BIOINORGANIC CHEMISTRY 7,297-301(1977)
297
CNDO Molecular Orbital Calculations on Porphyrins--II. Ground States of Dilithium and Disodium Porphyrin
S. J. CHANTRELL,
C. A. McAULIFFE,
R. W. MUNN, A. C_ PRATT
and R. F. WEAVER
Department of Chemistry, UMIST, Manchester M60 I QD, U.K. ABSTRACT CNDO/2 calculations are reported for dilithium and disodinm porphyrin. The total energy is calculated as a function of the metal-ring distance for symmetrical (D4h) structures. For dilithium porphyrin, the equilltrium metalring distance is 0.87 A and the metal-metal viirational frequency is 123 cm-l, For d&odium porphyrin, the distance is 1.64 A and the frequency is 77 cm’-I_ Little mixing of metal and porphyrin orbitals takes place; the two lowest unoccupied and the two highest occupied $10~ hardIy differ from those in porphyrin, but lower MOs are considerably rearranged.
INTRODUCTION In the preceding paper [l] we described CNDO calculations on porphyrin and two substituted free-base porphyrins. Here we report the results of similar calculations on two metalloporphyrins, dilithium and disodium porphyrin (abbreviated where necessary as Li2P and Na2P). No previous MO calculations on alkali metal porphyrins have been reported_ Salts of lithium and sodium with porphyrin itself have not been isolated, but the sodium salts of haematoporphyrin [2], tetraphenylporphyrin 13, 4] and aetioporphyrin [S], and the lithium salt of tetraphenylporphyrin 13, 4] are known. The metals prove to be weakly bonded, free base being rapidly produced when the salts are treated with water or dilute acetic acid 12, 3] _ As would be expected, lithium can displace sodium from the tetraphenylporphyrin salt. Presumably because of the lability of the compounds, their structures are not known, the main question being the location of the metal atoms. For L&P we have used the CNDO/2 method 163 as in the preceding paper and for Na,P the extension [7] to second-row atoms. For metal compounds like these there is no analogue of the CNDO/S parametrization [8] used in the preceding paper for excited-state calcuiations, and so only ground-state calculations are reported here. These are used to deduce likely structures, and to compare the two compounds with porphyrin itself_ 0 Ekvier
North-Holland, Inc., 1977
R. W. MUNN ET AL_
298
0.5
1.0
1.5
2.0
r/A l- Ckkulated total eIectronic energy of Lisp and NanP as a function of the metal-ring distance, r.
FIG.
RESULTS AND DISCUSSION Geometry We have adopted the assumption [9] that the metal atoms are symmetrically located above and below the centre of the porphyrin ring. The ring is taken to have the planar geometry used by Zemer and Gouterman [lo] _ The molecules thus have D,, symmetry_ Total eIectronic energfes were calculated for various metal-ring distances; for Na,P it was found that convergence in the iterative SCF procedure required damping (the smoothing of oscillatory slow convergence by constructing new coefficients from the preceding two instead of just the last one). The results are shown in Fig. I_ The equilibrium distance of the metal atoms from the porphyrin plane is 0.87 -4 for lithium and l-64 A for sodium_ The corresponding distances from the nitrogen atoms are then 2.23 A and 2.63 -8. The difference between these distances is consistent with the difference between the ionic radii (0.6 A for Li* and 095 A for Na+ [l l]), indicating that the equilibrium structure is determined primarily by the metal-nitrogen interactions rather than by the metalmetal interactions_ The minima of the ener,T curves in Fig- 1 are rather shallow, showing the weakness of the metal-porphyrin binding; for comparison, Fig. 1 also shows kT at 300 K. For L&P, the second derivative of the energy at the equilibrium
CNDO MO CALCULATIONS
ON PORPHYRINS-II
299
