Required keywords

geometry

Description: Specify atoms and their Cartesian coordinates
Datatype: vector
Values:
Vector of atoms provided in the following format { "atom" : "atom symbol",  "xyz" : [x, y, z] } Please see the end of the file for some examples.

basis

Description: Define default basis set used for the system
Datatype: string
Values:
Please refer to Basis sets and Effective core potential (ECP) basis sets for possible arguments. User defined basis sets are also possible.

df_basis

Description: Basis sets used for density fitting
Datatype: string
Values:
Please refer to Density fitting basis sets for possible arguments

Note

The use of mixed basis sets and/or density fitting basis sets is possible by specifying a different basis set other than the default for each atom (see example for Basis sets below).

Optional keywords

angstrom

Description: Specify units for atomic coordinates (Angstrom or Bohr)
Datatype: bool
true: use Angstrom
false: use Bohr
Default: false (Angstrom)

finite_nucleus

Description: Represent the nucleus as a Gaussian charge distribution with default exponents
Datatype: bool
Default: false

molden_file

Description: Filename of the molden file, which is required if "basis" : "molden" is specified.
Datatype: string
Recommendation: restarting from a molden file is not recommended, which is nevertheless sometimes useful.

cfmm

Description: Turn on RHF-FMM; for more details, refer to Hartree–Fock section.
Datatype: bool
Default: false
Recommendation: Use for calculations on very large systems.

schwarz_thresh

Description: Schwarz screening integral threshold, only used in RHF-FMM "cfmm" : "true". For more details, refer to Hartree–Fock section.
Datatype: double
Default: \(1.0\times 10^{-12}\)
Recommendation: Default, looser thresholds reduce accuracy but potentially increase speed.

dkh

Description: Option to use the second-order Douglas–Kroll–Hess Hamiltonian (DKH2).
Datatype: bool
Default: false

magnetic_field

Description: External magnetic field. External magnetic fields are available only for the Hartree–Fock and Dirac–Hartree–Fock modules.
Datatype: Array of three doubles (x, y, z)
Default: (0.0, 0.0, 0.0)

tesla

Description: External magnetic field in units of Tesla.
Datatype: bool
Default: false (i.e., atomic units are used)

basis_type

Description: Specify the type of atomic orbital basis functions, either standard Gaussian functions or gauge-including atomic orbitals (GIAOs).
Datatype: string
Values: gaussian / giao, london
Default: gaussian at zero magnetic field; giao when a field is applied

skip_self_interaction

Description: Skip the electrostatic interactions between the dummy atoms.
Datatype: bool
true: skip the electrostatic interactions between the dummies.
false: explicitly calculate the electrostatic interactions between the dummies.
Default: true

Basis sets

Orbital basis sets

The following basis sets are available in BAGEL library. The basis set name can be used with the basis keyword.

  • sto-3g
  • 3-21g
  • 6-31g
  • svp
  • tzvpp
  • qzvpp
  • cc-pvdz
  • cc-pvtz
  • cc-pvqz
  • cc-pv5z
  • cc-pv6z
  • cc-pcvdz
  • cc-pcvtz
  • cc-pcvqz
  • cc-pcv5z
  • cc-pcvdz-dk
  • cc-pcvtz-dk
  • aug-cc-pvdz
  • aug-cc-pvtz
  • aug-cc-pvqz
  • aug-cc-pv5z
  • aug-cc-pv6z
  • aug-cc-pcvdz
  • aug-cc-pcvtz
  • aug-cc-pcvqz
  • aug-cc-pcv5z
  • aug-cc-pcvdz-dk
  • aug-cc-pcvtz-dk
  • aug-cc-pcvqz-dk
  • aug-cc-pwcvdz
  • aug-cc-pwcvtz
  • aug-cc-pwcvqz
  • aug-cc-pwcv5z
  • d-aug-cc-pvdz
  • d-aug-cc-pvtz
  • d-aug-cc-pvqz
  • d-aug-cc-pv5z
  • ano-rcc

Density fitting basis sets

The following density fitting basis sets are available in BAGEL library. The basis set name can be used with the df_basis keyword.

  • svp-jkfit
  • tzvpp-jkfit
  • qzvpp-jkfit
  • cc-pvdz-jkfit
  • cc-pvtz-jkfit
  • cc-pvqz-jkfit
  • cc-pv5z-jkfit

Examples

{ "bagel" : [

{
  "title" : "molecule",
  "basis" : "svp",
  "df_basis" : "svp-jkfit",
  "angstrom" : false,
  "geometry" : [
      {"atom" : "H", "xyz" : [ -0.22767998367, -0.82511994081,  -2.66609980874]; },
      {"atom" : "O", "xyz" : [  0.18572998668, -0.14718998944,  -3.25788976629]; },
      {"atom" : "H", "xyz" : [  0.03000999785,  0.71438994875,  -2.79590979943]; }
  ]
},

