Kramers unrestricted Coupled-Cluster methods

See [Visscher1996] for the initial CCSD(T) implementation. The Fock-space CC implementation is described in [Visscher2001].

**RELCC

Specification of reference determinant, type of calculation, and general settings.

.FOCKSP

Activate the Fock space module. This option should be used for multireference calculations. See further *CCFSPC. Because the first sector of Fock space gives the same result as a regular CCSD calculation, the latter calculation is switched off. If you do wish to perform also a regular CC calculation (e.g. to get the CCSD(T) energy) you need to activate this explicitly via .ENERGY (see below).

.ENERGY

Activate the energy calculation. This is the preferred option for calculations on closed shell or simple open shell systems and need not be specified explictly in such cases. For Fock space calculations the keyword switches on a separate single reference calculation done prior to the FS calculation.

Default:

Perform energy calculation.

.GRADIENT

Calculate the effective 1-particle density matrix. This option can be used to calculate molecular properties. For closed-shell MP2 see [vanStralen2005]. For closed-shell CC see [Shee2016].

Default:

No gradient calculation.

.EOMCC

Activate the equation of motion (EOMCC) module. This option can be used to obtain excitation energies (EOM-EE), singly ionized (EOM-IP) and electron attached (EOM-EA) states starting from a closed shell reference and at the CCSD level, by solving for the right-hand eigenvalues and eigenvectors of the appropriate similarity-transformed Hamiltonian.

Unlike in Fock-space calculations, where the full model Hamiltonian for each sector is diagonalized, in EOMCC the user must specify the desired number of roots per symmetry, (see *EOMCC for further details) and these are determined via matrix-free diagonalization procedures such as the Davidson method (see *CCDIAG for the options available).

Default:

No EOM-CC calculation.

.EOMPROP

Activate the calculation of excited-state first-order properties for the EOMCC module for CCSD wavefunctions, by solving for the left-hand eigenvectors of the corresponding similarity-transformed Hamiltonian. It should be specified along with .EOMCC as it requires the right-hand eigenvectors and, as such, the same type of calculation (EOM-EE/IP/EA) will be performed. See *EOMPROP for further details.

Default:

No EOM-CC excited-state expectation value calculation.

.NELEC

Number of correlated electrons. This variable determines the reference determinant to be used in the exponential expansion of the wave function. Since the default values correspond to the information passed on by the MOLTRA code on basis of the Hartree-Fock occupations and chosen range of active orbitals in MOLTRA, for CLOSED SHELL systems there is usually no need to specify this variable manually. If you do chose to specify this manually, you should make sure to count electrons carefully as the numbers relate to the number of correlated electrons rather than the total number. This number may therefore change if you change tresholds in the integral transformation.

For OPEN SHELL systems it is usually better to employ the multireference Fock space approach, except for simple cases such as a high-spin open shell state. In this case the single reference CCSD(T) ansatz works rater well. For such cases it is easier to use the .NELEC_OPEN keyword that allows to just specify the distribution of open shell electrons over the irreps, but for backwards compatibility we retain the older NELEC option as well.

Arguments:

Integer (NELEC(I),I=1,NFSYM*2).

Default:

Number of correlated electrons in closed shells in these irreps (written by **MOLTRA).

.NELEC_OPEN

Distribution of correlated open shell electrons over the irreps. This determines the reference determinant for open shell single reference calculations.

This input should always be given for average-of-configuration SCF calculations that are followed by a CC calculation. The total number of electrons that is given should correspond to the number of open shell electrons.

Arguments:

Integer (NELEC_OPEN(I),I=1,NFSYM*2).

Default:

Zero. (note that this default leads to wrong results because a closed shell ion will be calculated if no input is given).

.NEL_F1

Number of electrons in the gerade irreps of the Abelian symmetry group. This works like the NELEC keyword, but uses the supersymmetry possible for linear groups in which irreps are ordered as 1/2, -1/2, 3/2, -3/2, 5/2, ... (with the number being the m_j value).

.NEL_F2

Number of electrons in the ungerade irreps of the Abelian symmetry group.

.PRINT

Print level.

Default:

.PRINT
 0

.COUNTMEM

Stop CC module after counting the total memory demand. Needs only MRCONEE.

.TIMING

Print detailed timing information.

Default:

Only limited timing information is printed.

