atomdb package

AtomDB, a database of atomic and ionic properties.

class atomdb.Element(elem)

Bases: object

Element properties.

Attributes

atnumint

Atomic number of the element.

symbolstr

Symbol of the element.

namestr

Name of the element.

property at_radius

atomic radius of the element.

Returns

at_radius : Dict[float]

Notes

This property is a dictionary with the following keys:

• “wc”

  • Source

    10. 20. Waber and D. T. Cromer, J. Chem. Phys. 42, 4116 (1965)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1063/1.1695904

  • Notes

    For each element, the largest radius of the outer orbitals is taken.

• “cr”

  • Source

    5. Clementi, D. L. Raimondi, W. P. Reinhardt, J. Chem. Phys. 47, 1300 (1967)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1063/1.1712084

property atnum

property c6

Isolated atom C6 dispersion coefficients of the element.

Returns

c6 : Dict[float]

Notes

This property is a dictionary with the following keys:

• “chu”

  • Source

    24. Chu & A. Dalgarno, J. Chem. Phys., 121(9), 4083–4088 (2004)

  • Units

    au

  • URL

    http://dx.doi.org/10.1063/1.1779576

  • Notes

    Theoretical value for hydrogen from this paper: K. T. Tang, J. M. Norbeck and P. R. Certain, J. Chem. Phys. 64, 3063 (1976) http://dx.doi.org/10.1063/1.432569

property cov_radius

Covalent radius of the element.

Returns

cov_radius : Dict[float]

Notes

This property is a dictionary with the following keys:

• “cordero”

  • Source

    B. Cordero, V. Gomez, A. E. Platero-Prats, M. Reves, J. Echeverria,E. Cremades, F. Barragan, and S. Alvarez, Dalton Trans. pp. 2832–2838 (2008)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1039/b801115j

  • Notes

    For carbon the number is a weighted average over the data for different hybridizations. For Mn, Fe, and Co, the number is a weighted average over the data for different spins (high spin and low spin)

• “bragg”

  • Source

    23. 12. Bragg, Phil. Mag. 40, 169 (1920)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1080/14786440808636111

• “slater”

  • Source

    10. 3. Slater, J. Chem. Phys. 41, 3199 (1964)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1063/1.1725697

property eneg

Electronegativity of the element.

Returns

eneg : Dict[float]

Notes

This property is a dictionary with the following keys:

• “pauling”

  • Source

    1. 12. Allred, J. Inorg. Nuc. Chem. 17, 215 (1961)

  • Units

    float

  • URL

    http://dx.doi.org/10.1016/0022-1902(61)80142-5

property group

Group of the element.

Returns

group : int

property mass

Atomic mass of the element.

Returns

mass : Dict[float]

Notes

This property is a dictionary with the following keys:

• “stb”

  • Source

    Thomas Prohaska et. al. Pure Appl. Chem. 2022, 94

  • Units

    amu

  • URL

    https://doi.org/10.1515/pac-2019-0603

  • Notes

    For Tc, Pm, Po - Ac, Np, Pu, Am-Og the mass of the most abundant isotope or with longer half-life taken from https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl

• “nist”

  • Units

    amu

  • URL

    https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl

  • Notes

    Mass of the most common isotope

property mult

Multiplicity of the element.

Returns

mult : int

property name

Name of the element.

Returns

name : str

property period

Period of the element.

Returns

period : int

property pold

Isolated atom dipole polarizability of the element.

Returns

pold : Dict[float]

Notes

This property is a dictionary with the following keys:

• “crc”

  • Source

    CRC Handbook of Chemistry and Physics (CRC, Boca Raton, FL, 2003).

  • Units

    angstrom**3

  • Notes

    If multiple values were present in the CRC book, the value used in Erin’s postg code is taken

• “chu”

  • Source

    24. Chu, A. Dalgarno, J. Chem. Phys., 121(9), 4083–4088 (2004)

  • Units

    au

  • URL

    http://dx.doi.org/10.1063/1.1779576

  • Notes

    Theoretical value for hydrogen from this paper: A.D. Buckingham, K.L. Clarke, Chem. Phys. Lett. 57(3), 321–325 (1978) http://dx.doi.org/10.1016/0009-2614(78)85517-1

• “sn”

  • Source

    Schwerdtfeger, P., Nagle, J. K. (2018). Molecular Physics, 117(9-12), 1200-1225.

  • Units

    au

  • URL

    https://doi.org/10.1080/00268976.2018.1535143

  • Notes

    For Lv no value currently available

property symbol

Symbol of the element.

Returns

symbol : str

property vdw_radius

van der Waals radius of the element.

Returns

vdw_radius : Dict[float]

Notes

This property is a dictionary with the following keys:

• “bondi”

  • Source

    1. Bondi, J. Phys. Chem. 68, 441 (1964)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1021/j100785a001

• “truhlar”

  • Source

    13. Mantina A. C. Chamberlin R. Valero C. J. Cramer D. G. Truhlar J. Phys. Chem. A 113 5806 (2009)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1021/jp8111556

• “rt”

  • Source

    18. 19. Rowland and R. Taylor, J. Phys. Chem. 100, 7384 (1996)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1021/jp953141+

• “batsanov”

  • Source

    19. 19. Batsanov Inorganic Materials 37 871 (2001)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1023/a%3a1011625728803

• “dreiding”

  • Source

    Stephen L. Mayo, Barry D. Olafson, and William A. Goddard III J. Phys. Chem. 94 8897 (1990)

  • Units

    2angstrom

  • URL

    http://dx.doi.org/10.1021/j100389a010

  • Notes

    R_0 parameter, unit 2angstrom is used so that numbers are divided by 2 upon reading

• “uff”

  • Source

    1. 11. Rappi, C. J. Casewit, K. S. Colwell, W. A. Goddard III, and W. M. Skid J. Am. Chem. Soc. 114 10024 (1992)

  • Units

    2angstrom

  • URL

    http://dx.doi.org/10.1021/ja00051a040

  • Notes

    x_I parameter, unit 2angstrom is used so that numbers are divided by 2 upon reading

• “mm3”

  • Source

    14. 12. Allinger, X. Zhou, and J. Bergsma, Journal of Molecular Structure: THEOCHEM 312, 69 (1994)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1016/s0166-1280(09)80008-0

class atomdb.Promolecule

Bases: object

Promolecule class.

A promolecule is an approximation of a molecule constructed from a linear combination of atomic and/or ionic species. Properties of this promolecule can be computed from those of the atomic and/or ionic species, depending on whether the property is an extensive one or an intensive one.

For an extensive property, the formula is a linear combination:

\[\text{prop.}_{\text{mol;extensive}} = \sum_{A=1}^{N_{\text{atoms}}} c_A \text{prop.}_A\]

For an intensive property, the formula is a mean:

\[\text{prop.}_{\text{mol;intensive}} = {\left\langle \left\{ \text{prop.}_A \right\}_{A=1}^{N_{\text{atoms}}} \right\rangle}_p\]

where the parameter p defines the type of mean used (1 = linear, 2 = geometric, etc.).

Attributes

atoms: list of Species

Species instances out of which the promolecule is composed.

coords: np.ndarray((N, 3), dtype=float)

Coordinates of each species component of the promolecule.

coeffs: np.ndarray((N,), dtype=float)

Coefficients of each species component of the promolecule.

charge()

Compute the charge of the promolecule.

Returns

charge: float

Charge of the promolecule.

density(points, spin='t', log=False)

Compute the electron density of the promolecule at the desired points.

Parameters

points: np.ndarray((N, 3), dtype=float)

Points at which to compute the density.

spin: (‘t’ | ‘a’ | ‘b’ | ‘m’), default=’t’

Type of density to compute; either total, alpha-spin, beta-spin, or magnetization density.

log: bool, default=False

Whether to compute the log of the density instead of the density. May be slightly more accurate.

Returns

density: np.ndarray((N,), dtype=float)

Density evaluated at N points.

energy()

Compute the energy of the promolecule.

Returns

energy: float

Energy of the promolecule.

eta(p=1)

Compute the chemical hardness of the promolecule.

Parameters

p: int, default=1 (linear mean)

Type of mean used in the computation.

Returns

eta: float

Chemical hardness of the promolecule.

gradient(points, spin='t', log=False)

Compute the electron density gradient of the promolecule at the desired points.

Promolecular gradient:

\[\nabla \rho_{\text{mol}}^{(0)} (\mathbf{R}) = \sum_{A=1}^{N_{\text{atoms}}}\ c_A \nabla \rho_A^{(0)}(\mathbf{R})\]

where

\(N_{\text{atoms}}\) is the number of atoms in the molecule,

\(c_A\) are the coefficients of the species,

\(R\) are points in 3D cartesian coordinates,

\(\nabla \rho_A^{(0)}(\mathbf{R})\) is the gradient of the species.

Parameters

points: np.ndarray((N, 3), dtype=float)

Points at which to compute the electron density gradient.

spin: (‘t’ | ‘a’ | ‘b’ | ‘m’), default=’t’

Type of density to compute; either total, alpha-spin, beta-spin, or magnetization density.

log: bool, default=False

Whether to compute the log of the density instead of the density. May be slightly more accurate.