{
  "title" : "hf"
}

]}

Example with mixed basis sets and density fitting basis sets:

{ "bagel" : [

{
  "title" : "molecule",
  "symmetry" : "C1",
  "basis" : "svp",
  "df_basis" : "svp-jkfit",
  "angstrom" : "false",
  "geometry" : [
    { "atom" : "F",  "xyz" : [ -0.000000,     -0.000000,      2.720616]},
    { "atom" : "H",  "xyz" : [ -0.000000,     -0.000000,      0.305956],
                     "basis" : "cc-pvqz", "df_basis" : "cc-pvqz-jkfit" }
  ]
},

{
  "title" : "hf"
}

]}

Example with running a calculation from a molden file using the keyword "basis" : "molden" and providing a value for "molden_file":

{ "bagel" : [

{
  "title" : "molecule",
  "symmetry" : "C1",
  "basis" : "molden",
  "df_basis" : "svp-jkfit",
  "cartesian" : true,
  "molden_file" : "hf_write_mol_cart.molden"
}

]}

(refer to Molden in Miscellaneous features for more details)

Example with external magnetic field using Gauge-invariant atomic orbitals (GIAO):

{ "bagel" : [

{
  "title" : "molecule",
  "symmetry" : "C1",
  "basis" : "svp",
  "df_basis" : "svp-jkfit",
  "angstrom" : "false",
  "basis_type" : "giao",
  "tesla" : "false",
  "magnetic_field" : [  0.2000,   0.3000,  -0.1500   ],
  "geometry" : [
    { "atom" : "F",  "xyz" : [ -1.200000,      2.500000,      2.720616]},
    { "atom" : "H",  "xyz" : [ -1.200000,      2.500000,      0.305956]}
  ]
},

{
  "title" : "hf"
}

]}

Auxiliary basis sets

The following MP2-fit basis sets are available in BAGEL. The basis set name can be used with the aux_basis keyword in the method block (refer to Møller–Plesset perturbation theory (MP2) for more details).

  • cc-pvdz-ri
  • cc-pvtz-ri
  • cc-pvqz-ri
  • cc-pv5z-ri

Example

An example using cc-pvdz-ri in MP2 calculation.

{ "bagel" : [

{
  "title" : "molecule",
  "basis" : "cc-pvdz",
  "df_basis" : "cc-pvdz-jkfit",
  "angstrom" : "true",
  "geometry" : [
    { "atom" : "C", "xyz" : [ -1.20433891360,  0.54285096106, -0.04748199659] },
    { "atom" : "C", "xyz" : [ -1.20543291352, -0.83826393986,  0.12432899108] },
    { "atom" : "C", "xyz" : [ -0.00000600000, -1.52953889027,  0.20833398505] },
    { "atom" : "C", "xyz" : [  1.20544091352, -0.83825393987,  0.12432799108] },
    { "atom" : "C", "xyz" : [  1.20433091360,  0.54284396106, -0.04748099659] },
    { "atom" : "C", "xyz" : [  0.00000400000,  1.23314191154, -0.13372399041] },
    { "atom" : "H", "xyz" : [ -2.13410484690,  1.07591192282, -0.12500499103] },
    { "atom" : "H", "xyz" : [ -2.13651384673, -1.37179190159,  0.18742198655] },
    { "atom" : "H", "xyz" : [  0.00000000000, -2.59646181374,  0.33932597566] },
    { "atom" : "H", "xyz" : [  2.13651384673, -1.37179290159,  0.18742198655] },
    { "atom" : "H", "xyz" : [  2.13410684690,  1.07591292282, -0.12500599103] },
    { "atom" : "H", "xyz" : [ -0.00000000000,  2.29608983528, -0.28688797942] }
  ]
},

{
  "title" : "mp2",
  "aux_basis" : "cc-pvdz-ri",
  "frozen" : true
}

]}

Effective core potential (ECP) basis sets

The following auxiliary basis sets are available in BAGEL library. The basis set name can be used with the basis keyword.

  • ecp10mdf
  • ecp28mdf
  • ecp46mdf
  • ecp60mdf
  • ecp78mdf
  • def2-SVP-ecp
  • def2-SVP-2c-ecp
  • lanl2dz-ecp

Note

User-defined ECP basis sets need to contain the keyword “ecp” in the names. Refer to User defined basis sets for more details.