.DEBUG

Print debug information.

Default:

Debug information is not printed.

.RESTART

Reuses information from prior calculations to resume the calculation from the last sucessfully recorded checkpoint. In order for a restart to be possible, the appropriate files from both the 4-index transformation - e.g. MRCONEE, MDCINT (and MDCINX* for parallel runs) and, if the transformation of property operators was requested, MDPROP - and from the previous coupled cluster run (ft.* for the sorting of integrals, MCCRES* for the amplitudes) have to be present at the scratch directory. Given the size and number of these files, this means in practice one must request the the scratch directory is kept at the end of the runs (see the pam script options for details)

Default:

No restart is performed.

.NOSORT

Forces the code to skip the sorting of integrals coming from the 4-index transformation into six integral classes. Using this option without the integral sorting stap having been properly carried out may produce incorrect results.

Default:

Sorting of integrals into classes is performed.

*CCENER

Covers options related to energy.

.NOMP2

Deactivate MP2 calculation.

.NOSD

Deactivate CCSD calculation.

.NOSDT

Deactivate the calculation of perturbative triples. This is potentially useful when running into memory problems for very big calculations and will also save some CPU time.

.MAXIT

Set maximum number of iterations allowed to solve the CC equations.

.MAXDIM

Set maximum number of amplitude vectors used in the DIIS extrapolation.

.NTOL

Specify requested convergence (10^-NTOL) in the amplitudes.

.NOSING

Eliminate T1 amplitudes in the calculation (only interesting for test purposes, this gives no computational speed-up).

.NODOUB

Eliminate T2 amplitudes in the calculation (only interesting for test purposes, this gives no computational speed-up). Deactivate contribution from doubles; corresponds to a CCS calculation.

*CCFOPR

Calculate first-order properties (expectation values) for the MP2 and CCSD wave function.

.MP2G

Use MP2 wave function.

.CCSDG

Use CCSD wave function.

.NATORB

Calculate natural orbitals (currently only for MP2 density matrix)

.RELAXED

Use orbital-relaxed density matrix (currently only for MP2). The current default for MP2 and CC wave functions is to use the unrelaxed density matrix. This is computationally less expensive, but also less accurate.

*EOMCC

write me

.EE

write me

Arguments: two integers, the first specifying the state symmetry and the second the number of states for this symmetry

.IP

write me

Arguments: two integers, the first specifying the state symmetry and the second the number of states for this symmetry

.EA

write me

Arguments: two integers, the first specifying the state symmetry and the second the number of states for this symmetry

*EOMPROP

.EXCPRP

number of excited states to calculate expectation values for, on a given symmetry.

Arguments: two integers, the first specifying the state symmetry and the second the number of states for this symmetry

*CCDIAG

write me

.MAXITER

Controls the maximum number of iterations in the Davidson procedure

.NOR2L

Do not use the right-hand side vectors as guess for the left-hand side, but rather one of the TRV options.

.NOOVERLAP

Disables overlap in sorting the left/right-hand side eigenvalues and eigenvectors.

.TRV_I

Creates trial vectors based on unit vectors sorted by lowest energy.

.TRV_FU

Creates unit trial vectors.

.TRV_CCS

Creates trial vectors from the eigenvectors of the singles-singles EOM-EE/IP/EA blocks.

*CCFSPC

Perform a Fock space MRCC calculation. Fock space allows variable particle number. Sectors \((m,n)\) in Fock space corresponds to \(N+n-m\) - electron states obtained by the generation of \(m\) holes (electron removal) and \(n\) particles (electron attachment) with respect to a closed-shell reference determinant, the \((0,0)\) sector. Within each specified sector (and the lower ones), an effective Hamiltonian is built and diagonalized to give CC energies for a set of states.

.DOIH

Use the Intermediate Hamiltonian formalism in which an auxiliary space is used to prevent the “intruder state” problem. Default: IH formalism not used.

.DOEA

Calculate electron affinities (add one electron to the reference state, allowing occupation of the active virtual orbitals, corresponding to the \((0,1)\) sector).

.DOIE

Calculate ionization energies (remove one electron from the reference state, allowing depletion of the active occupied orbitals, corresponding to the \((1,0)\) sector).

.DOEA2

Calculate second electron affinities (add two electrons to the reference state, allowing occupation of the active virtual orbitals, corresponding to the \((0,2)\) sector).

