The equation-of-motion singles, doubles and triples (EOM-CCSDT) method
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is an extension of EOM-CCSD method in which
full triples are included both at the CC and EOM levels (in addition to singles and doubles).
Conceptually, EOM-CCSD and EOM-CCSDT are similar; the difference lies only in
the truncation level.
The CC Hamiltonian matrix being non-Hermitian, the left and right eigenvectors
are not Hermitian conjugates of each other but can be chosen to form
a mutually biorthogonal set. Using Eq. (7.97), the right eigenvectors
can be obtained and this is sufficient for obtaining energies (and excitation
energies) of
the corresponding target states. For gradients and properties, one must in addition
solve for the left eigenvectors of the respective states.
In EOM-CCSDT, the CCSDT Hamiltonian matrix is constructed up to the triples block
so as to give one-, two-, and three-body eigenvectors of the CC Hamiltonian.
As a result, the EOM-CCSDT computed energies and properties
are highly accurate as compared even to
the EOM-CCSD ones, by almost an order of magnitude. For example,
EOM-CCSDT provides an accuracy of eV for singly excited states and single
bond-breaking, and an accuracy of 0.1–0.2 eV for doubly excited states. In contrast,
at the EOM-CCSD levels these errors are on the order of 0.1–0.2 eV and eV, respectively.
EOM-CCSDT has scaling versus for EOM-CCSD.
Unlike EOM-CC(2,3), the EOM-CCSDT approach is rigorously size-intensive, as is EOM-CCSD,
but it is expensive enough that it can only be used with careful memory management.
Currently, the SF, EE, IP, EA, DIP, and DEA
variants of EOM-CCSDT are available,
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,
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for single point energy computations only, and can be requested by setting
METHOD = EOM-CCSDT. EOM-CCSDT is implemented within the new
coupled-cluster suite (CCMAN2) both within double and within singe precision.
Other job-control variables are similar to EOM-CCSD ones.
Illustrative examples employing EOM-CCSDT for computing excitation energies are given below.
Note: For non-trivial calculations we recommend using CC_BACKEND=XM.
Example 7.152 Computation of first excited singlet (B) and first excited triplet (B) energies of BH using EOM-EE-CCSDT/STO-3G in a single-precision setup.
$comment Computation of energies singlet and a triplet excited states of BH using EOM-EE-CCSDT/STO-3G $end $molecule 0 1 B H 1 1.234347 $end $rem basis=sto-3g job_type=sp method eom-ccsdt cc_single_prec=1 eom_single_prec=1 n_frozen_core fc ee_singlets=[0,0,1,0] ee_triplets=[0,0,0,1] $end
Example 7.153 Computation of singlet ground state and lowest triplet state energies of BH using EOM-SF-CCSDT/STO-3G in a double-precision setup.
$comment Computation of spin-flipping excitation energies of BH using EOM-SF-CCSDT/STO-3G, UHF reference $end $molecule 0 3 B H 1 1.191857 $end $rem jobtype=sp method eom-ccsdt basis=sto-3g sf_states=[1,0,0,1] eom_nguess_singles=4 n_frozen_core fc $end
Illustrative examples employing EOM-CCSDT method for computing ionization energies/electron affinities are given below.
Example 7.154 Computation of the singlet ground state and lowest four IP state energies of N using EOM-IP-CCSDT/6-31G* in a double-precision setup.
$molecule 0 1 N N 1 1.097685 $end $rem method=eom-ccsdt IP_states=[4] basis=6-31G* cc_symmetry=false EOM_davidson_convergence=6 job_type=sp $end
Example 7.155 Computation of singlet ground state and lowest four EA state energies of C using EOM-EA-CCSDT/6-31G* in a double-precision setup.
$molecule 0 1 C C 1 1.243 $end $rem method=eom-ccsdt EA_states=[4] basis=6-31G* cc_symmetry=false EOM_davidson_convergence=6 job_type=sp $end
Example 7.156 Computation of singlet ground state and lowest two DIP state energies of O using EOM-DIP-CCSDT/6-31G in a double-precision setup.
$molecule -2 1 O $end $rem method=eom-ccsdt basis=6-31g DIP_STATES=[2] cc_symmetry=false $end
Example 7.157 Computation of singlet ground state and lowest two DEA state energies of C using EOM-DEA-CCSDT/6-31G in a double-precision setup.
$molecule 2 1 C $end $rem method=eom-ccsdt basis=6-31g DEA_STATES=[2] cc_symmetry=false $end