^{1,2,a)}, Gary W. Trucks

^{2}and Michael J. Frisch

^{2}

### Abstract

In this work, we quantitatively investigate the difference between the linear response (LR) and the equation of motion (EOM) coupled cluster (CC) approaches in the calculation of transition properties, namely, dipole and oscillator strengths, for the most widely used truncated CC wave function, which includes single and double excitation operators. We compare systems of increasing size, where the size-extensivity may be important. Our results suggest that, for small molecules, the difference is small even with large basis sets. The difference increases with the size of the system, but it is numerically small until hundreds of electron pairs are correlated. Although these calculations may be possible in a few years, at present the EOM approach is more advantageous, albeit more approximate, because it is computationally less demanding.

I. INTRODUCTION

II. NONINTERACTING LiH MOLECULES

III. POLYENES

IV. DONOR-ACCEPTOR POLYENES (DA-POLYENES)

V. CONCLUSIONS

### Key Topics

- Basis sets
- 26.0
- Oscillators
- 16.0
- Ground states
- 9.0
- Wave functions
- 6.0
- Excited states
- 4.0

## Figures

Dipole strength (a.u.) as a function of the number of noninteracting LiH molecules, calculated with EOM-CCSD and LR-CCSD with various basis sets. The Li–H distance is 4.0 a.u. as in Ref. 7. At this distance the HF wave function has a singlet-triplet instability. The label Dunning refers to the Dunning’s basis set reported in Table I. The numbers inside the plot indicate the number of LiH when the EOM dipole strength becomes negative.

Dipole strength (a.u.) as a function of the number of noninteracting LiH molecules, calculated with EOM-CCSD and LR-CCSD with various basis sets. The Li–H distance is 4.0 a.u. as in Ref. 7. At this distance the HF wave function has a singlet-triplet instability. The label Dunning refers to the Dunning’s basis set reported in Table I. The numbers inside the plot indicate the number of LiH when the EOM dipole strength becomes negative.

Dipole strength (a.u.) as a function of the number of noninteracting LiH molecules, calculated with EOM-CCSD and LR-CCSD with various basis sets. The Li–H distance is 3.004 465 89 a.u., optimized at B3LYP/aug-cc-pVTZ level. At this distance the HF wave function is stable. The label Dunning refers to the Dunning’s basis set reported in Table I. The numbers inside the plot indicate the number of LiH when the EOM dipole strength becomes negative.

Dipole strength (a.u.) as a function of the number of noninteracting LiH molecules, calculated with EOM-CCSD and LR-CCSD with various basis sets. The Li–H distance is 3.004 465 89 a.u., optimized at B3LYP/aug-cc-pVTZ level. At this distance the HF wave function is stable. The label Dunning refers to the Dunning’s basis set reported in Table I. The numbers inside the plot indicate the number of LiH when the EOM dipole strength becomes negative.

Experimental and calculated (at EOM-CCSD level with two basis sets) transition energies (eV) relative to butadiene.

Experimental and calculated (at EOM-CCSD level with two basis sets) transition energies (eV) relative to butadiene.

Oscillator strength as a function of the transition energy for the linear polyenes of increasing size. EOM and LR approaches with two basis sets are used in the calculation.

Oscillator strength as a function of the transition energy for the linear polyenes of increasing size. EOM and LR approaches with two basis sets are used in the calculation.

Oscillator strength as a function of the number of conjugated double bonds for the linear polyenes of increasing size. EOM and LR approaches with two basis sets are used in the calculation.

Oscillator strength as a function of the number of conjugated double bonds for the linear polyenes of increasing size. EOM and LR approaches with two basis sets are used in the calculation.

UV spectrum for butadiene obtained with different basis sets and the EOM and LR oscillator strengths. The experimental spectrum is in Ref. 11.

UV spectrum for butadiene obtained with different basis sets and the EOM and LR oscillator strengths. The experimental spectrum is in Ref. 11.

Oscillator strength as a function of the basis set for the first transition of butadiene.

Oscillator strength as a function of the basis set for the first transition of butadiene.

Oscillator strength as a function of the transition energy for the DA-polyenes of increasing size. EOM and LR approaches with two basis sets are used in the calculation.

Oscillator strength as a function of the transition energy for the DA-polyenes of increasing size. EOM and LR approaches with two basis sets are used in the calculation.

Oscillator strength as a function of the number of conjugated CC double bonds for the DA-polyenes of increasing size. EOM and LR approaches with two basis sets are used in the calculation.

Oscillator strength as a function of the number of conjugated CC double bonds for the DA-polyenes of increasing size. EOM and LR approaches with two basis sets are used in the calculation.

Oscillator strength as a function of the basis set for the first transition of the smallest DA-polyene.

Oscillator strength as a function of the basis set for the first transition of the smallest DA-polyene.

## Tables

Dunning basis set used in the LiH calculation ( functions) (Ref. 9).

Dunning basis set used in the LiH calculation ( functions) (Ref. 9).

Dipole strengths for the noninteracting LiH molecules. Li–H internuclear distance is 4.0 a.u.

Dipole strengths for the noninteracting LiH molecules. Li–H internuclear distance is 4.0 a.u.

Dipole strengths for the noninteracting LiH molecules. Li–H internuclear distance is 3.004 465 89 a.u. (optimized geometry).

Dipole strengths for the noninteracting LiH molecules. Li–H internuclear distance is 3.004 465 89 a.u. (optimized geometry).

Transition energies (eV) for the polyenes from 2 to 5 conjugated double bonds. The experimental data are from Refs. 11–19.

Transition energies (eV) for the polyenes from 2 to 5 conjugated double bonds. The experimental data are from Refs. 11–19.

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