distance with respect to the metal-metal distance is 0.193 eV AW2. This implies a force constant for symmetrical vibration of the lithium atoms relative to the porphyrin plane of 3.09 N m-1 (i N m-l = 1W2 mdyn A-l) and a vibrational frequency of 3.69 THz or 123 cm- 1_ For Na2P the derivative is 0250 eV Am2, leading to a force constant of 4.01 N m-1 and a frequency of 231 THz or 77 cm-l. These vibrations might be observable by Raman spectroscopy. Because of their low frequency, they should be substantially excited at room temperature; this factor, combined with vibrational anharmonicity, means that the average metal-metal distance determined experimentally would depart significantly from the equilibrium distance_ MO Structure Orbitals in which more than half the electron population (EP) is localized on the metal atoms all have energies above zero, and are unoccupied_ It is also found that very few orbitals have comparable amounts of EP on the metal atoms and on the ring, the EP on the metal atoms being typically below 20% or above 80%. Thus little mixing of metal and porphyrin MOs takes place: as would be expected, the bonding is mainly ionic. The two lowest unoccupied MOs (LUMOs) and all the occupied MOs have energies below zero, and are derived principally from the ring. In Fig. 2 are shown energies and symmetries for the two LUMOs and some of the highest occupied MOs (HOMOs), with those of porphyrin itself [l, 121 for comparison. The two LUMOs in porphyrin collapse to a degenerate pair under the higher symmetry of the metalloporphyrins, but their mean energy is hardly changed_ HOMO1 and HOMO2 suffer only small quantitative changes, similar to those calculated [12] for magnesium(H) porphyrin, with the ordering reversed from that in the porphyrin dianion. The lower HOMOs of the free base undergo substantial rearrangement in the metalloporphyrins. The porphyrin x-orbital HOMO3 is considerably stabilized by the out-of-plane metal substitution, becoming one of the degenerate pairs HOM05/6 in Li2P and HOM04/5 in Na2P by combining with a much Iower orbital (not shown in the figure). At the-same time, the porphyrin o-orbital HOMO4 is little affected, and so becomes HOMO3 in both metalloporphyrins. This reversal of order is largely attributable to the higher symmetry: it can also be seen in the porphyrin dianion [12] _However, the relative insensitivity of the o-orbital to metal substitution also depends on the metal atoms being out of the porphyrin plane, as comparison of results for in-plane and out-of-plane magnesium(H) porphyrin 1121 shows_ The lower HOMOs of Li2P and Na,P differ in the position of the b 2U orbital, which is higher than the eg and e, pairs of orbit* b Li2P but lower in Na2P. The order in Na,P is the same as in the porphyrin dianion [12], consistent with the seater distance of sodium from the ring than lithium. However, this ordering in Na2P may not be entirely realistic, since
R. W. MUNN ET AL,.
300
O-
b 3g--b -- ==_ 2g--
---
%i--
-
-1
-a? ___-a,--4-__ b --______----a
al, ---_^-
111
b39’ ag--\;
2u
_-------b,,___
bzu=;\
b lu
y:
,,.
b,, %-I,‘= = *;-xz:s’ -e, -_*b2u b1g=+-- ‘- -___a29 -b 3u
Porphyrin
LizP
FIG. 2. Calculated orbital energies and symmetries Na2P.
NazP for porphyrin,
LizP
the 3d orbitals in the CND0/2 method are taken as having the same orbital exponent as the 3s and 3p orbitals [7] _This implies that the sodium 3d orbitals are relatively contracted and so interact less strongly with neighbouring atoms than in re4ity. A further similarity between LiaP and NaaP and the porphyrin dianion is the order of the degenerate pairs of orbitals, the es orbitals lying above the e, orbitals. This order is reversed in D,, and D,, magnesium(II) porphyrin [12], where the metal-ring interactions are less weak.
CONCLUSIONS We have predicted the structures and metal-metal vibrational frequencies for dihthium and disodium porphyrin. The possibility of observing these low frequencies seems worth investigating.
CNDO MO CALCULATIONS
ON PORPHYRINS-II
301
The molecuku orbitals calculated by the CNDO12 method give a consistent picture of porphyrin, its dianion, and its lithium, sodium and ma~esium(II) salts. The two LUMOs and two HOMOs remain remarkably unaffected by the substitution of metals. This would explain why the four-orbital model [13] is successful in explaining the observed similarities between the electronic spectra of dilithium and disodium tetraphenylporphyrin [4] and tfiose of other metalloporphyrins. The CNDO/2 method has been extended to compounds containing atoms of the first transition series [14], and applied to copper(I1) porphyrin [IS]. It would appear worthwhile to perform similar cahzulations for other metalloporphyrins, and also to develop analogues of the CNDO/S parametrization [S] for calculating the excited states of complexes containing second and third-row elements_ Although the CNDO method is semi-empirical, it is found to give results for porphyrins broadly comparable with those obtained by ab initio methods [16,17] _ We thank the SRC for a Research Studenship (SIC).
