Reduction of the virtual space for coupled-cluster excitation energies of large molecules and embedded systems

Abstract

We investigate how the reduction of the virtual space affects coupled-cluster excitation energies at the approximate singles and doubles coupled-cluster level (CC2). In this reduced-virtual-space (RVS) approach, all virtual orbitals above a certain energy threshold are omitted in the correlation calculation. The effects of the RVS approach are assessed by calculations on the two lowest excitation energies of 11 biochromophores using different sizes of the virtual space. Our set of biochromophores consists of common model systems for the chromophores of the photoactive yellow protein, the green fluorescent protein, and rhodopsin. The RVS calculations show that most of the high-lying virtual orbitals can be neglected without significantly affecting the accuracy of the obtained excitation energies. Omitting all virtual orbitals above 50 eV in the correlation calculation introduces errors in the excitation energies that are smaller than 0.1 eV. By using a RVS energy threshold of 50 eV, the CC2 calculations using triple-ζ basis sets (TZVP) on protonated Schiff base retinal are accelerated by a factor of 6. We demonstrate the applicability of the RVS approach by performing CC2/TZVP calculations on the lowest singlet excitation energy of a rhodopsin model consisting of 165 atoms using RVS thresholds between 20 eV and 120 eV. The calculations on the rhodopsin model show that the RVS errors determined in the gas-phase are a very good approximation to the RVS errors in the protein environment. The RVS approach thus renders purely quantum mechanical treatments of chromophores in protein environments feasible and offers an ab initio alternative to quantum mechanics/molecular mechanics separation schemes.

Figure 1

The molecular structures of the studied molecules: (a) the rhodopsin chromophore models; (b) the photoactive yellow protein chromophore models; and (c) the green fluorescent protein chromophore models.

Figure 2

The molecular structure of the model used for retinal embedded in a protein environment. The rhodopsin model consists of 165 atoms.

Figure 3

The relative error (in eV) of the first singlet excitation energy is given as a function of the energy threshold (in eV) used in the reduction of the virtual space. No orbitals were frozen in the reference CC2 calculation. (a) photoactive yellow protein chromophore models; (b) green fluorescent protein chromophore models; and (c) rhodopsin chromophore models.

Figure 4

The relative error (in eV) of the second singlet excitation energy is given as a function of the energy threshold (in eV) used in the reduction of the virtual space. No orbitals were frozen in the reference CC2 calculation. (a) photoactive yellow protein chromophore models; (b) green fluorescent protein chromophore models; and (c) rhodopsin chromophore models.

Figure 5

The relative error (in eV) of the first singlet excitation energy of pHBDI⁻ as a function of the energy threshold (in eV) used in the reduction of the virtual space is shown for different sizes of the basis set.

Figure 6

The computing time (in CPU hours) and the error of the first singlet excitation energy of PSBT⁺ (in eV) as a function of the energy threshold (in eV) used in the reduction of the virtual space. The TZVP basis set was employed.

Figure 7

The relative error (in eV) of the first singlet excitation energy of ${\mathrm{PSB}11\mathrm{Me}}_2^{+}$ in the gas phase and of the rhodopsin model as a function of the energy threshold (in eV) used in the reduction of the virtual space. It is assumed that the excitation energy error for the rhodopsin and retinal states are identical at a RVS threshold of 120 eV. The TZVP basis set was employed.