Returns

gradient: np.ndarray((N, 3), dtype=float)

Electron density gradient of the promolecule evaluated at N points.

hessian(points, spin='t', log=False)

Compute the promolecule’s electron density Hessian at the desired points.

Parameters

points: np.ndarray((N, 3), dtype=float)

Points at which to compute the electron density Hessian.

spin: (‘t’ | ‘a’ | ‘b’ | ‘m’), default=’t’

Type of density to compute; either total, alpha-spin, beta-spin, or magnetization density.

log: bool, default=False

Whether to compute the log of the density instead of the density. May be slightly more accurate.

Returns

hess: np.ndarray((N, 3, 3), dtype=float)

Electron density Hessian of the promolecule evaluated at N points.

ip(p=1)

Compute the ionization potential of the promolecule.

Parameters

p: int, default=1 (linear mean)

Type of mean used in the computation.

Returns

ip: float

Ionization potential of the promolecule.

ked(points, spin='t', log=False)

Compute the kinetic energy density of the promolecule at the desired points.

points: np.ndarray((N, 3), dtype=float)

Points at which to compute the kinetic energy density.

spin: (‘t’ | ‘a’ | ‘b’ | ‘m’), default=’t’

Type of density to compute; either total, alpha-spin, beta-spin, or magnetization density.

log: bool, default=False

Whether to compute the log of the density instead of the density. May be slightly more accurate.

Returns

ked: np.ndarray((N,), dtype=float)

Kinetic energy density evaluated at N points.

laplacian(points, spin='t', log=False)

Compute the promolecule’s electron density Laplacian at the desired points.

Parameters

points: np.ndarray((N, 3), dtype=float)

Points at which to compute the electron density Laplacian.

spin: (‘t’ | ‘a’ | ‘b’ | ‘m’), default=’t’

Type of density to compute; either total, alpha-spin, beta-spin, or magnetization density.

log: bool, default=False

Whether to compute the log of the density instead of the density. May be slightly more accurate.

Returns

laplacian: np.ndarray((N,), dtype=float)

Electron density Laplacian of the promolecule evaluated at N points.

mass()

Compute the mass of the promolecule.

Returns

mass: float

Mass of the promolecule.

mu(p=1)

Compute the chemical potential of the promolecule.

Parameters

p: int, default=1 (linear mean)

Type of mean used in the computation.

Returns

mu: float

Chemical potential of the promolecule.

mult(p=1)

Compute the multiplicity of the promolecule.

Parameters

p: int, default=1 (linear mean)

Type of mean used in the computation.

Returns

mult: float

Multiplicity of the promolecule.

nelec()

Compute the electron number of the promolecule.

Returns

nelec: float

Number of electrons in the promolecule.

nspin(p=1)

Compute the spin number of the promolecule.

Parameters

p: int, default=1 (linear mean)

Type of mean used in the computation.

Returns

nspin: float

Spin number of the promolecule.

class atomdb.Species(dataset, fields, spinpol=1)

Bases: object

Properties of atomic and ionic species.

property at_radius

Atomic radius.

Returns

at_radiusdict, float

The return dictionary contains atomic radii types wc and cr. For references corresponding to each type check theochem/AtomDB

property atmass

Atomic mass in atomic units.

Returns

atmassdict

Two options are available: the isotopically averaged mass ‘stb’, and the mass of the most common isotope ‘nist’. For references corresponding to each type check theochem/AtomDB

property atnum

Atomic number.

Returns

atnum : int

property charge

Charge

\[Q = Z - N\]

Where Q is the charge, Z the atomic number and N the total number of electrons stored in SpeciesData object.

Returns

charge : int

property cov_radius

Covalent radius (derived from crystallographic data).

Returns

cov_radiusdict, float

The return dictionary contains crystallographic covalent radii types cordero, bragg and slater. For references corresponding to each type check theochem/AtomDB

d_dens_func(spin='t', index=None, log=False)

Return a cubic spline of the first derivative of the electronic density.

The derivarive of the density as a function of the distance to the atomic center (a set of points along a 1-D grid) is modeled by a cubic spline. The property can be computed for the alpha, beta, alpha + beta, and alpha - beta components of the electron density.

Parameters

spinstr, optional

Type of occupied spin orbitals which can be either “a” (for alpha), “b” (for beta), “ab” (for alpha + beta), and, “m” (for alpha - beta), by default ‘ab’

indexsequence of int, optional

Sequence of integers representing the spin orbitals which are indexed from 1 to the number basis functions. If None, all orbitals of the given spin(s) are included

logbool, optional

Whether the logarithm of the density property is used for interpolation

Returns

Callable[[np.ndarray(N,), int] -> np.ndarray(N,)]

a callable function evaluating the derivative of the density given a set of radial points (1-D array).

property dataset

Name of the type of dataset.

Returns

dataset : string

dd_dens_func(spin='t', index=None, log=False)

Return a cubic spline of the second derivative of the electronic density.

Parameters

spinstr, default=”t”

Type of occupied spin orbitals. Can be either “t” (for alpha + beta), “a” (for alpha), “b” (for beta), or “m” (for alpha - beta).

indexsequence of int, optional

Sequence of integers representing the spin orbitals. These are indexed from 0 to the number of basis functions. By default, all orbitals of the given spin(s) are included.

logbool, default=False

Whether the logarithm of the density is used for interpolation.

Returns

Callable[[np.ndarray(N,), int] -> np.ndarray(N,)]

a callable function evaluating the second derivative of the density given a set of radial points (1-D array).

dd_dens_lapl_func(spin='t', index=None, log=False)

Return the function for the electronic density Laplacian.

\[\nabla^2 \rho(\mathbf{r}) = \frac{d^2 \rho(r)}{dr^2} + \frac{2}{r} \frac{d \rho(r)}{dr}\]

Parameters

spinstr, default=”t”

Type of occupied spin orbitals. Can be either “t” (for alpha + beta), “a” (for alpha), “b” (for beta), or “m” (for alpha - beta).

indexsequence of int, optional

Sequence of integers representing the spin orbitals. These are indexed from 0 to the number of basis functions. By default, all orbitals of the given spin(s) are included.

logbool, default=False

Whether the logarithm of the density is used for interpolation.

Returns

Callable[np.ndarray(N,) -> np.ndarray(N,)]

a callable function evaluating the Laplacian of the density given a set of radial points (1-D array).

Notes

When this function is evaluated at a point close to zero, the Laplacian becomes undefined. In this case, this function returns zero.

dens_func(spin='t', index=None, log=False)

Return a cubic spline of the electronic density.

Parameters

spinstr, default=”t”

Type of occupied spin orbitals. Can be either “t” (for alpha + beta), “a” (for alpha), “b” (for beta), or “m” (for alpha - beta).

indexsequence of int, optional

Sequence of integers representing the spin orbitals. These are indexed from 0 to the number of basis functions. By default, all orbitals of the given spin(s) are included.

logbool, default=False

Whether the logarithm of the density is used for interpolation.

Returns

DensitySpline

A DensitySpline instance for the density and its derivatives. Given a set of radial points, it can evaluate densities and derivatives up to order 2.

property dispersion_c6

Isolated atom C6 dispersion coefficients.

Returns

dispersion_c6dict, float

The return dictionary contains isolated atom C6 dispersion coefficients types chu. For references corresponding to each type check theochem/AtomDB

property elem

Element symbol.

Returns

elem : string

property energy

Energy.

Returns

energy : float

property eta

Chemical hardness.

Returns

eta : float

get_docstring()

Docstring of the species’ dataset.

property ip

Ionization potential.

Returns

ip : float

ked_func(spin='t', index=None, log=False)

Return a cubic spline of the kinetic energy density.

Parameters

spinstr, default=”t”

Type of occupied spin orbitals. Can be either “t” (for alpha + beta), “a” (for alpha), “b” (for beta), or “m” (for alpha - beta).

indexsequence of int, optional

Sequence of integers representing the spin orbitals. These are indexed from 0 to the number of basis functions. By default, all orbitals of the given spin(s) are included.

logbool, default=False

Whether the logarithm of the density is used for interpolation.

Returns

DensitySpline

A DensitySpline instance for the density and its derivatives. Given a set of radial points, it can evaluate densities and derivatives up to order 2.

property mu

Chemical potential.

Returns

mu : float

property mult

Multiplicity

\[M = \left|N_S\right| + 1\]

Where \(\left|N_S\right|\) is the spin number.

Returns

mult : int

property nelec

Number of electrons.

Returns

nelec : int

property nexc

Excitation number.

Returns

nexc : int

property nspin

Spin number

\[N_S = N_α - N_β\]

Where \(N_S\) is the spin number and \(N_α\) and \(N_β\) number of alpha and

beta electrons.

Returns

nspin : int

property obasis_name

Basis name.

Returns

obasis_name : string

property polarizability

Isolated atom dipole polarizability.

Returns

polarizabilitydict, float

The return dictionary contains isolated atom dipole polarizability types crc and chu. For references corresponding to each type check theochem/AtomDB

property spinpol

Spin polarization direction (±1).

Returns

spinpol : int

to_dict()

Return the dictionary representation of the Species instance.

to_json()

Return the JSON string representation of the Species instance.

property vdw_radius

Van der Waals radii.