Example

Example for CuH2 using cc-pvtz basis set for H and lanl2dz-ecp for the heavy atom Cu

{ "bagel" : [

{
  "title" : "molecule",
  "symmetry" : "C1",
  "basis" : "lanl2dz-ecp",
  "df_basis" : "svp-jkfit",
  "angstrom" : "true",
  "geometry" : [
    { "atom" : "Cu",  "xyz" : [  0.000000,      0.000000,      0.000000]},
    { "atom" :  "H",  "xyz" : [  0.000000,      0.000000,     -1.560000],
                      "basis" : "cc-pvtz"},
    { "atom" :  "H",  "xyz" : [  0.000000,      0.000000,      1.560000],
                      "basis" : "cc-pvtz"}
  ]
},

{
  "title" : "hf",
  "charge" : "-1"
}

]}

User defined basis sets

The basis set file is in the following format

{
 "H" : [
   {
     "angular" : "s",
     "prim" : [5.4471780, 0.8245470],
     "cont" : [[0.1562850, 0.9046910]]
   }, {
     "angular" : "s",
     "prim" : [0.1831920],
     "cont" : [[1.0000000]]
   }
 ],
 "He" : [
   {
     "angular" : "s",
     "prim" : [13.6267000, 1.9993500],
     "cont" : [[0.1752300, 0.8934830]]
   }, {
     "angular" : "s",
     "prim" : [0.3829930],
     "cont" : [[1.0000000]]
   }
 ]
}

The file is essentially one large array, the elements of which are further arrays, each corresponding to the basis set for a given element. The basis set for associated with each element is then made up of further arrays, each of which contains information specifying the properties of a single basis function.

  • angular defines the kind of orbital (s,p,d,f...) .
  • prim is a array containing the exponents of the primitive orbitals from which the basis function is composed.
  • cont is an array containing the coefficients associated with each of these primitive orbitals.

The user can specify their own basis set using the above format, or use one of the predefined basis sets listed in Basis sets.

Note

Not all of the the basis sets are defined for all atoms; an error message of form “No such node(X)”, where X is the element, typically means that the relevant element was not found in the basis set file. Refer to the EMSL Basis set exchange library for more basis sets (https://bse.pnl.gov/bse/portal).

To use a user specified basis the explicit path to the basis set file must be specified in the basis set block.

Example

{ "bagel" : [

{
  "title" : "molecule",
  "basis" : "/path/to/my/basis",
  "df_basis" : "/path/to/my/basis",
  "angstrom" : false,
  "geometry" : [
      {"atom" : "H", "xyz" : [ -0.22767998367, -0.82511994081,  -2.66609980874]; },
      {"atom" : "O", "xyz" : [  0.18572998668, -0.14718998944,  -3.25788976629]; },
      {"atom" : "H", "xyz" : [  0.03000999785,  0.71438994875,  -2.79590979943]; }
  ]
},

{
  "title" : "hf"
}

]}

Other features

Dummy atoms

Artificial point charges can be included in the calculation. They introduce a user specified charge into the system, but have no associated basis functions. Introduction of such a charge is accomplished by inclusion of an additional line in the geometry block for an atom of element “Q”.

Example

A dihydrogen molecule with a nearby dummy charge of +0.2. Note that the charge specified in the “hf” block does not include the charge associated with the dummy atom.

{ "bagel" : [

{
  "title" : "molecule",
  "symmetry" : "C1",
  "basis" : "tzvpp",
  "df_basis" : "tzvpp-jkfit",
  "angstrom" : "true",
  "geometry" : [
    { "atom" :  "Q",  "xyz" : [  0.000000,   0.000000,   2.0000], "charge" : "0.2"},
    { "atom" :  "H",  "xyz" : [  0.000000,   0.000000,   0.7414]},
    { "atom" :  "H",  "xyz" : [  0.000000,   0.000000,   0.0000]}
  ]
},

{
  "title" : "hf"
}

]}

from which one obtains

=== RHF iteration (tzvpp) ===

             o Fock build                                  0.01
    0         -1.12552716          0.00743295           0.01
             o DIIS                                        0.00
             o Diag                                        0.00
             o Post process                                0.00
             o Fock build                                  0.01
    1         -1.12987462          0.00139213           0.01
             o DIIS                                        0.00
             o Diag                                        0.00
             o Post process                                0.00
             o Fock build                                  0.01
    2         -1.13008781          0.00009095           0.01
             o DIIS                                        0.00
             o Diag                                        0.00
             o Post process                                0.00
             o Fock build                                  0.01
    3         -1.13008889          0.00000614           0.01
             o DIIS                                        0.00
             o Diag                                        0.00
             o Post process                                0.00
             o Fock build                                  0.01
    4         -1.13008889          0.00000054           0.01
             o DIIS                                        0.00
             o Diag                                        0.00
             o Post process                                0.00
             o Fock build                                  0.01
    5         -1.13008889          0.00000007           0.01
             o DIIS                                        0.00
             o Diag                                        0.00
             o Post process                                0.00
             o Fock build                                  0.01
    6         -1.13008889          0.00000000           0.01

  * SCF iteration converged.

  * Permanent dipole moment:
         (    0.000000,    -0.000000,    -0.427736) a.u.

References

Description of Reference Reference
General text on electronic structure theory A. Szabo and N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory (McGraw-Hill, New York, 1989).
Gauge invariant atomic orbitals R. Ditchfield, Mol. Phys. 27, 789 (1974).