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# Treatment Of Electronically Excited States

Electronically excited states can be investigated using CFOUR using several theoretical approaches: Those are (a) CIS, (b) CIS(D), (c) EOM-CC2, (d) EOM-CCSD(2),(e) EOM-CCSD, (f) EOM-CC3, (g) EOM-CCSDT-3, (h) EOM-CCSDT, (i) EOM-CCSDTQ, (j) EOM-CCSD*, (k) EOM-CCSD(T)(a). Additional excited-state treatments involving higher than quadruple excitations are possible using the program MRCC by M. Kallay interfaced to CFOUR.

Running excited-state calculations requires specification of a corresponding ground-state method (via the keyword CALC) together with the corresponding option for EXCITE. The following combinations are currently available:

 Method CALCLEVEL EXCITE CIS SCF or HF CIS CIS(D) MP2 or MBPT(2) CIS(D) EOM-CC2 CC2 EOMEE EOM-CCSD(2) MP2 or MBPT(2) EOMEE EOM-CCSD CCSD EOMEE EOM-CC3 CC3 EOMEE EOM-CCSDT-3 CCSDT-3 EOMEE EOM-CCSDT CCSDT EOMEE EOM-CCSDTQ CCSDTQ EOMEE

There are also some options for non-iterative corrections to EOM-CCSD, which are discussed elsewhere.

For all approaches, an iterative diagonalization algorithm (a modified Davidson algorithm) is used to find the root of interest. The CIS(D) approach augments a CIS calculation by a perturbative treatment of double excitations.

Two distinct input formats can be used to direct the program in finding the corresponding eigenvalues and -vectors.

a) Input via the keyword ESTATE_SYM

With this keyword, the number of desired final states of each symmetry can be specified. For example, with ESTATE_SYM=2/3/1/1 one requests that the two lowest states are searched for within the first irreducible representation, the three lowest in the second, etc.

b) Input via an additional %excite* section

Via this section, specific initial guesses for the desired excited state vectors are supplied. The corresponding section is organized as follows: (1) the first entry (after the %excite* card) gives the number of roots to be searched for; (2) for each root the corresponding initial guess vectors are supplied by giving the number of entries for this guess (i.e., the number of non-zero amplitudes or coefficients for this vector) and then the corresponding values for this amplitudes together with the associated orbital indices. An example is the following input section

  %excite*
3
1
1 10 0 11 0 1.0
1
3 10 10 11 11 1.0
2
1 10 0 11 0 2.0
3 10 10 11 11 1.0


Three roots are here to be determined. For the first root the coefficient for the single excitation from orbital 10 to 11 is chosen to be 1.0 in the guess vector (all other amplitudes are set to zero), while for the second root the coefficient for the double excitation from orbital 10 to 11 is chosen to be set to 1. For the third root, the initial guess vector contains two entries, the first for the single excitation from orbital 10 to 11 with a value of 2.0 and the second for the double excitation from orbital 10 to 11 with value 1.0.

To be more specific, the convention for the input is that

single excitations

1 i 0 a 0 single excitation (alpha spin) from occupied orbital i to virtual orbital a
2 i 0 a 0 single excitation (beta spin) from occupied orbital i to virtual orbital a
double excitations

1 i j a b double excitation (alpha, alpha spin case) from occupied orbitals i and j to virtual orbitals a and b
2 i j a b double excitation (beta, beta spin case) from occupied orbitals i and j to virtual orbitals a and b
3 i j a b double excitation (alpha, beta spin case) from occupied orbitals i and j to virtual orbitals a and b

Note that the orbital ordering used is based on the orbital energies starting with the occupied with the lowest orbital energy (with the exception of continuum orbitals which are placed in either the HOMO or LUMO positions regardless or energy ordering). The ordering is not biased by any symmetry blocking and is separately done for alpha and beta spin-orbitals in the case of UHF calculations. In addition, orbitals which have been dropped from the correlated calculation (via DROPMO or FROZEN_CORE keywords) are included in the numbering, although excitations from these orbitals are not valid. For quick reference, the ordering used is the same as when the orbitals are printed at the end of the SCF calculation.

c) The %nearthis option

If you have two lines of this form in your ZMAT file:

%nearthis
0.1928

this will direct the calculation to use whatever initial guess strategy you have chosen for the first iteration but thereafter always follow the root of the minimatrix which is nearest the number below the %nearthis card. This is experimental and may require refinement with time.