Returns

vdw_radiusdict, float

The return dictionary contains van der wals radii types bondi, truhlar, rt, batsanov, dreiding, uff and mm3. For references corresponding to each type check theochem/AtomDB

atomdb.compile_species(elem, charge, mult, nexc=0, dataset='slater', datapath='/home/runner/.local/lib/python3.12/site-packages/atomdb/datasets')

Compile an atomic or ionic species into the AtomDB database.

Parameters

elemstr

Element symbol.

chargeint

Charge.

multint

Multiplicity.

nexcint, optional

Excitation level, by default 0.

datasetstr, optional

Dataset name, by default DEFAULT_DATASET.

datapathstr, optional

Path to the local AtomDB cache, by default DEFAULT_DATAPATH variable value.

atomdb.dump(*species, datapath='/home/runner/.local/lib/python3.12/site-packages/atomdb/datasets')

Dump the Species instance(s) to a MessagePack file in the database.

Parameters

species: Iterable

Iterables of objects of class Species

datapathstr, optional

Path to the local AtomDB cache, by default DEFAULT_DATAPATH variable value.

atomdb.element_name(elem)

Return the element name from a string or int.

Parameters

elem: (str | int)

Symbol, name, or number of an element.

Returns

namestr

Element name.

atomdb.element_number(elem)

Return the element number from a string or int.

Parameters

elem: (str | int)

Symbol, name, or number of an element.

Returns

atnumint

Atomic number.

atomdb.element_symbol(elem)

Return the element symbol from a string or int.

Parameters

elem: (str | int)

Symbol, name, or number of an element.

Returns

symbolstr

Element symbol.

atomdb.load(elem, charge, mult, nexc=0, dataset='slater', datapath='/home/runner/.local/lib/python3.12/site-packages/atomdb/datasets', remotepath='https://raw.githubusercontent.com/theochem/AtomDBdata/main/')

Load one or many atomic or ionic species from the AtomDB database.

Parameters

elemstr

Element symbol.

chargeint

Charge.

multint

Multiplicity.

nexcint, optional

Excitation level, by default 0.

datasetstr, optional

Dataset name, by default DEFAULT_DATASET.

datapathstr, optional

Path to the local AtomDB cache, by default DEFAULT_DATAPATH variable value.

remotepathstr, optional

Remote URL for AtomDB datasets, by default DEFAULT_REMOTE variable value

Returns

Object of class Species

atomdb.make_promolecule(atnums, coords, charges=None, mults=None, units=None, dataset='slater', datapath='/home/runner/.local/lib/python3.12/site-packages/atomdb/datasets', remotepath='https://raw.githubusercontent.com/theochem/AtomDBdata/main/')

Construct a Promolecule instance from a set of atoms and their coordinates, charges, and multiplicities.

Parameters

atnums: list of (str|int)

List of element number for each atom.

coords: list of np.ndarray((3,), dtype=float)

List of coordinates for each atom.

charges: list of (int | float), default=[0, …, 0]

List of charges.

mults: list of (int), default=[1, …, 1]

List of multiplicities for each atom.

units: (‘bohr’ | ‘angstrom’)

Units of coords values. Default is Bohr.

dataset: str, default=DEFAULT_DATASET

Data set from which to load atomic species.

datapath: str, default=DEFAULT_DATAPATH

System path where the desired data set is located.

remotepath: str, default=DEFAULT_REMOTE

Remote path where the desired data set is located.

Returns

promol: Promolecule

Promolecule instance.

atomdb.raw_datafile(suffix, elem, charge, mult, nexc=0, dataset='slater', datapath='/home/runner/.local/lib/python3.12/site-packages/atomdb/datasets', remotepath='https://raw.githubusercontent.com/theochem/AtomDBdata/main/')

Returns the local path to the raw data file of a species

This function retrieves the raw data file of a species from the AtomDB cache if present. If the file is not found, it is downloaded from the remote URL.

Parameters

suffixstr

File extension of the raw data file.

elemstr

Element symbol.

chargeint

Charge.

multint

Multiplicity.

nexcint, optional

Excitation level, by default 0.

datasetstr, optional

Dataset name, by default DEFAULT_DATASET.

datapathstr, optional

Path to the local AtomDB cache, by default DEFAULT_DATAPATH variable value.

remotepathstr, optional

Remote URL for AtomDB datasets, by default DEFAULT_REMOTE variable value.

Returns

str

Path to the raw data file.

Subpackages

• atomdb.datasets package
  • Subpackages
    • atomdb.datasets.gaussian package
      • Submodules
      • atomdb.datasets.gaussian.run module
    • atomdb.datasets.hci package
      • Submodules
      • atomdb.datasets.hci.run module
    • atomdb.datasets.nist package
      • Submodules
      • atomdb.datasets.nist.run module
    • atomdb.datasets.numeric package
      • Submodules
      • atomdb.datasets.numeric.run module
    • atomdb.datasets.slater package
      • Submodules
      • atomdb.datasets.slater.run module
    • atomdb.datasets.uhf_augccpvdz package
      • Submodules
      • atomdb.datasets.uhf_augccpvdz.run module
  • Submodules
  • atomdb.datasets.tools module

Submodules

atomdb.periodic module

class atomdb.periodic.Element(elem)

Bases: object

Element properties.

Attributes

atnumint

Atomic number of the element.

symbolstr

Symbol of the element.

namestr

Name of the element.

property at_radius

atomic radius of the element.

Returns

at_radius : Dict[float]

Notes

This property is a dictionary with the following keys:

• “wc”

  • Source

    10. 20. Waber and D. T. Cromer, J. Chem. Phys. 42, 4116 (1965)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1063/1.1695904

  • Notes

    For each element, the largest radius of the outer orbitals is taken.

• “cr”

  • Source

    5. Clementi, D. L. Raimondi, W. P. Reinhardt, J. Chem. Phys. 47, 1300 (1967)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1063/1.1712084

property atnum

property c6

Isolated atom C6 dispersion coefficients of the element.

Returns

c6 : Dict[float]

Notes

This property is a dictionary with the following keys:

• “chu”

  • Source

    24. Chu & A. Dalgarno, J. Chem. Phys., 121(9), 4083–4088 (2004)

  • Units

    au

  • URL

    http://dx.doi.org/10.1063/1.1779576

  • Notes

    Theoretical value for hydrogen from this paper: K. T. Tang, J. M. Norbeck and P. R. Certain, J. Chem. Phys. 64, 3063 (1976) http://dx.doi.org/10.1063/1.432569

property cov_radius

Covalent radius of the element.

Returns

cov_radius : Dict[float]

Notes

This property is a dictionary with the following keys:

• “cordero”

  • Source

    B. Cordero, V. Gomez, A. E. Platero-Prats, M. Reves, J. Echeverria,E. Cremades, F. Barragan, and S. Alvarez, Dalton Trans. pp. 2832–2838 (2008)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1039/b801115j

  • Notes

    For carbon the number is a weighted average over the data for different hybridizations. For Mn, Fe, and Co, the number is a weighted average over the data for different spins (high spin and low spin)

• “bragg”

  • Source

    23. 12. Bragg, Phil. Mag. 40, 169 (1920)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1080/14786440808636111

• “slater”

  • Source

    10. 3. Slater, J. Chem. Phys. 41, 3199 (1964)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1063/1.1725697

property eneg

Electronegativity of the element.

Returns

eneg : Dict[float]

Notes

This property is a dictionary with the following keys:

• “pauling”

  • Source

    1. 12. Allred, J. Inorg. Nuc. Chem. 17, 215 (1961)

  • Units

    float

  • URL

    http://dx.doi.org/10.1016/0022-1902(61)80142-5

property group

Group of the element.

Returns

group : int

property mass

Atomic mass of the element.

Returns

mass : Dict[float]

Notes

This property is a dictionary with the following keys:

• “stb”

  • Source

    Thomas Prohaska et. al. Pure Appl. Chem. 2022, 94

  • Units

    amu

  • URL

    https://doi.org/10.1515/pac-2019-0603

  • Notes

    For Tc, Pm, Po - Ac, Np, Pu, Am-Og the mass of the most abundant isotope or with longer half-life taken from https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl

• “nist”

  • Units

    amu

  • URL

    https://physics.nist.gov/cgi-bin/Compositions/stand_alone.pl

  • Notes

    Mass of the most common isotope

property mult

Multiplicity of the element.

Returns

mult : int

property name

Name of the element.

Returns

name : str

property period

Period of the element.

Returns

period : int

property pold

Isolated atom dipole polarizability of the element.

Returns

pold : Dict[float]

Notes

This property is a dictionary with the following keys:

• “crc”

  • Source

    CRC Handbook of Chemistry and Physics (CRC, Boca Raton, FL, 2003).

  • Units

    angstrom**3

  • Notes

    If multiple values were present in the CRC book, the value used in Erin’s postg code is taken

• “chu”

  • Source

    24. Chu, A. Dalgarno, J. Chem. Phys., 121(9), 4083–4088 (2004)

  • Units

    au

  • URL

    http://dx.doi.org/10.1063/1.1779576

  • Notes

    Theoretical value for hydrogen from this paper: A.D. Buckingham, K.L. Clarke, Chem. Phys. Lett. 57(3), 321–325 (1978) http://dx.doi.org/10.1016/0009-2614(78)85517-1

• “sn”

  • Source

    Schwerdtfeger, P., Nagle, J. K. (2018). Molecular Physics, 117(9-12), 1200-1225.