REFERENCES 1. S. J. Chantrell, C A. McAuBffe, R. W. Munn, A. C. Pratt and R. V. Weaver, preceding paper, Part I, Bioinorg. Chem. 7 (4), (1977). 2. R. HiII, Biochem. J. 19,341(1925X 3. J_ W. Barnes and G. D. Dorough,J. Amer. CEem Sec. 72,404s (195d). 4. G. D. Dorough, J. R. MiUer and F. M. Huennekens, J. Amer. Chem Sot. 73,431s (1951). 5. J. W. Dodd and N. S. Hush,1 Chem Sot. 4607 (1964). 6. J. A. Pople and D. L. Beveridge, Approximate Molecular Orbital Theory, hkGrawHi& New York, 1970. 7_ D. P. Santry and G. A. SegaI,J. Chem. Phys. 47,158 (1967). 8. R. L. EIIis, G. Kuehnienz and H. H. Jaff& Theor. Chim. Acta 26,131 (1972). 9. J. E. FaIk, Porphyrins and Metalloporphyrins EIsevier, Amsterdam, 1964, p_ 30. 1C. M. Zemer and M. Goutennan, Theor. Chim. Acta 4,44 (1966). ll- L. PauIing, GenetaZ Chemistry. Freeman, San Francisco, 1970, Chap. 6,3rd ed. 12. G. M. hIaggiora,J. Amer. Gem. Sot. 95,6555 (1973). 13. M. Gouterrnan, J. Gem Phys. 30, 1139 (1959); J. Mol. Spectrosc. 6, 138 (1961); M. Gouterman, G. H. Wagni&e and L. C. Snyder,1 Mol. Spectrosc. 11,108 (1963). 14. D. W. clack, N. S. Hush and J. R. YandIe,J. Chem Phys. 57,3503 (1972). 15. D. W. Clack and M. S. F animond, JCS Dalton. 29 (1972). 16. J. AL-nlGf,Intern J. Quantum Chem. 8,915 (1974). 17. D. SpangIer, R. McKinney, R. E. Christoffersen, G. M. Maggiora and L. L. Shipman, Chem. Phys. Letters 36,427 (1975). Received 30 November
1976; revised 22 December
I976
297
CNDO Molecular Orbital Calculations on Porphyrins--II. Ground States of Dilithium and Disodium Porphyrin
S. J. CHANTRELL,
C. A. McAULIFFE,
R. W. MUNN, A. C_ PRATT
and R. F. WEAVER
Department of Chemistry, UMIST, Manchester M60 I QD, U.K. ABSTRACT CNDO/2 calculations are reported for dilithium and disodinm porphyrin. The total energy is calculated as a function of the metal-ring distance for symmetrical (D4h) structures. For dilithium porphyrin, the equilltrium metalring distance is 0.87 A and the metal-metal viirational frequency is 123 cm-l, For d&odium porphyrin, the distance is 1.64 A and the frequency is 77 cm’-I_ Little mixing of metal and porphyrin orbitals takes place; the two lowest unoccupied and the two highest occupied $10~ hardIy differ from those in porphyrin, but lower MOs are considerably rearranged.
INTRODUCTION In the preceding paper [l] we described CNDO calculations on porphyrin and two substituted free-base porphyrins. Here we report the results of similar calculations on two metalloporphyrins, dilithium and disodium porphyrin (abbreviated where necessary as Li2P and Na2P). No previous MO calculations on alkali metal porphyrins have been reported_ Salts of lithium and sodium with porphyrin itself have not been isolated, but the sodium salts of haematoporphyrin [2], tetraphenylporphyrin 13, 4] and aetioporphyrin [S], and the lithium salt of tetraphenylporphyrin 13, 4] are known. The metals prove to be weakly bonded, free base being rapidly produced when the salts are treated with water or dilute acetic acid 12, 3] _ As would be expected, lithium can displace sodium from the tetraphenylporphyrin salt. Presumably because of the lability of the compounds, their structures are not known, the main question being the location of the metal atoms. For L&P we have used the CNDO/2 method 163 as in the preceding paper and for Na,P the extension [7] to second-row atoms. For metal compounds like these there is no analogue of the CNDO/S parametrization [8] used in the preceding paper for excited-state calcuiations, and so only ground-state calculations are reported here. These are used to deduce likely structures, and to compare the two compounds with porphyrin itself_ 0 Ekvier
North-Holland, Inc., 1977
R. W. MUNN ET AL_
298
0.5
1.0
1.5
2.0
r/A l- Ckkulated total eIectronic energy of Lisp and NanP as a function of the metal-ring distance, r.
