^{1,2}, Y. Anusooya Pati

^{1,a)}and S. Ramasesha

^{1}

### Abstract

The symmetrized density matrix renormalization group method is used to study linear and nonlinear optical properties of free base porphine and metalloporphine. Long-range interacting model, namely, Pariser-Parr-Pople model is employed to capture the quantum many-body effect in these systems. The nonlinear optical coefficients are computed within the correction vector method. The computed singlet and triplet low-lying excited state energies and their charge densities are in excellent agreement with experimental as well as many other theoretical results. The rearrangement of the charge density at carbon and nitrogen sites, on excitation, is discussed. From our bond order calculation, we conclude that porphine is well described by the 18-annulenic structure in the ground state and the molecule expands upon excitation. We have modeled the regular metalloporphine by taking an effective electric field due to the metal ion and computed the excitation spectrum. Metalloporphines have D_{4h} symmetry and hence have more degenerate excited states. The ground state of metalloporphines shows 20-annulenic structure, as the charge on the metal ion increases. The linear polarizability seems to increase with the charge initially and then saturates. The same trend is observed in third order polarizability coefficients.

MK thanks UGC India for financial support. SR thanks DST India for funding through different programmes.

I. INTRODUCTION

II. METHODOLOGY

III. RESULTS AND DISCUSSION

A. Free base porphine

1. Electron density and bond order analysis

B. Metalloporphines

1. Ground statecharge density and bond orders

2. Optical properties

3. Triplet-triplet spectra

IV. NONLINEAR OPTICAL PROPERTIES OF PORPHINES

A. Results and discussion

V. CONCLUSION

### Key Topics

- Excited states
- 46.0
- Chemical bonds
- 32.0
- Macromolecules
- 23.0
- Carrier density
- 14.0
- Oxidation
- 13.0

## Figures

General structure of FBP. Sites are numbered in bold and transfer integrals (in eV) are given in blue color. Labelling of the sites meso, α and β are also shown in the figure. The system has D_{2} symmetry and all other bond transfers are given by symmetry.

General structure of FBP. Sites are numbered in bold and transfer integrals (in eV) are given in blue color. Labelling of the sites meso, α and β are also shown in the figure. The system has D_{2} symmetry and all other bond transfers are given by symmetry.

A highly accurate scheme for building the porphine structure for DMRG calculations. At every step of the DMRG algorithm, we add two new sites shown by filled circles. Positive integers correspond to the sites of the left block and negative integers to the sites of the right block.

A highly accurate scheme for building the porphine structure for DMRG calculations. At every step of the DMRG algorithm, we add two new sites shown by filled circles. Positive integers correspond to the sites of the left block and negative integers to the sites of the right block.

Electron density and b.o. for the gs of porphine. Charge densities are shown on the left part of the structure while b.o.s are shown on the right part. The site indices and bond indices are given in red and blue, respectively, for half of the system. The symmetry gives value for remaining sites and bonds of the molecule.

Electron density and b.o. for the gs of porphine. Charge densities are shown on the left part of the structure while b.o.s are shown on the right part. The site indices and bond indices are given in red and blue, respectively, for half of the system. The symmetry gives value for remaining sites and bonds of the molecule.

Two possible equilibrium geometries in gs: (a) 18-sites annulenic structure and (b) 20-sites annulenic structure, shown by bold lines.

Two possible equilibrium geometries in gs: (a) 18-sites annulenic structure and (b) 20-sites annulenic structure, shown by bold lines.

Electron density, spin density and b.o.s for the lowest triplet state of porphine. Spin and charge densities are shown on the left part of the structure while b.o.s are shown on the right part. The symmetry gives value for other half of the molecule.

Electron density, spin density and b.o.s for the lowest triplet state of porphine. Spin and charge densities are shown on the left part of the structure while b.o.s are shown on the right part. The symmetry gives value for other half of the molecule.

Tumbling averaged linear polarizability (α) vs *q* _{ m } at three different frequencies.