  • Units

    au

  • URL

    https://doi.org/10.1080/00268976.2018.1535143

  • Notes

    For Lv no value currently available

property symbol

Symbol of the element.

Returns

symbol : str

property vdw_radius

van der Waals radius of the element.

Returns

vdw_radius : Dict[float]

Notes

This property is a dictionary with the following keys:

• “bondi”

  • Source

    1. Bondi, J. Phys. Chem. 68, 441 (1964)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1021/j100785a001

• “truhlar”

  • Source

    13. Mantina A. C. Chamberlin R. Valero C. J. Cramer D. G. Truhlar J. Phys. Chem. A 113 5806 (2009)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1021/jp8111556

• “rt”

  • Source

    18. 19. Rowland and R. Taylor, J. Phys. Chem. 100, 7384 (1996)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1021/jp953141+

• “batsanov”

  • Source

    19. 19. Batsanov Inorganic Materials 37 871 (2001)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1023/a%3a1011625728803

• “dreiding”

  • Source

    Stephen L. Mayo, Barry D. Olafson, and William A. Goddard III J. Phys. Chem. 94 8897 (1990)

  • Units

    2angstrom

  • URL

    http://dx.doi.org/10.1021/j100389a010

  • Notes

    R_0 parameter, unit 2angstrom is used so that numbers are divided by 2 upon reading

• “uff”

  • Source

    1. 11. Rappi, C. J. Casewit, K. S. Colwell, W. A. Goddard III, and W. M. Skid J. Am. Chem. Soc. 114 10024 (1992)

  • Units

    2angstrom

  • URL

    http://dx.doi.org/10.1021/ja00051a040

  • Notes

    x_I parameter, unit 2angstrom is used so that numbers are divided by 2 upon reading

• “mm3”

  • Source

    14. 12. Allinger, X. Zhou, and J. Bergsma, Journal of Molecular Structure: THEOCHEM 312, 69 (1994)

  • Units

    angstrom

  • URL

    http://dx.doi.org/10.1016/s0166-1280(09)80008-0

atomdb.periodic.element_name(elem)

Return the element name from a string or int.

Parameters

elem: (str | int)

Symbol, name, or number of an element.

Returns

namestr

Element name.

atomdb.periodic.element_number(elem)

Return the element number from a string or int.

Parameters

elem: (str | int)

Symbol, name, or number of an element.

Returns

atnumint

Atomic number.

atomdb.periodic.element_symbol(elem)

Return the element symbol from a string or int.

Parameters

elem: (str | int)

Symbol, name, or number of an element.

Returns

symbolstr

Element symbol.

atomdb.promolecule module

AtomDB promolecule submodule.

class atomdb.promolecule.Promolecule

Bases: object

Promolecule class.

A promolecule is an approximation of a molecule constructed from a linear combination of atomic and/or ionic species. Properties of this promolecule can be computed from those of the atomic and/or ionic species, depending on whether the property is an extensive one or an intensive one.

For an extensive property, the formula is a linear combination:

\[\text{prop.}_{\text{mol;extensive}} = \sum_{A=1}^{N_{\text{atoms}}} c_A \text{prop.}_A\]

For an intensive property, the formula is a mean:

\[\text{prop.}_{\text{mol;intensive}} = {\left\langle \left\{ \text{prop.}_A \right\}_{A=1}^{N_{\text{atoms}}} \right\rangle}_p\]

where the parameter p defines the type of mean used (1 = linear, 2 = geometric, etc.).

Attributes

atoms: list of Species

Species instances out of which the promolecule is composed.

coords: np.ndarray((N, 3), dtype=float)

Coordinates of each species component of the promolecule.

coeffs: np.ndarray((N,), dtype=float)

Coefficients of each species component of the promolecule.

charge()

Compute the charge of the promolecule.

Returns

charge: float

Charge of the promolecule.

density(points, spin='t', log=False)

Compute the electron density of the promolecule at the desired points.

Parameters

points: np.ndarray((N, 3), dtype=float)

Points at which to compute the density.

spin: (‘t’ | ‘a’ | ‘b’ | ‘m’), default=’t’

Type of density to compute; either total, alpha-spin, beta-spin, or magnetization density.

log: bool, default=False

Whether to compute the log of the density instead of the density. May be slightly more accurate.

Returns

density: np.ndarray((N,), dtype=float)

Density evaluated at N points.

energy()

Compute the energy of the promolecule.

Returns

energy: float

Energy of the promolecule.

eta(p=1)

Compute the chemical hardness of the promolecule.

Parameters

p: int, default=1 (linear mean)

Type of mean used in the computation.

Returns

eta: float

Chemical hardness of the promolecule.

gradient(points, spin='t', log=False)

Compute the electron density gradient of the promolecule at the desired points.

Promolecular gradient:

\[\nabla \rho_{\text{mol}}^{(0)} (\mathbf{R}) = \sum_{A=1}^{N_{\text{atoms}}}\ c_A \nabla \rho_A^{(0)}(\mathbf{R})\]

where

\(N_{\text{atoms}}\) is the number of atoms in the molecule,

\(c_A\) are the coefficients of the species,

\(R\) are points in 3D cartesian coordinates,

\(\nabla \rho_A^{(0)}(\mathbf{R})\) is the gradient of the species.

Parameters

points: np.ndarray((N, 3), dtype=float)

Points at which to compute the electron density gradient.

spin: (‘t’ | ‘a’ | ‘b’ | ‘m’), default=’t’

Type of density to compute; either total, alpha-spin, beta-spin, or magnetization density.

log: bool, default=False

Whether to compute the log of the density instead of the density. May be slightly more accurate.

Returns

gradient: np.ndarray((N, 3), dtype=float)

Electron density gradient of the promolecule evaluated at N points.

hessian(points, spin='t', log=False)

Compute the promolecule’s electron density Hessian at the desired points.

Parameters

points: np.ndarray((N, 3), dtype=float)

Points at which to compute the electron density Hessian.

spin: (‘t’ | ‘a’ | ‘b’ | ‘m’), default=’t’

Type of density to compute; either total, alpha-spin, beta-spin, or magnetization density.

log: bool, default=False

Whether to compute the log of the density instead of the density. May be slightly more accurate.

Returns

hess: np.ndarray((N, 3, 3), dtype=float)

Electron density Hessian of the promolecule evaluated at N points.

ip(p=1)

Compute the ionization potential of the promolecule.

Parameters

p: int, default=1 (linear mean)

Type of mean used in the computation.

Returns

ip: float

Ionization potential of the promolecule.

ked(points, spin='t', log=False)

Compute the kinetic energy density of the promolecule at the desired points.

points: np.ndarray((N, 3), dtype=float)

Points at which to compute the kinetic energy density.

spin: (‘t’ | ‘a’ | ‘b’ | ‘m’), default=’t’

Type of density to compute; either total, alpha-spin, beta-spin, or magnetization density.

log: bool, default=False

Whether to compute the log of the density instead of the density. May be slightly more accurate.

Returns

ked: np.ndarray((N,), dtype=float)

Kinetic energy density evaluated at N points.

laplacian(points, spin='t', log=False)

Compute the promolecule’s electron density Laplacian at the desired points.

Parameters

points: np.ndarray((N, 3), dtype=float)

Points at which to compute the electron density Laplacian.

spin: (‘t’ | ‘a’ | ‘b’ | ‘m’), default=’t’

Type of density to compute; either total, alpha-spin, beta-spin, or magnetization density.

log: bool, default=False

Whether to compute the log of the density instead of the density. May be slightly more accurate.

Returns

laplacian: np.ndarray((N,), dtype=float)

Electron density Laplacian of the promolecule evaluated at N points.

mass()

Compute the mass of the promolecule.

Returns

mass: float

Mass of the promolecule.

mu(p=1)

Compute the chemical potential of the promolecule.

Parameters

p: int, default=1 (linear mean)

Type of mean used in the computation.

Returns

mu: float

Chemical potential of the promolecule.

mult(p=1)

Compute the multiplicity of the promolecule.

Parameters

p: int, default=1 (linear mean)

Type of mean used in the computation.

Returns

mult: float

Multiplicity of the promolecule.

nelec()

Compute the electron number of the promolecule.

Returns

nelec: float

Number of electrons in the promolecule.

nspin(p=1)

Compute the spin number of the promolecule.

Parameters

p: int, default=1 (linear mean)

Type of mean used in the computation.

Returns

nspin: float

Spin number of the promolecule.

atomdb.promolecule.make_promolecule(atnums, coords, charges=None, mults=None, units=None, dataset='slater', datapath='/home/runner/.local/lib/python3.12/site-packages/atomdb/datasets', remotepath='https://raw.githubusercontent.com/theochem/AtomDBdata/main/')

Construct a Promolecule instance from a set of atoms and their coordinates, charges, and multiplicities.