FIG.
RESULTS AND DISCUSSION Geometry We have adopted the assumption [9] that the metal atoms are symmetrically located above and below the centre of the porphyrin ring. The ring is taken to have the planar geometry used by Zemer and Gouterman [lo] _ The molecules thus have D,, symmetry_ Total eIectronic energfes were calculated for various metal-ring distances; for Na,P it was found that convergence in the iterative SCF procedure required damping (the smoothing of oscillatory slow convergence by constructing new coefficients from the preceding two instead of just the last one). The results are shown in Fig. I_ The equilibrium distance of the metal atoms from the porphyrin plane is 0.87 -4 for lithium and l-64 A for sodium_ The corresponding distances from the nitrogen atoms are then 2.23 A and 2.63 -8. The difference between these distances is consistent with the difference between the ionic radii (0.6 A for Li* and 095 A for Na+ [l l]), indicating that the equilibrium structure is determined primarily by the metal-nitrogen interactions rather than by the metalmetal interactions_ The minima of the ener,T curves in Fig- 1 are rather shallow, showing the weakness of the metal-porphyrin binding; for comparison, Fig. 1 also shows kT at 300 K. For L&P, the second derivative of the energy at the equilibrium
CNDO MO CALCULATIONS
ON PORPHYRINS-II
299
distance with respect to the metal-metal distance is 0.193 eV AW2. This implies a force constant for symmetrical vibration of the lithium atoms relative to the porphyrin plane of 3.09 N m-1 (i N m-l = 1W2 mdyn A-l) and a vibrational frequency of 3.69 THz or 123 cm- 1_ For Na2P the derivative is 0250 eV Am2, leading to a force constant of 4.01 N m-1 and a frequency of 231 THz or 77 cm-l. These vibrations might be observable by Raman spectroscopy. Because of their low frequency, they should be substantially excited at room temperature; this factor, combined with vibrational anharmonicity, means that the average metal-metal distance determined experimentally would depart significantly from the equilibrium distance_ MO Structure Orbitals in which more than half the electron population (EP) is localized on the metal atoms all have energies above zero, and are unoccupied_ It is also found that very few orbitals have comparable amounts of EP on the metal atoms and on the ring, the EP on the metal atoms being typically below 20% or above 80%. Thus little mixing of metal and porphyrin MOs takes place: as would be expected, the bonding is mainly ionic. The two lowest unoccupied MOs (LUMOs) and all the occupied MOs have energies below zero, and are derived principally from the ring. In Fig. 2 are shown energies and symmetries for the two LUMOs and some of the highest occupied MOs (HOMOs), with those of porphyrin itself [l, 121 for comparison. The two LUMOs in porphyrin collapse to a degenerate pair under the higher symmetry of the metalloporphyrins, but their mean energy is hardly changed_ HOMO1 and HOMO2 suffer only small quantitative changes, similar to those calculated [12] for magnesium(H) porphyrin, with the ordering reversed from that in the porphyrin dianion. The lower HOMOs of the free base undergo substantial rearrangement in the metalloporphyrins. The porphyrin x-orbital HOMO3 is considerably stabilized by the out-of-plane metal substitution, becoming one of the degenerate pairs HOM05/6 in Li2P and HOM04/5 in Na2P by combining with a much Iower orbital (not shown in the figure). At the-same time, the porphyrin o-orbital HOMO4 is little affected, and so becomes HOMO3 in both metalloporphyrins. This reversal of order is largely attributable to the higher symmetry: it can also be seen in the porphyrin dianion [12] _However, the relative insensitivity of the o-orbital to metal substitution also depends on the metal atoms being out of the porphyrin plane, as comparison of results for in-plane and out-of-plane magnesium(H) porphyrin 1121 shows_ The lower HOMOs of Li2P and Na,P differ in the position of the b 2U orbital, which is higher than the eg and e, pairs of orbit* b Li2P but lower in Na2P. The order in Na,P is the same as in the porphyrin dianion [12], consistent with the seater distance of sodium from the ring than lithium. However, this ordering in Na2P may not be entirely realistic, since
R. W. MUNN ET AL,.
300
O-
b 3g--b -- ==_ 2g--
---
%i--
-
-1
-a? ___-a,--4-__ b --______----a
al, ---_^-
111
b39’ ag--\;
2u
_-------b,,___
bzu=;\
b lu
y:
,,.
b,, %-I,‘= = *;-xz:s’ -e, -_*b2u b1g=+-- ‘- -___a29 -b 3u
Porphyrin
LizP
FIG. 2. Calculated orbital energies and symmetries Na2P.