.DOIE2

Calculate second ionization energies (remove two electrons from the reference state, allowing depletion of the active occupied orbitals, corresponding to the \((2,0)\) sector).

.DOEXC

Calculate excitation energies (allow excitation from the set of active occupied orbitals to the set of active virtual orbitals, corresponding to the \((1,1)\) sector).

.NACTH

Specification of the set of active hole orbitals (from which ionization/excitation takes place)

.NACTP

Specification of the set of active particle orbitals (to which electron attachment/excitation takes place)

.MAXIT

Maximum number of iterations allowed to solve the FSCC equations

.MAXDIM

Set maximum number of amplitude vectors used in the DIIS extrapolation.

.NTOL

Specify requested convergence (10^-NTOL) in the amplitudes.

.GESTAT

Specify the state number in the last active sector to pick the energy from (remember to account for degeneracies) for a state-specific FSCC geometry optimization based on a numerical gradient.

*CCIH

Options for intermediate hamiltonian in FSCC.

.EHMIN

Minimum orbital energy of occupied orbitals forming the auxiliary (Pi) space. Orbitals with energies lower than this energy are taken in the secundary (Q) space and do not contribute to the model space.

low limit of orbital energies of active occupied orbitals, which constitute the secondary Pi space. Could be used in (1,0), (2,0) and (1,1) sectors. Arguments: real.

.EHMAX

Maximum orbital energy of occupied orbitals forming the auxiliary (Pi) space. Orbitals with energies higher than this energy are taken in the primary (Pm) space.

This is upper limit of one-electronic energies of active occupied orbitals, which constitute the secondary Pi space. Could be used in (1,0), (2,0) and (1,1) sectors. Arguments: real.

.EPMIN

Minimum orbital energy of virtual orbitals forming the auxiliary (Pi) space. Orbitals with energies lower than this energy are taken in the primary (Pm) space.

This is the low limit of orbital energies of active virtual orbitals, which constitute the secondary Pi space. Could be used in (0,1), (0,2) and (1,1) sectors. Arguments: real.

.EPMAX

Maximum orbital energy of virtual orbitals forming the auxiliary (Pi) space. Orbitals with energies higher than this energy are taken in the secundary (Q) space and do not contribute to the model space.

This is the upper limit of one-electronic energies of active virtual orbitals, which constitute the secondary Pi space. Could be used in (0,1), (0,2) and (1,1) sectors. Arguments: real.

Other Intermediate Hamiltonian (IH) input parameters

For experts only.

Following keywords belong to the CCIH namelist section.

.IHSCHEME

Choose particular IH scheme. Arguments: Integer IHSCHEME = 1, or 2.

The IHSCHEME=1 corresponds to the extrapolated IH (XIH) approach, described in the paper [Eliav2005].

Main idea: proper modification of the energetic denominators, containing problematic Pi -> Q transition. The original denominator 1/(E_Pi - E_Q) , used during CC iterations, is substituted by the following expression (1)

\[\frac{(1-[\frac{AIH*SHIFT}{(E_{Pi} - E_{Q} + SHIFT)}]^{NIH})}{\frac{(1-AIH*SHIFT}{(E_{Pi} - E_{Q} + SHIFT))}},\]

here AIH, SHIFT,NIH are parameters, specially chosen for overcoming of the intruder states problem. These parameters could be used in the procedure of the extrapolation of the “exact” effective Hamiltonian solutions from corresponding IH CC energies and wave functions.

The IHSCHEME=2 corresponds to the simplified IH-2 approach, described in the paper [Landau2004].

Here the problematic denominators \(1/(E_{Pi} - E_{Q})\) are substituted simply by the factor 0.

Default: IHSCHEME = 2

Next key options are used only in case of XIH (IHSCHEME = 1).

.SHIFTH11

Energy shift for the one-electronic excitations in (1,0) sector. Arguments: real.

.SHIFTH12

Energy shift for the two-electronic excitations in (1,0) sector. Arguments: real.

.SHIFTH2

Energy shift for the two-electronic excitations in (2,0) sector. Arguments: real.

.SHIFTP11

Energy shift for the one-electronic excitations in (0,1) sector. Arguments: real.

.SHIFTP12

Energy shift for the two-electronic excitations in (0,1) sector. Arguments: real.