Parameters

atnums: list of (str|int)

List of element number for each atom.

coords: list of np.ndarray((3,), dtype=float)

List of coordinates for each atom.

charges: list of (int | float), default=[0, …, 0]

List of charges.

mults: list of (int), default=[1, …, 1]

List of multiplicities for each atom.

units: (‘bohr’ | ‘angstrom’)

Units of coords values. Default is Bohr.

dataset: str, default=DEFAULT_DATASET

Data set from which to load atomic species.

datapath: str, default=DEFAULT_DATAPATH

System path where the desired data set is located.

remotepath: str, default=DEFAULT_REMOTE

Remote path where the desired data set is located.

Returns

promol: Promolecule

Promolecule instance.

atomdb.species module

AtomDB, a database of atomic and ionic properties.

class atomdb.species.Species(dataset, fields, spinpol=1)

Bases: object

Properties of atomic and ionic species.

property at_radius

Atomic radius.

Returns

at_radiusdict, float

The return dictionary contains atomic radii types wc and cr. For references corresponding to each type check theochem/AtomDB

property atmass

Atomic mass in atomic units.

Returns

atmassdict

Two options are available: the isotopically averaged mass ‘stb’, and the mass of the most common isotope ‘nist’. For references corresponding to each type check theochem/AtomDB

property atnum

Atomic number.

Returns

atnum : int

property charge

Charge

\[Q = Z - N\]

Where Q is the charge, Z the atomic number and N the total number of electrons stored in SpeciesData object.

Returns

charge : int

property cov_radius

Covalent radius (derived from crystallographic data).

Returns

cov_radiusdict, float

The return dictionary contains crystallographic covalent radii types cordero, bragg and slater. For references corresponding to each type check theochem/AtomDB

d_dens_func(spin='t', index=None, log=False)

Return a cubic spline of the first derivative of the electronic density.

The derivarive of the density as a function of the distance to the atomic center (a set of points along a 1-D grid) is modeled by a cubic spline. The property can be computed for the alpha, beta, alpha + beta, and alpha - beta components of the electron density.

Parameters

spinstr, optional

Type of occupied spin orbitals which can be either “a” (for alpha), “b” (for beta), “ab” (for alpha + beta), and, “m” (for alpha - beta), by default ‘ab’

indexsequence of int, optional

Sequence of integers representing the spin orbitals which are indexed from 1 to the number basis functions. If None, all orbitals of the given spin(s) are included

logbool, optional

Whether the logarithm of the density property is used for interpolation

Returns

Callable[[np.ndarray(N,), int] -> np.ndarray(N,)]

a callable function evaluating the derivative of the density given a set of radial points (1-D array).

property dataset

Name of the type of dataset.

Returns

dataset : string

dd_dens_func(spin='t', index=None, log=False)

Return a cubic spline of the second derivative of the electronic density.

Parameters

spinstr, default=”t”

Type of occupied spin orbitals. Can be either “t” (for alpha + beta), “a” (for alpha), “b” (for beta), or “m” (for alpha - beta).

indexsequence of int, optional

Sequence of integers representing the spin orbitals. These are indexed from 0 to the number of basis functions. By default, all orbitals of the given spin(s) are included.

logbool, default=False

Whether the logarithm of the density is used for interpolation.

Returns

Callable[[np.ndarray(N,), int] -> np.ndarray(N,)]

a callable function evaluating the second derivative of the density given a set of radial points (1-D array).

dd_dens_lapl_func(spin='t', index=None, log=False)

Return the function for the electronic density Laplacian.

\[\nabla^2 \rho(\mathbf{r}) = \frac{d^2 \rho(r)}{dr^2} + \frac{2}{r} \frac{d \rho(r)}{dr}\]

Parameters

spinstr, default=”t”

Type of occupied spin orbitals. Can be either “t” (for alpha + beta), “a” (for alpha), “b” (for beta), or “m” (for alpha - beta).

indexsequence of int, optional

Sequence of integers representing the spin orbitals. These are indexed from 0 to the number of basis functions. By default, all orbitals of the given spin(s) are included.

logbool, default=False

Whether the logarithm of the density is used for interpolation.

Returns

Callable[np.ndarray(N,) -> np.ndarray(N,)]

a callable function evaluating the Laplacian of the density given a set of radial points (1-D array).

Notes

When this function is evaluated at a point close to zero, the Laplacian becomes undefined. In this case, this function returns zero.

dens_func(spin='t', index=None, log=False)

Return a cubic spline of the electronic density.

Parameters

spinstr, default=”t”

Type of occupied spin orbitals. Can be either “t” (for alpha + beta), “a” (for alpha), “b” (for beta), or “m” (for alpha - beta).

indexsequence of int, optional

Sequence of integers representing the spin orbitals. These are indexed from 0 to the number of basis functions. By default, all orbitals of the given spin(s) are included.

logbool, default=False

Whether the logarithm of the density is used for interpolation.

Returns

DensitySpline

A DensitySpline instance for the density and its derivatives. Given a set of radial points, it can evaluate densities and derivatives up to order 2.

property dispersion_c6

Isolated atom C6 dispersion coefficients.

Returns

dispersion_c6dict, float

The return dictionary contains isolated atom C6 dispersion coefficients types chu. For references corresponding to each type check theochem/AtomDB

property elem

Element symbol.

Returns

elem : string

property energy

Energy.

Returns

energy : float

property eta

Chemical hardness.

Returns

eta : float

get_docstring()

Docstring of the species’ dataset.

property ip

Ionization potential.

Returns

ip : float

ked_func(spin='t', index=None, log=False)

Return a cubic spline of the kinetic energy density.

Parameters

spinstr, default=”t”

Type of occupied spin orbitals. Can be either “t” (for alpha + beta), “a” (for alpha), “b” (for beta), or “m” (for alpha - beta).

indexsequence of int, optional

Sequence of integers representing the spin orbitals. These are indexed from 0 to the number of basis functions. By default, all orbitals of the given spin(s) are included.

logbool, default=False

Whether the logarithm of the density is used for interpolation.

Returns

DensitySpline

A DensitySpline instance for the density and its derivatives. Given a set of radial points, it can evaluate densities and derivatives up to order 2.

property mu

Chemical potential.

Returns

mu : float

property mult

Multiplicity

\[M = \left|N_S\right| + 1\]

Where \(\left|N_S\right|\) is the spin number.

Returns

mult : int

property nelec

Number of electrons.

Returns

nelec : int

property nexc

Excitation number.

Returns

nexc : int

property nspin

Spin number

\[N_S = N_α - N_β\]

Where \(N_S\) is the spin number and \(N_α\) and \(N_β\) number of alpha and

beta electrons.

Returns

nspin : int

property obasis_name

Basis name.

Returns

obasis_name : string

property polarizability

Isolated atom dipole polarizability.

Returns

polarizabilitydict, float

The return dictionary contains isolated atom dipole polarizability types crc and chu. For references corresponding to each type check theochem/AtomDB

property spinpol

Spin polarization direction (±1).

Returns

spinpol : int

to_dict()

Return the dictionary representation of the Species instance.

to_json()

Return the JSON string representation of the Species instance.

property vdw_radius

Van der Waals radii.

Returns

vdw_radiusdict, float

The return dictionary contains van der wals radii types bondi, truhlar, rt, batsanov, dreiding, uff and mm3. For references corresponding to each type check theochem/AtomDB

atomdb.species.compile_species(elem, charge, mult, nexc=0, dataset='slater', datapath='/home/runner/.local/lib/python3.12/site-packages/atomdb/datasets')

Compile an atomic or ionic species into the AtomDB database.

Parameters

elemstr

Element symbol.

chargeint

Charge.

multint

Multiplicity.

nexcint, optional

Excitation level, by default 0.

datasetstr, optional

Dataset name, by default DEFAULT_DATASET.

datapathstr, optional

Path to the local AtomDB cache, by default DEFAULT_DATAPATH variable value.

atomdb.species.dump(*species, datapath='/home/runner/.local/lib/python3.12/site-packages/atomdb/datasets')

Dump the Species instance(s) to a MessagePack file in the database.

Parameters

species: Iterable

Iterables of objects of class Species

datapathstr, optional

Path to the local AtomDB cache, by default DEFAULT_DATAPATH variable value.

atomdb.species.load(elem, charge, mult, nexc=0, dataset='slater', datapath='/home/runner/.local/lib/python3.12/site-packages/atomdb/datasets', remotepath='https://raw.githubusercontent.com/theochem/AtomDBdata/main/')

Load one or many atomic or ionic species from the AtomDB database.

Parameters

elemstr

Element symbol.

chargeint

Charge.

multint

Multiplicity.

nexcint, optional

Excitation level, by default 0.

datasetstr, optional

Dataset name, by default DEFAULT_DATASET.

datapathstr, optional

Path to the local AtomDB cache, by default DEFAULT_DATAPATH variable value.

remotepathstr, optional

Remote URL for AtomDB datasets, by default DEFAULT_REMOTE variable value

Returns

Object of class Species

atomdb.species.raw_datafile(suffix, elem, charge, mult, nexc=0, dataset='slater', datapath='/home/runner/.local/lib/python3.12/site-packages/atomdb/datasets', remotepath='https://raw.githubusercontent.com/theochem/AtomDBdata/main/')

Returns the local path to the raw data file of a species

This function retrieves the raw data file of a species from the AtomDB cache if present. If the file is not found, it is downloaded from the remote URL.

