^{1,2,a)}, Benedetta Mennucci

^{3}, Giovanni Scalmani

^{2}, Gary W. Trucks

^{2}and Michael J. Frisch

^{2}

### Abstract

We present a study of excitation energies in solution at the equation of motioncoupled cluster singles and doubles (EOM-CCSD) level of theory. The solvent effect is introduced with a state specific polarizable continuum model (PCM), where the solute-solvent interaction is specific for the state of interest. Three definitions of the excited state one-particle density matrix (1PDM) are tested in order to gain information for the development of an integrated EOM-CCSD/PCM method. The calculations show the accuracy of this approach for the computation of such property in solution. Solvent shifts between nonpolar and polar solvents are in good agreement with experiment for the test cases. The completely unrelaxed 1PDM is shown to be a balanced choice between computational effort and accuracy for vertical excitation energies, whereas the response of the ground state CCSD amplitudes and of the molecular orbitals is important for other properties, as for instance the dipole moment.

I. INTRODUCTION

II. COMPUTATIONAL DETAILS

III. RESULTS

IV. CONCLUSIONS

### Key Topics

- Solvents
- 60.0
- Ground states
- 13.0
- Excited states
- 12.0
- Polarization
- 6.0
- Excitation energies
- 5.0

## Figures

Acrolein.

Acrolein.

MCP.

MCP.

Convergence of the transition energy (eV) for the PCM macroiterations with the equilibrium (Eq) and nonequilibrium (NEq) schemes for the first transition of acrolein in water with the 1PDM-U. The X axis reports the number of iterations.

Convergence of the transition energy (eV) for the PCM macroiterations with the equilibrium (Eq) and nonequilibrium (NEq) schemes for the first transition of acrolein in water with the 1PDM-U. The X axis reports the number of iterations.

Convergence of the transition energy (eV) for the PCM macroiterations with the equilibrium (Eq) and nonequilibrium (NEq) schemes for the second transition of acrolein in water with the 1PDM-U. The X axis reports the number of iterations.

Convergence of the transition energy (eV) for the PCM macroiterations with the equilibrium (Eq) and nonequilibrium (NEq) schemes for the second transition of acrolein in water with the 1PDM-U. The X axis reports the number of iterations.

## Tables

Nonequilibrium (vertical) transition energies and solvent shift (eV) for the first excited state of acrolein in gas phase, in water , and in cyclohexane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Nonequilibrium (vertical) transition energies and solvent shift (eV) for the first excited state of acrolein in gas phase, in water , and in cyclohexane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Nonequilibrium (vertical) transition energies and solvent shift (eV) for the second excited state of acrolein in gas phase, in water , and in cyclohexane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Nonequilibrium (vertical) transition energies and solvent shift (eV) for the second excited state of acrolein in gas phase, in water , and in cyclohexane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Equilibrium transition energies and solvent shift (eV) for the first excited state of acrolein in gas phase, in water , and in cyclohexane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Equilibrium transition energies and solvent shift (eV) for the first excited state of acrolein in gas phase, in water , and in cyclohexane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Equilibrium transition energies and solvent shift (eV) for the second excited state of acrolein in gas phase, in water , and in cyclohexane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Equilibrium transition energies and solvent shift (eV) for the second excited state of acrolein in gas phase, in water , and in cyclohexane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Nonequilibrium (vertical) transition energies and solvent shift (eV) for the first excited state of MCP in gas phase, in methanol , and in n-pentane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Nonequilibrium (vertical) transition energies and solvent shift (eV) for the first excited state of MCP in gas phase, in methanol , and in n-pentane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Nonequilibrium (vertical) transition energies and solvent shift (eV) for the second excited state of MCP in gas phase, in methanol , and in n-pentane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Nonequilibrium (vertical) transition energies and solvent shift (eV) for the second excited state of MCP in gas phase, in methanol , and in n-pentane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Equilibrium transition energies and solvent shift (eV) for the first excited state of MCP in gas phase, in methanol , and in n-pentane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Equilibrium transition energies and solvent shift (eV) for the first excited state of MCP in gas phase, in methanol , and in n-pentane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Equilibrium transition energies and solvent shift (eV) for the second excited state of MCP in gas phase, in methanol , and in n-pentane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Equilibrium transition energies and solvent shift (eV) for the second excited state of MCP in gas phase, in methanol , and in n-pentane with the different choices of the 1PDM, defined in Sec. II, and two basis sets (VDZ is short for aug-cc-pVDZ). The transition energy calculations are performed at the optimized geometry in the corresponding medium.

Dipole moments (D) of the ground and the first excited states of MCP in methanol. The excited state dipoles are calculated with the various definitions of the 1PDM at the geometry of the ground state.

Dipole moments (D) of the ground and the first excited states of MCP in methanol. The excited state dipoles are calculated with the various definitions of the 1PDM at the geometry of the ground state.

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