.SHIFTP2

Energy shift for the two-electronic excitations in (0,2) sector. Arguments: real. Usually we choose the approximate difference between the highest orbital energy belonging to Pi and the lowest orbital energy belonging to the Pm space. Works only with the old style of RELCC input.

.SHIFTHP

Energy shift for the two-electronic excitations in (1,1) sector. Arguments: real

.AIH

Compensation factor, used in expression (1). Arguments: real positive, not greater then 1.0.

.NIH

Compensation power, used in expression (1). Arguments: integer.

In the case of the limit: AIH=1.0 and NIH -> “infinity” ( NIH>100, in practice) we have so called “full compensation” method, corresponding to the extrapolation of the effective Hamiltonian from the intermediate one.

*CCSORT

Specialist options related to the sorting of two-electron integrals and the calculation of the reference Fock matrix.

.NORECMP

Do not recompute the Fock matrix, but assume a diagonal matrix with the orbital energies taken from the SCF program on the dioagonal. This is usually not recommended as the latter correspond to a restricted open shell expression and RELCCSD uses an unrestricted formalism. For closed shell systems the two expressions are identical and this option merely suppresses a build-in check on the accuracy of transformed integrals.

.USEOE

Ignore recomputed Fock matrix and use orbital energies supplied by the SCF program. This option is sometimes useful for degenerate open shell cases in which case the perturbation theory for the unrestricted formalism is not invariant for rotations among degenerate orbitals. It should only change the outcome of the [T], (T) and -T energy corrections.

*CCRESTART

Control parameters for the restart option. The default behavior of the restart option is to verify whether in the RELCCSD the successive checkpoints have been passed, and restart the calculation at the first one which is not flagged as “Completed, restartable”.

For example, one would have

Status of the calculations
Integral sort # 1 :                   Completed, restartable
Integral sort # 2 :                   Completed, restartable
Fock matrix build :                   Completed, restartable
MP2 energy calculation :              Completed, restartable
CCSD energy calculation :             Completed, restartable
CCSD(T) energy calculation :          Completed, restartable

if a calculations has successfully has passed through all checkpoints.

For the single-reference calculations the restart is straightforward and in general no additional keywords are necessary. Users must nevertheless be careful that the restart is performed for exactly the same calculation, as there are no interla consistency checks in place in the case of a restart: this means that, for example, if either the geometry or the number of corrlated electrons or virtual spinors has been changed after the initial calculations, if the RESTART option is on the code will proceed with the old checkpoint data (sorted integrals, etc) and any results will be erroneous.

Fock-space calculations can also be restarted, but for these additional care must be taken: (1) One must redo the integral sorting steps if the model (P) or correlation (Q) spaces change dimension. A change in the values that define the partition between main (Pm) and intermediate (Pi) model spaces, on the other hand, does not require the integral sorting to be redone. (2) One has to specifically indentify which which sectors of Fock space are to be (re)calculated and which should be skipped. Some examples of such a procedure can be found in the test set.

.UNCONVERGED

Forces results from unconverged iterative procedures to be considered as converged.

Default:

False

.FORCER

Forces restart even if setup is potentially different (number of electrons, active/inactive spinors etc).

Default:

False

.REDOCCSD

Forces the iterative procedure to solve the CCSD (or CCD or CCS) equations to be performed, even if in a prior run it has been marked as completed.

Default:

False

.REDOSECT

In the case of fock-space calculations, indicate which sectors are to be relcalculated during the restart.

This keyword expects two lines as input; on the first line, an integer specifying how many sectors are recalculated and in the second line a list of the sectors in question in the RELCC notation.

.REDOSECT
 2
 00 01

will redo sectors 0h0p and 0h1p

Default:

All sectors are recalculated

.SKIPSECT

In the case of fock-space calculations, indicate which sectors are to be skipped during the restart

This keyword expects two lines as input; on the first line, an integer specifying how many sectors are recalculated and in the second line a list of the sectors in question in the RELCC notation.

.SKIPSECT
 2
 00 01

will bypass the calculation of sectors 0h0p and 0h1p.

Default:

No sectors are skipped

.REDOSORT

Forces the sorting into the six integral classes to be performed again, even if prior sorting was completed.

Default:

False. integrals are not resorted if the prior sorting was completed.