Parameters

suffixstr

File extension of the raw data file.

elemstr

Element symbol.

chargeint

Charge.

multint

Multiplicity.

nexcint, optional

Excitation level, by default 0.

datasetstr, optional

Dataset name, by default DEFAULT_DATASET.

datapathstr, optional

Path to the local AtomDB cache, by default DEFAULT_DATAPATH variable value.

remotepathstr, optional

Remote URL for AtomDB datasets, by default DEFAULT_REMOTE variable value.

Returns

str

Path to the raw data file.

atomdb.utils module

Constants and utility functions.

atomdb.utils.DEFAULT_DATAPATH = '/home/runner/.local/lib/python3.12/site-packages/atomdb/datasets'

The path for AtomDB local cache.

atomdb.utils.DEFAULT_DATASET = 'slater'

Default dataset to query.

atomdb.utils.DEFAULT_REMOTE = 'https://raw.githubusercontent.com/theochem/AtomDBdata/main/'

Default remote URL for AtomDB datasets.

atomdb.utils.MODULE_DATAPATH = '/home/runner/.local/lib/python3.12/site-packages/atomdb/data'

The path for AtomDB data files.

atomdb.utils.MULTIPLICITIES = {(1, -2): 2, (1, -1): 1, (1, 0): 2, (2, -2): 1, (2, -1): 2, (2, 0): 1, (2, 1): 2, (3, -2): 2, (3, -1): 1, (3, 0): 2, (3, 1): 1, (3, 2): 2, (4, -2): 3, (4, -1): 2, (4, 0): 1, (4, 1): 2, (4, 2): 1, (4, 3): 2, (5, -2): 4, (5, -1): 3, (5, 0): 2, (5, 1): 1, (5, 2): 2, (5, 3): 1, (5, 4): 2, (6, -2): 3, (6, -1): 4, (6, 0): 3, (6, 1): 2, (6, 2): 1, (6, 3): 2, (6, 4): 1, (6, 5): 2, (7, -2): 2, (7, -1): 3, (7, 0): 4, (7, 1): 3, (7, 2): 2, (7, 3): 1, (7, 4): 2, (7, 5): 1, (7, 6): 2, (8, -2): 1, (8, -1): 2, (8, 0): 3, (8, 1): 4, (8, 2): 3, (8, 3): 2, (8, 4): 1, (8, 5): 2, (8, 6): 1, (8, 7): 2, (9, -2): 2, (9, -1): 1, (9, 0): 2, (9, 1): 3, (9, 2): 4, (9, 3): 3, (9, 4): 2, (9, 5): 1, (9, 6): 2, (9, 7): 1, (9, 8): 2, (10, -2): 1, (10, -1): 2, (10, 0): 1, (10, 1): 2, (10, 2): 3, (10, 3): 4, (10, 4): 3, (10, 5): 2, (10, 6): 1, (10, 7): 2, (10, 8): 1, (10, 9): 2, (11, -2): 2, (11, -1): 1, (11, 0): 2, (11, 1): 1, (11, 2): 2, (11, 3): 3, (11, 4): 4, (11, 5): 3, (11, 6): 2, (11, 7): 1, (11, 8): 2, (11, 9): 1, (11, 10): 2, (12, -2): 3, (12, -1): 2, (12, 0): 1, (12, 1): 2, (12, 2): 1, (12, 3): 2, (12, 4): 3, (12, 5): 4, (12, 6): 3, (12, 7): 2, (12, 8): 1, (12, 9): 2, (12, 10): 1, (12, 11): 2, (13, -2): 4, (13, -1): 3, (13, 0): 2, (13, 1): 1, (13, 2): 2, (13, 3): 1, (13, 4): 2, (13, 5): 3, (13, 6): 4, (13, 7): 3, (13, 8): 2, (13, 9): 1, (13, 10): 2, (13, 11): 1, (13, 12): 2, (14, -2): 3, (14, -1): 4, (14, 0): 3, (14, 1): 2, (14, 2): 1, (14, 3): 2, (14, 4): 1, (14, 5): 2, (14, 6): 3, (14, 7): 4, (14, 8): 3, (14, 9): 2, (14, 10): 1, (14, 11): 2, (14, 12): 1, (14, 13): 2, (15, -2): 2, (15, -1): 3, (15, 0): 4, (15, 1): 3, (15, 2): 2, (15, 3): 1, (15, 4): 2, (15, 5): 1, (15, 6): 2, (15, 7): 3, (15, 8): 4, (15, 9): 3, (15, 10): 2, (15, 11): 1, (15, 12): 2, (15, 13): 1, (15, 14): 2, (16, -2): 1, (16, -1): 2, (16, 0): 3, (16, 1): 4, (16, 2): 3, (16, 3): 2, (16, 4): 1, (16, 5): 2, (16, 6): 1, (16, 7): 2, (16, 8): 3, (16, 9): 4, (16, 10): 3, (16, 11): 2, (16, 12): 1, (16, 13): 2, (16, 14): 1, (16, 15): 2, (17, -2): 2, (17, -1): 1, (17, 0): 2, (17, 1): 3, (17, 2): 4, (17, 3): 3, (17, 4): 2, (17, 5): 1, (17, 6): 2, (17, 7): 1, (17, 8): 2, (17, 9): 3, (17, 10): 4, (17, 11): 3, (17, 12): 2, (17, 13): 1, (17, 14): 2, (17, 15): 1, (17, 16): 2, (18, -2): 1, (18, -1): 2, (18, 0): 1, (18, 1): 2, (18, 2): 3, (18, 3): 4, (18, 4): 3, (18, 5): 2, (18, 6): 1, (18, 7): 2, (18, 8): 1, (18, 9): 2, (18, 10): 3, (18, 11): 4, (18, 12): 3, (18, 13): 2, (18, 14): 1, (18, 15): 2, (18, 16): 1, (18, 17): 2, (19, -2): 2, (19, -1): 1, (19, 0): 2, (19, 1): 1, (19, 2): 2, (19, 3): 3, (19, 4): 4, (19, 5): 3, (19, 6): 2, (19, 7): 1, (19, 8): 2, (19, 9): 1, (19, 10): 2, (19, 11): 3, (19, 12): 4, (19, 13): 3, (19, 14): 2, (19, 15): 1, (19, 16): 2, (19, 17): 1, (19, 18): 2, (20, -2): 3, (20, -1): 2, (20, 0): 1, (20, 1): 2, (20, 2): 1, (20, 3): 2, (20, 4): 3, (20, 5): 4, (20, 6): 3, (20, 7): 2, (20, 8): 1, (20, 9): 2, (20, 10): 1, (20, 11): 2, (20, 12): 3, (20, 13): 4, (20, 14): 3, (20, 15): 2, (20, 16): 1, (20, 17): 2, (20, 18): 1, (20, 19): 2, (21, -2): 4, (21, -1): 3, (21, 0): 2, (21, 1): 3, (21, 2): 2, (21, 3): 1, (21, 4): 2, (21, 5): 3, (21, 6): 4, (21, 7): 3, (21, 8): 2, (21, 9): 1, (21, 10): 2, (21, 11): 1, (21, 12): 2, (21, 13): 3, (21, 14): 4, (21, 15): 3, (21, 16): 2, (21, 17): 1, (21, 18): 2, (21, 19): 1, (21, 20): 2, (22, -2): 7, (22, -1): 4, (22, 0): 3, (22, 1): 4, (22, 2): 3, (22, 3): 2, (22, 4): 1, (22, 5): 2, (22, 6): 3, (22, 7): 4, (22, 8): 3, (22, 9): 2, (22, 10): 1, (22, 11): 2, (22, 12): 1, (22, 13): 2, (22, 14): 3, (22, 15): 4, (22, 16): 3, (22, 17): 2, (22, 18): 1, (22, 19): 2, (22, 20): 1, (22, 21): 2, (23, -2): 6, (23, -1): 7, (23, 0): 4, (23, 1): 5, (23, 2): 4, (23, 3): 3, (23, 4): 2, (23, 5): 1, (23, 6): 2, (23, 7): 3, (23, 8): 4, (23, 9): 3, (23, 10): 2, (23, 11): 1, (23, 12): 2, (23, 13): 1, (23, 14): 2, (23, 15): 3, (23, 16): 4, (23, 17): 3, (23, 18): 2, (23, 19): 1, (23, 20): 2, (23, 21): 1, (23, 22): 2, (24, -2): 5, (24, -1): 6, (24, 0): 7, (24, 1): 6, (24, 2): 5, (24, 3): 4, (24, 4): 3, (24, 5): 2, (24, 6): 1, (24, 7): 2, (24, 8): 3, (24, 9): 4, (24, 10): 3, (24, 11): 2, (24, 12): 1, (24, 13): 2, (24, 14): 1, (24, 15): 2, (24, 16): 3, (24, 17): 4, (24, 18): 3, (24, 19): 2, (24, 20): 1, (24, 21): 2, (24, 22): 1, (24, 23): 2, (25, -2): 4, (25, -1): 5, (25, 0): 