. L. Ellis, G. KuehnJenz and H. H. Jaff& Theor. Chim Acta 26,131 (1972). 7.

15. M. Zemer and M_ Gouterman, Theor. Chim. Acta 4,44 (1966). D. F--Koenig, Acta Cryst. 18,663 (1965). Tables of Interatomic Distancesand Configurationin fi~oleculesand Ions, The Chemical Society (1958). 16. J_ L. Hoard, M. J_ Hamor and T_ A_ Hamor,J. Amer. Chem Sot. 85,2334 (1963). 17. E. B_ FIeischer, Acts Chem. Res. 3,105 (1970). 18. S. J. Silvers and A. Tulinsky,J. Amer Chem Sot. 89,333l (1967). 19_ A. WoIberg,J: Mol. Struct. 21,61 (1974). 20. T_ Koopmans,Physica 1,104 (1933): 21_ A. Stanienda, 2. Nantrforsch.B23,1285 (1968). 22_ D_ Dolphin and R. H. Felton, Acts Chem Res. 7,26 (1974). 23. W- S. Caughey, iu Inorganic3iochemhtry (G. L. Eichhom, ed.), EIsevier, Amsterdam, 14_ 15.

1973, pp- 797. G. M. Maggiora and L. J. Weimann, C/rem Phys. Letters 22,297

25. 26.

(1973). M. Gouterman and G. Khalil,J. Mol. Spectrosc. 53,88 (1974). M_ Goutenmn.J. Chem. Phys. 30,1139 (1959);5. Mol. Spectrosc. 6,138 (1961).

27. 28.

R. W. Munn, unpublished calculations_ W. G. van Dorp, M. Soma, J_ A. Kooter and J. H. van der WaaLs,MoZ_ Phyx

24.

(1974). 29.

H. Levanon and A. Wolberg, Chem. Phys. Letters 24,96 (1974).

Received 30 November 1976; Revised 22 December 1977

28,1551

CNDO molecular orbital calculations on porphyrins--I. Ground and excited states of porphyrin, divinylporphyrin and tetraphenylporphyrin.

BIOINORGAiVIC CHEMISTRY 7,283-296 (1977) 283 CNDO Molecular Orbital CalcuIations on Porphyrins--I. Ground and Excited States of Porphyrin, Divinylp...
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