25.2.2 Start guess for molecular orbitals

TURBOMOLE provides a flexible variety of possibilities to generate the start guesses for the molecular orbitals that are needed for the SCF iterations in the Hartree-Fock and DFT codes.

define provides possibilities to generate start orbitals using either an Extended Hückel Theory (EHT) guess with several options to specify the orbital occupation. This is the recommended option for difficult situations where simpler automatic start vector generations may fail. It also contains the possibility to generate start MOs from a preceeding calculation that either used a different basis set or a different point group symmetry.

For molecular calculations, the dscf and ridft programs provide internally three possibilities for generating start MOs, if no MO are found on file:

start density from superposition of atomic densities (default)
EHT guess for start MOs
core hamiltonian guess (fall back option, not recommended)

If no MOs are found in the control file, start orbitals will by default be generated from a superposition of spherically averaged atomic densities. This start density is then used to build a Fock matrix which is diagonalized. The coefficients for the start MOs are determined from the eigenvectors of the Fock matrix. If also no occupation numbers found on file, it will be tried to guess them from the eigenvalues of the Fock matrix according to the Aufbau principle (dscf, ridft and riper). Note that the guess is performed at the same level of theory as the SCF calculation. That is, the guess can utilize MARI-J, senex, and semilocal DFT for efficiency. In 2-component runs, a 1-component superposition of atomic densities is carried out before the initial construction of spinors. To use the two-component generalization of the guess, the keyword $atmgs2c can additionally be set (default starting from V8.0.1) and $noatmgs2c uses 1c orbitals to directly construct spinors. Then, the start coefficients are determined from the eigenvectors of the two-component Fock matrix including spin–orbit effects. This way, spin–orbit coupling is directly included and a better energy will be obtained after the first iteration. The atomdens data group can be used to set multiple options. For example, it may look like this:

 $atomdens total_charge=0 unpaired=0
   pcharge=+2.1d0  1-3
   pcharge=+3.0d0  4-13
   pcharge=-2.1d0  14-31
   aos=eht
   occ=ceo

total_charge=int

defines the total charge of the system (integer, default: 0). Input for the charge equilibration and for determining the occupation, if not specified in control.

unpaired=int

defines the difference between the number of $\alpha$- and $\beta$-spin electrons (integer, default: 0). Only used as input for determining the occupation, if not specified in control. In the 2-component guess, this value is set to normalize the individual spin at each atom for the non-collinear guess. If this is not set and no UHF/UKS occupation could be determined, only the total particle density will be used in the 2-component guess if not forcespin (see below) is set.

pcharge=val list

sets the charge for the atoms in “list“ to “val“ (floating point value). If only specified for a subset of atoms, 0 will used for those atoms for which no partial charge is set.

aos

defines the atomic orbitals that will be used for the generation of the atomic densities. Possible choices are

eht: the EHT basis (default)
iao: the reference atomic orbitals for the calculation of intrinisic atomic orbitals (only recommended if the EHT basis is not sufficient)
basis: the orbital basis itself (only meaningful for generally contracted basis sets where the first contracted orbitals are close to atomic orbitals)

Default: aos=eht.

occ

occupation scheme used for spherically averaged atomic densities

ceo: canonical ensemble densities for atoms in molecules (default)
eht: canonical ensemble densities for neutral isolated atoms

sxeig/syeig/szeig list

direction of spins for atoms in “list”. z direction is the default. The direction can also be set with the polar angles and “sueig theta phi list” (theta and phi are the respective angles). Please make sure that your input and the global option in the control are a meaningful combination.

nospin

do not use spin densities in the 2-component guess.

forcespin

use spin densities in the 2-component guess without normalization of the total spin to properly match the number of unpaired electrons.

tbpcharges

partial charges of all atoms are determined from the structure and a charge equilibration scheme (default for dscf, ridft, and molcular part of riper).

hf

performs the initial guess at the Hartree–Fock level using MARI-J/RI-J in ridft or conventional integrals in dscf. This option is ignored by riper and only included for legacy support.

By default, partial charges for all atoms in molecular system are be determined from the structure and the specified total charge using a charge equilibration scheme. User-specified charges replace this scheme by the input charges. Periodic calculations do not use partial charges so the corresponding option needs to be set in this case.

The EHT guess build-in in dscf and ridft is activated with the data group $eht:

   $eht charge=n   unpaired=m  glueck=K

n: is an integer number which defines the overall charge of the molecular system (default: n=0)
m: is the difference between the number of electrons with $\alpha$ spin and the number of electrons with $\beta$ spin (default: m=0)
K: is the global scaling factor for the EHT Hamiltonian matrix: $H_{ij} = K S_{ij}(E_i+E_j)/2$ (default: K=1.7)

For m$=0$ the occupation numbers and MOs will be set for a spin-restriced closed-shell calculation and for m$\neq 0$ a spin-unrestriced open-shell calculation. The occupied orbitals will be selected according to the Aufbau principle using the EHT orbital energies.

As a simple fall-back option, the coefficients for the start MOs can be determined from the eigenvectors of the one-electron core Hamiltonian matrix, i.e. the sum of the kinetic energy energy and the nuclear attraction potential for the electrons. This option is requested for spin-restricted calculations with

  $scfmo none

and for spin-unrestricred calculations with

  $uhfmo_alpha none
  $uhfmo_beta none

It requires that prior to the start of the dscf or ridft program the occupation numbers have been set in the control file.

RHF

$closed shells

Specification of MO occupation for RHF, e.g.

 a1g     1-4                                    ( 2 )
 a2g     1                                      ( 2 )

$open shells type=1

MO occupation of open shells and number of open shells. type=1 here means that there is only a single open shell consisting e.g. of two MOs:

b2g     1                                      ( 1 )
b3g     1                                      ( 1 )

$roothaan         1
a = 1      b = 2

$roothaan

Roothaan parameters for the open shell, here a triplet case. define recognizes most cases and suggests good Roothaan parameters.

For further information on ROHF calculations, see the sample input in Section 26.6 and the tables of Roothaan parameters in Section 6.4.

UHF

$uhf

directs the program to carry out a UHF run,e.g.

$alpha shells
 a1g     1-4                                    ( 1 )
 a2g     1                                      ( 1 )
$beta shells
 a1g     1-4                                    ( 1 )
 a2g     1                                      ( 1 )

The specification of MO occupation for UHF, $uhf overwrites closed-shell occupation specification.