6, (25, 1): 7, (25, 2): 6, (25, 3): 5, (25, 4): 4, (25, 5): 3, (25, 6): 2, (25, 7): 1, (25, 8): 2, (25, 9): 3, (25, 10): 4, (25, 11): 3, (25, 12): 2, (25, 13): 1, (25, 14): 2, (25, 15): 1, (25, 16): 2, (25, 17): 3, (25, 18): 4, (25, 19): 3, (25, 20): 2, (25, 21): 1, (25, 22): 2, (25, 23): 1, (25, 24): 2, (26, -2): 3, (26, -1): 4, (26, 0): 5, (26, 1): 6, (26, 2): 5, (26, 3): 6, (26, 4): 5, (26, 5): 4, (26, 6): 3, (26, 7): 2, (26, 8): 1, (26, 9): 2, (26, 10): 3, (26, 11): 4, (26, 12): 3, (26, 13): 2, (26, 14): 1, (26, 15): 2, (26, 16): 1, (26, 17): 2, (26, 18): 3, (26, 19): 4, (26, 20): 3, (26, 21): 2, (26, 22): 1, (26, 23): 2, (26, 24): 1, (26, 25): 2, (27, -2): 2, (27, -1): 3, (27, 0): 4, (27, 1): 3, (27, 2): 4, (27, 3): 5, (27, 4): 6, (27, 5): 5, (27, 6): 4, (27, 7): 3, (27, 8): 2, (27, 9): 1, (27, 10): 2, (27, 11): 3, (27, 12): 4, (27, 13): 3, (27, 14): 2, (27, 15): 1, (27, 16): 2, (27, 17): 1, (27, 18): 2, (27, 19): 3, (27, 20): 4, (27, 21): 3, (27, 22): 2, (27, 23): 1, (27, 24): 2, (27, 25): 1, (27, 26): 2, (28, -2): 1, (28, -1): 2, (28, 0): 3, (28, 1): 2, (28, 2): 3, (28, 3): 4, (28, 4): 5, (28, 5): 6, (28, 6): 5, (28, 7): 4, (28, 8): 3, (28, 9): 2, (28, 10): 1, (28, 11): 2, (28, 12): 3, (28, 13): 4, (28, 14): 3, (28, 15): 2, (28, 16): 1, (28, 17): 2, (28, 18): 1, (28, 19): 2, (28, 20): 3, (28, 21): 4, (28, 22): 3, (28, 23): 2, (28, 24): 1, (28, 25): 2, (28, 26): 1, (28, 27): 2, (29, -2): 2, (29, -1): 1, (29, 0): 2, (29, 1): 1, (29, 2): 2, (29, 3): 3, (29, 4): 4, (29, 5): 5, (29, 6): 6, (29, 7): 5, (29, 8): 4, (29, 9): 3, (29, 10): 2, (29, 11): 1, (29, 12): 2, (29, 13): 3, (29, 14): 4, (29, 15): 3, (29, 16): 2, (29, 17): 1, (29, 18): 2, (29, 19): 1, (29, 20): 2, (29, 21): 3, (29, 22): 4, (29, 23): 3, (29, 24): 2, (29, 25): 1, (29, 26): 2, (29, 27): 1, (29, 28): 2, (30, -2): 3, (30, -1): 2, (30, 0): 1, (30, 1): 2, (30, 2): 1, (30, 3): 2, (30, 4): 3, (30, 5): 4, (30, 6): 5, (30, 7): 6, (30, 8): 5, (30, 9): 4, (30, 10): 3, (30, 11): 2, (30, 12): 1, (30, 13): 2, (30, 14): 3, (30, 15): 4, (30, 16): 3, (30, 17): 2, (30, 18): 1, (30, 19): 2, (30, 20): 1, (30, 21): 2, (30, 22): 3, (30, 23): 4, (30, 24): 3, (30, 25): 2, (30, 26): 1, (30, 27): 2, (30, 28): 1, (30, 29): 2, (31, -2): 4, (31, -1): 3, (31, 0): 2, (31, 1): 1, (31, 2): 2, (31, 3): 1, (31, 4): 2, (31, 5): 3, (31, 6): 4, (31, 7): 5, (31, 8): 6, (31, 9): 5, (31, 10): 4, (31, 11): 3, (31, 12): 2, (31, 13): 1, (31, 14): 2, (31, 15): 3, (31, 16): 4, (31, 17): 3, (31, 18): 2, (31, 19): 1, (31, 20): 2, (31, 21): 1, (31, 22): 2, (31, 23): 3, (31, 24): 4, (31, 25): 3, (31, 26): 2, (31, 27): 1, (31, 28): 2, (31, 29): 1, (31, 30): 2, (32, -2): 3, (32, -1): 4, (32, 0): 3, (32, 1): 2, (32, 2): 1, (32, 3): 2, (32, 4): 1, (32, 5): 2, (32, 6): 3, (32, 7): 4, (32, 8): 5, (32, 9): 6, (32, 10): 5, (32, 11): 4, (32, 12): 3, (32, 13): 2, (32, 14): 1, (32, 15): 2, (32, 16): 3, (32, 17): 4, (32, 18): 3, (32, 19): 2, (32, 20): 1, (32, 21): 2, (32, 22): 1, (32, 23): 2, (32, 24): 3, (32, 25): 4, (32, 26): 3, (32, 27): 2, (32, 28): 1, (32, 29): 2, (32, 30): 1, (32, 31): 2, (33, -2): 2, (33, -1): 3, (33, 0): 4, (33, 1): 3, (33, 2): 2, (33, 3): 1, (33, 4): 2, (33, 5): 1, (33, 6): 2, (33, 7): 3, (33, 8): 4, (33, 9): 5, (33, 10): 6, (33, 11): 5, (33, 12): 4, (33, 13): 3, (33, 14): 2, (33, 15): 1, (33, 16): 2, (33, 17): 3, (33, 18): 4, (33, 19): 3, (33, 20): 2, (33, 21): 1, (33, 22): 2, (33, 23): 1, (33, 24): 2, (33, 25): 3, (33, 26): 4, (33, 27): 3, (33, 28): 2, (33, 29): 1, (33, 30): 2, (33, 31): 1, (33, 32): 2, (34, -2): 1, (34, -1): 2, (34, 0): 3, (34, 1): 4, (34, 2): 3, (34, 3): 2, (34, 4): 1, (34, 5): 2, (34, 6): 1, (34, 7): 2, (34, 8): 3, (34, 9): 4, (34, 10): 5, (34, 11): 6, (34, 12): 5, (34, 13): 4, (34, 14): 3, (34, 15): 2, (34, 16): 1, (34, 17): 2, (34, 18): 3, (34, 19): 4, (34, 20): 3, (34, 21): 2, (34, 22): 1, (34, 23): 2, (34, 24): 1, (34, 25): 2, (34, 26): 3, (34, 27): 4, (34, 28): 3, (34, 29): 2, (34, 30): 1, (34, 31): 2, (34, 32): 1, (34, 33): 2, (35, -2): 2, (35, -1): 1, (35, 0): 2, (35, 1): 3, (35, 2): 4, (35, 3): 3, (35, 4): 2, (35, 5): 1, (35, 6): 2, (35, 7): 1, (35, 8): 2, (35, 9): 3, (35, 10): 4, (35, 11): 5, (35, 12): 6, (35, 13): 5, (35, 14): 4, (35, 15): 3, (35, 16): 2, (35, 17): 1, (35, 18): 2, (35, 19): 3, (35, 20): 4, (35, 21): 3, (35, 22): 2, (35, 23): 1, (35, 24): 2, (35, 25): 1, (35, 26): 2, (35, 27): 3, (35, 28): 4, (35, 29): 3, (35, 30): 2, (35, 31): 1, (35, 32): 2, (35, 33): 1, (35, 34): 2, (36, -2): 1, (36, -1): 2, (36, 0): 1, (36, 1): 2, (36, 2): 3, (36, 3): 4, (36, 4): 3, (36, 5): 2, (36, 6): 1, (36, 7): 2, (36, 8): 1, (36, 9): 2, (36, 10): 3, (36, 11): 4, (36, 12): 5, (36, 13): 6, (36, 14): 5, (36, 15): 4, (36, 16): 3, (36, 17): 2, (36, 18): 1, (36, 19): 2, (36, 20): 3, (36, 21): 4, (36, 22): 3, (36, 23): 2, (36, 24): 1, (36, 25): 2, (36, 26): 1, (36, 27): 2, (36, 28): 3, (36, 29): 4, (36, 30): 3, (36, 31): 2, (36, 32): 1, (36, 33): 2, (36, 34): 1, (36, 35): 2, (37, -2): 2, (37, -1): 1, (37, 0): 2, (37, 1): 1, (37, 2): 2, (37, 3): 3, (37, 4): 4, (37, 5): 3, (37, 6): 2, (37, 7): 1, (37, 8): 2, (37, 9): 1, (37, 10): 2, (37, 11): 3, (37, 12): 4, (37, 13): 5, (37, 14): 6, (37, 15): 5, (37, 16): 4, (37, 17): 3, (37, 18): 2, (37, 19): 1, (37, 20): 2, (37, 21): 3, (37, 22): 4, (37, 23): 3, (37, 24): 2, (37, 25): 1, (37, 26): 2, (37, 27): 1, (37, 28): 2, (37, 29): 3, (37, 30): 4, (37, 