Tumbling averaged linear polarizability (α) vs *q* _{ m } at three different frequencies.

## Tables

Comparison of excitation gaps and transition dipole moments between DMRG and exact calculations in the non-interacting limit. Gaps are given in eV and transition dipoles are in a.u.

Comparison of excitation gaps and transition dipole moments between DMRG and exact calculations in the non-interacting limit. Gaps are given in eV and transition dipoles are in a.u.

Excitation gaps of six low-lying excited states and corresponding transition dipole moments compared with the experimental results for optically allowed states. Calculated oscillator strengths are given in parenthesis. Experimental results are from Ref. 42. The experimental oscillator strengths are normalized with respect to the most intense absorption. The sum of calculated intensity ( + ) for the state 3 and 4 is taken to be unity as they are nearly degenerate and all others are normalized with respect to it. Transition dipole between gs and all excited *A* states strictly vanishes by symmetry.

Excitation gaps of six low-lying excited states and corresponding transition dipole moments compared with the experimental results for optically allowed states. Calculated oscillator strengths are given in parenthesis. Experimental results are from Ref. 42. The experimental oscillator strengths are normalized with respect to the most intense absorption. The sum of calculated intensity ( + ) for the state 3 and 4 is taken to be unity as they are nearly degenerate and all others are normalized with respect to it. Transition dipole between gs and all excited *A* states strictly vanishes by symmetry.

Excitation gaps of low-lying excited states and transition dipole moments in triplet manifolds. Note that all the excitations are from *B* to *A* space. Experimental results are from references (Ref. 44).

Excitation gaps of low-lying excited states and transition dipole moments in triplet manifolds. Note that all the excitations are from *B* to *A* space. Experimental results are from references (Ref. 44).

Comparison of experimental excitation gaps and one-photon intensities with calculated values from DMRG and other techniques. The intensity of the most intense transition in each case is arbitrarily fixed at unity and all other intensities are quoted as fractions of the intensity of this transition and are given in parentheses.

Comparison of experimental excitation gaps and one-photon intensities with calculated values from DMRG and other techniques. The intensity of the most intense transition in each case is arbitrarily fixed at unity and all other intensities are quoted as fractions of the intensity of this transition and are given in parentheses.

Electron density ρ for gs and difference of electron density δρ for the optically allowed states with respect to gs.

Electron density ρ for gs and difference of electron density δρ for the optically allowed states with respect to gs.

Bond orders of gs and difference in b.o. for six low-lying states with respect to gs, in the singlet manifold are given. Symmetry space of states are given in parentheses.

Bond orders of gs and difference in b.o. for six low-lying states with respect to gs, in the singlet manifold are given. Symmetry space of states are given in parentheses.

Charge densities on unique sites of metalloporphine for different oxidation states of the metal ion.

Charge densities on unique sites of metalloporphine for different oxidation states of the metal ion.

The variation in b.o.s of the porphine bonds with different oxidation states of the central metal ion. B.o.s of bonds for which the value is not quoted can be obtained by imposing symmetry of the porphine.

The variation in b.o.s of the porphine bonds with different oxidation states of the central metal ion. B.o.s of bonds for which the value is not quoted can be obtained by imposing symmetry of the porphine.

Excitation gaps for singlet-singlet transition of five lowest optically allowed states and transition dipole moments for different metallic charges.

Excitation gaps for singlet-singlet transition of five lowest optically allowed states and transition dipole moments for different metallic charges.

Triplet state energies, T-T gaps and corresponding transition dipole moments of metalloporphine for different oxidation states of metal ions.

Triplet state energies, T-T gaps and corresponding transition dipole moments of metalloporphine for different oxidation states of metal ions.

Tumbling averaged THG coefficient γ_{ av } in 10^{3} a.u., for different excitation frequencies and oxidation states of the central metal ion.

Tumbling averaged THG coefficient γ_{ av } in 10^{3} a.u., for different excitation frequencies and oxidation states of the central metal ion.

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