Features¶

Restricted and unrestricted Hartree-Fock¶

Restricted closed-shell Hartree-Fock (RHF) can be used for single-point calculations, geometry optimizations, properties (dipole and quadrupole), population analysis (Mulliken and/or Loewdin), and as a reference wave function for coupled cluster calculations. RHF can be used within the Cavity Born-Oppenheimer approximation for single-point calculations.

Restricted open-shell Hartree-Fock (ROHF) can be used for single-point calculations.

Unrestricted Hartree-Fock (UHF) can be used for single-point calculations.

Setting up a Hartree-Fock calculation

Multilevel Hartree-Fock¶

Multilevel Hartree-Fock can be used for single-point calculations, and as a reference wave function for reduced space coupled cluster calculations.

Setting up a multilevel Hartree-Fock calculation

Quantum electrodynamics Hartree-Fock¶

Quantum electrodynamics Hartree-Fock supports the same features as restricted closed-shell Hartree-Fock (RHF) including molecular gradients, but the current geometry optimization does not work.

Strong coupling Quantum electrodynamics Hartree-Fock¶

Strong coupling quantum electrodynamics Hartree-Fock (SC-QED-HF) is available for calculations of ground state energies.

Time-dependent Hartree-Fock¶

Excitation energies and oscillator strengths at the TDHF level of theory are available either within the random phase (RPA) or the Tamm-Dancoff approximation (TDA). In addition, static and frequency-dependent polarizabilities can be obtained.

Quantum electrodynamics time-dependent Hartree-Fock¶

Quantum electrodynamics time-dependent Hartree-Fock supports the same features as time-dependent Hartree-Fock except the polarizabilities. In addition, a measure of the photon character of each excitation is computed.

CCS, CC2, CCSD, CC3 and CCSDT¶

For CCS, CC2, CCSD, and CC3, eT offers ground and excited state calculations in addition to dipole and quadrupole moments, EOM oscillator strengths and EOM Dyson orbitals.

Core-excited states for these methods are available employing core-valence separation (CVS). Ionized and core-ionized states can be computed using the diffuse orbital trick and CVS.

Core-excited states for these methods are available employing core-valence separation (CVS). Ionized and core-ionized states can be computed using the diffuse orbital trick and CVS.

For CCS, CC2, and CCSD also EOM polarizabilities and linear response oscillator strengths as well as polarizabilities are implemented. It is also possible to carry out the EOM polarizability calculations based on an asymmetric expression.

For CCS, CC2, and CCSD triplet excitation energies are implemented.

For CCSDT, ground and excited state energies are implemented.

Ground state energies for all CC methods in the Cavity Born-Oppenheimer approximation are implemented.

CCSD(T)¶

Ground state energies at the CCSD(T) level of theory are implemented.

Low-memory CC2¶

In eT, there are two versions of the CC2 code. The standard CC2 code has a memory requirement proportional to \(n_o^2 n_v^2\) , where \(n_o\) is the number of occupied orbitals and \(n_v\) is the number of virtual orbitals. However, the low-memory CC2 implementation has an \(N^2\) memory requirement, where \(N\) is the number of orbitals.

Currently, only ground and excited state energies are available with the low-memory CC2 code.

Multilevel coupled cluster¶

The multilevel CC2 (MLCC2) and multilevel CCSD (MLCCSD) methods are available with correlated natural transition orbitals, Cholesky orbitals (occupied and virtual), and projected atomic orbitals.

Currently, only ground and excited states are available at the MLCCSD level of theory.

Setting up a multilevel coupled cluster calculation

Time-dependent coupled cluster¶

Real-time propagation is available for CCS and CCSD methods. It solves the differential equations describing the time evolution of cluster amplitudes and Lagrange multipliers. The available integrators are

• Euler

• Gauss-Legendre (with order 2, 4 and 6)

• Runge-Kutta (with order 4)

• Dormand-Prince (with orders 5(4) and 8(5,3))

The time dependent quantities that are available as output are:

• Amplitudes

• Multipliers

• MO density matrix

• Energy

• Electric field

• Dipole moment

In addition, visualizable time-dependent density and spectra given by the Fast Fourier Transform of the dipole moment and of the electric field can be requested as output.

Quantum electrodynamics coupled cluster¶

Ground and excited state energies at the QED-CCSD level are implemented.

Warning

Excitation energies are only obtainable by requesting left eigenvectors in the solver cc es section.

Cholesky decomposition of the ERIs¶

The coupled cluster code is based on Cholesky decomposed electron repulsion integrals (ERIs). For sufficiently small systems, T1-transformed ERIs are constructed from the Cholesky vectors and stored in memory. For systems where the ERIs cannot be placed in memory, the T1-transformed Cholesky vectors are stored in memory if possible and ERIs are constructed from these vectors on the fly. For larger systems, the Cholesky vectors are stored on disk.

FCI¶

Full CI calculations are available for both closed (RHF reference) and open (ROHF reference) shells. In addition, dipole and quadrupole moments can be calculated for the ground state. Ground state energies can be calculated within the Cavity Born-Oppenheimer approximation.

QED-FCI¶

QED Full CI calculations are available for both closed (QED-HF or RHF reference) and open (ROHF or UHF reference) shells. In addition, dipole and quadrupole moments can be calculated for the ground state. Also transition dipole and quadrupole moments can be calculated.

MP2¶

Ground state energies at the MP2 level of theory are implemented.

Environments¶

The available QM/MM methods are

• Electrostatic embedding (non-polarizable)

• Polarizable QM/Fluctuating charges

• Polarizable Continuum Model

These methods can be coupled both with HF or CC wave functions. In case of QM/FQ, only HF ground state Fock and MOs are affected by QM/FQ.

Ground state energy calculations within the Cavity Born-Oppenheimer approximation can be run for HF, CC and CI. The photonic degrees of freedom are treated as a non-polarizable embedding.

Ground state¶

Analytical gradients are available at the HF and CCSD level of theory. Numerical gradients are available for HF and all CC methods.

Excited state¶

Analytical gradients are available at the CCSD level of theory. Numerical gradients are available for all CC methods.