NazP for porphyrin,
LizP
the 3d orbitals in the CND0/2 method are taken as having the same orbital exponent as the 3s and 3p orbitals [7] _This implies that the sodium 3d orbitals are relatively contracted and so interact less strongly with neighbouring atoms than in re4ity. A further similarity between LiaP and NaaP and the porphyrin dianion is the order of the degenerate pairs of orbitals, the es orbitals lying above the e, orbitals. This order is reversed in D,, and D,, magnesium(II) porphyrin [12], where the metal-ring interactions are less weak.
CONCLUSIONS We have predicted the structures and metal-metal vibrational frequencies for dihthium and disodium porphyrin. The possibility of observing these low frequencies seems worth investigating.
CNDO MO CALCULATIONS
ON PORPHYRINS-II
301
The molecuku orbitals calculated by the CNDO12 method give a consistent picture of porphyrin, its dianion, and its lithium, sodium and ma~esium(II) salts. The two LUMOs and two HOMOs remain remarkably unaffected by the substitution of metals. This would explain why the four-orbital model [13] is successful in explaining the observed similarities between the electronic spectra of dilithium and disodium tetraphenylporphyrin [4] and tfiose of other metalloporphyrins. The CNDO/2 method has been extended to compounds containing atoms of the first transition series [14], and applied to copper(I1) porphyrin [IS]. It would appear worthwhile to perform similar cahzulations for other metalloporphyrins, and also to develop analogues of the CNDO/S parametrization [S] for calculating the excited states of complexes containing second and third-row elements_ Although the CNDO method is semi-empirical, it is found to give results for porphyrins broadly comparable with those obtained by ab initio methods [16,17] _ We thank the SRC for a Research Studenship (SIC).
REFERENCES 1. S. J. Chantrell, C A. McAuBffe, R. W. Munn, A. C. Pratt and R. V. Weaver, preceding paper, Part I, Bioinorg. Chem. 7 (4), (1977). 2. R. HiII, Biochem. J. 19,341(1925X 3. J_ W. Barnes and G. D. Dorough,J. Amer. CEem Sec. 72,404s (195d). 4. G. D. Dorough, J. R. MiUer and F. M. Huennekens, J. Amer. Chem Sot. 73,431s (1951). 5. J. W. Dodd and N. S. Hush,1 Chem Sot. 4607 (1964). 6. J. A. Pople and D. L. Beveridge, Approximate Molecular Orbital Theory, hkGrawHi& New York, 1970. 7_ D. P. Santry and G. A. SegaI,J. Chem. Phys. 47,158 (1967). 8. R. L. EIIis, G. Kuehnienz and H. H. Jaff& Theor. Chim. Acta 26,131 (1972). 9. J. E. FaIk, Porphyrins and Metalloporphyrins EIsevier, Amsterdam, 1964, p_ 30. 1C. M. Zemer and M. Goutennan, Theor. Chim. Acta 4,44 (1966). ll- L. PauIing, GenetaZ Chemistry. Freeman, San Francisco, 1970, Chap. 6,3rd ed. 12. G. M. hIaggiora,J. Amer. Gem. Sot. 95,6555 (1973). 13. M. Gouterrnan, J. Gem Phys. 30, 1139 (1959); J. Mol. Spectrosc. 6, 138 (1961); M. Gouterman, G. H. Wagni&e and L. C. Snyder,1 Mol. Spectrosc. 11,108 (1963). 14. D. W. clack, N. S. Hush and J. R. YandIe,J. Chem Phys. 57,3503 (1972). 15. D. W. Clack and M. S. F animond, JCS Dalton. 29 (1972). 16. J. AL-nlGf,Intern J. Quantum Chem. 8,915 (1974). 17. D. SpangIer, R. McKinney, R. E. Christoffersen, G. M. Maggiora and L. L. Shipman, Chem. Phys. Letters 36,427 (1975). Received 30 November
1976; revised 22 December
I976