31): 3, (37, 32): 2, (37, 33): 1, (37, 34): 2, (37, 35): 1, (37, 36): 2, (38, -2): 3, (38, -1): 2, (38, 0): 1, (38, 1): 2, (38, 2): 1, (38, 3): 2, (38, 4): 3, (38, 5): 4, (38, 6): 3, (38, 7): 2, (38, 8): 1, (38, 9): 2, (38, 10): 1, (38, 11): 2, (38, 12): 3, (38, 13): 4, (38, 14): 5, (38, 15): 6, (38, 16): 5, (38, 17): 4, (38, 18): 3, (38, 19): 2, (38, 20): 1, (38, 21): 2, (38, 22): 3, (38, 23): 4, (38, 24): 3, (38, 25): 2, (38, 26): 1, (38, 27): 2, (38, 28): 1, (38, 29): 2, (38, 30): 3, (38, 31): 4, (38, 32): 3, (38, 33): 2, (38, 34): 1, (38, 35): 2, (38, 36): 1, (38, 37): 2, (39, -2): 6, (39, -1): 3, (39, 0): 2, (39, 1): 1, (39, 2): 2, (39, 3): 1, (39, 4): 2, (39, 5): 3, (39, 6): 4, (39, 7): 3, (39, 8): 2, (39, 9): 1, (39, 10): 2, (39, 11): 1, (39, 12): 2, (39, 13): 3, (39, 14): 4, (39, 15): 5, (39, 16): 6, (39, 17): 5, (39, 18): 4, (39, 19): 3, (39, 20): 2, (39, 21): 1, (39, 22): 2, (39, 23): 3, (39, 24): 4, (39, 25): 3, (39, 26): 2, (39, 27): 1, (39, 28): 2, (39, 29): 1, (39, 30): 2, (39, 31): 3, (39, 33): 3, (39, 34): 2, (39, 35): 1, (39, 36): 2, (39, 37): 1, (39, 38): 2, (40, -2): 7, (40, -1): 6, (40, 0): 3, (40, 1): 4, (40, 2): 3, (40, 3): 2, (40, 4): 1, (40, 5): 2, (40, 6): 3, (40, 7): 4, (40, 8): 3, (40, 9): 2, (40, 10): 1, (40, 11): 2, (40, 12): 1, (40, 13): 2, (40, 14): 3, (40, 15): 4, (40, 16): 5, (40, 17): 6, (40, 18): 5, (40, 19): 4, (40, 20): 3, (40, 21): 2, (40, 22): 1, (40, 23): 2, (40, 24): 3, (40, 25): 4, (40, 26): 3, (40, 27): 2, (40, 28): 1, (40, 29): 2, (40, 30): 1, (40, 31): 2, (40, 32): 3, (40, 34): 3, (40, 35): 2, (40, 36): 1, (40, 37): 2, (40, 38): 1, (40, 39): 2, (41, -2): 6, (41, -1): 7, (41, 0): 6, (41, 1): 5, (41, 2): 4, (41, 3): 3, (41, 4): 2, (41, 5): 1, (41, 6): 2, (41, 7): 3, (41, 8): 4, (41, 9): 3, (41, 10): 2, (41, 11): 1, (41, 12): 2, (41, 13): 1, (41, 14): 2, (41, 15): 3, (41, 16): 4, (41, 17): 5, (41, 18): 6, (41, 19): 5, (41, 20): 4, (41, 21): 3, (41, 22): 2, (41, 23): 1, (41, 24): 2, (41, 25): 3, (41, 26): 4, (41, 27): 3, (41, 28): 2, (41, 29): 1, (41, 30): 2, (41, 31): 1, (41, 32): 2, (41, 33): 3, (41, 35): 3, (41, 36): 2, (41, 37): 1, (41, 38): 2, (41, 39): 1, (41, 40): 2, (42, -2): 5, (42, -1): 6, (42, 0): 7, (42, 1): 6, (42, 2): 5, (42, 3): 4, (42, 4): 3, (42, 5): 2, (42, 6): 1, (42, 7): 2, (42, 8): 3, (42, 9): 4, (42, 10): 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(90, 26): 3, (90, 27): 2, (90, 28): 1, (90, 29): 2, (90, 30): 1, (90, 31): 2, (90, 33): 4, (90, 34): 5, (90, 35): 6, (90, 36): 7, (90, 37): 8, (90, 38): 7, (90, 39): 6, (90, 40): 5, (90, 41): 4, (90, 42): 3, (90, 43): 2, (90, 44): 1, (90, 45): 2, (90, 46): 3, (90, 47): 4, (90, 48): 5, (90, 50): 5, (90, 51): 4, (90, 52): 3, (90, 53): 2, (90, 54): 1, (90, 55): 2, (90, 56): 3, (90, 58): 3, (90, 59): 2, (90, 60): 1, (90, 61): 2, (90, 62): 1, (90, 63): 2, (90, 64): 3, (90, 65): 4, (90, 68): 5, (90, 69): 4, (90, 70): 3, (90, 71): 2, (90, 72): 1, (90, 73): 2, (90, 74): 3, (90, 75): 2, (90, 76): 3, (90, 77): 2, (90, 78): 1, (90, 79): 2, (90, 80): 1, (90, 81): 2, (90, 82): 3, (90, 84): 3, (90, 85): 2, (90, 86): 1, (90, 87): 2, (90, 88): 1, (90, 89): 2, (91, -2): 6, (91, -1): 5, (91, 0): 4, (91, 1): 3, (91, 2): 4, (91, 3): 3, (91, 4): 2, (91, 5): 1, (91, 6): 2, (91, 7): 3, (91, 8): 4, (91, 9): 3, (91, 10): 2, (91, 11): 1, (91, 12): 2, (91, 13): 1, (91, 14): 2, (91, 15): 3, (91, 16): 4, (91, 17): 5, (91, 18): 6, (91, 19): 5, (91, 20): 4, (91, 21): 3, (91, 22): 2, (91, 23): 1, (91, 24): 2, (91, 25): 3, (91, 26): 2, (91, 27): 3, (91, 28): 2, (91, 29): 1, (91, 30): 2, (91, 31): 1, (91, 32): 2, (91, 34): 4, (91, 35): 5, (91, 36): 6, (91, 37): 7, (91, 38): 8, (91, 39): 7, (91, 40): 6, (91, 41): 5, (91, 42): 4, (91, 43): 3, (91, 44): 2, (91, 45): 1, (91, 46): 2, (91, 47): 3, (91, 48): 4, (91, 49): 5, (91, 51): 5, (91, 52): 4, (91, 53): 3, (91, 54): 2, (91, 55): 1, (91, 56): 2, (91, 57): 3, (91, 59): 3, (91, 60): 2, (91, 61): 1, (91, 62): 2, (91, 63): 1, (91, 64): 2, (91, 65): 3, (91, 66): 4, (91, 69): 5, (91, 70): 4, (91, 71): 3, (91, 72): 2, (91, 73): 1, (91, 74): 2, (91, 75): 3, (91, 76): 2, (91, 77): 3, (91, 78): 2, (91, 79): 1, (91, 80): 2, (91, 81): 1, (91, 82): 2, (91, 83): 3, (91, 85): 3, (91, 86): 2, (91, 87): 1, (91, 88): 2, (91, 89): 1, (91, 90): 2, (92, -2): 7, (92, -1): 6, (92, 0): 5, (92, 1): 4, (92, 2): 5, (92, 3): 4, (92, 4): 3, (92, 5): 2, (92, 6): 1, (92, 7): 2, (92, 8): 3, (92, 9): 4, (92, 10): 3, (92, 11): 2, (92, 12): 1, (92, 13): 2, (92, 14): 1, (92, 15): 2, (92, 16): 3, (92, 17): 4, (92, 18): 5, (92, 19): 6, (92, 20): 5, (92, 21): 4, (92, 22): 3, (92, 23): 2, (92, 24): 1, (92, 25): 2, (92, 26): 3, (92, 27): 2, (92, 28): 3, (92, 29): 2, (92, 30): 1, (92, 31): 2, (92, 32): 1, (92, 33): 2, (92, 35): 4, (92, 36): 5, (92, 37): 6, (92, 38): 7, (92, 39): 8, (92, 40): 7, (92, 41): 6, (92, 42): 5, (92, 43): 4, (92, 44): 3, (92, 45): 2, (92, 46): 1, (92, 47): 2, (92, 48): 3, (92, 49): 4, (92, 50): 5, (92, 52): 5, (92, 53): 4, (92, 54): 3, (92, 55): 2, (92, 56): 1, (92, 57): 2, (92, 58): 3, (92, 60): 3, (92, 61): 2, (92, 62): 1, (92, 63): 2, (92, 64): 1, (92, 65): 2, (92, 66): 3, (92, 67): 4, (92, 70): 5, (92, 71): 4, (92, 72): 3, (92, 73): 2, (92, 74): 1, (92, 75): 2, (92, 76): 3, (92, 77): 2, (92, 78): 3, (92, 79): 2, (92, 80): 1, (92, 81): 2, (92, 82): 1, (92, 83): 2, (92, 84): 3, (92, 86): 3, (92, 87): 2, (92, 88): 1, (92, 89): 2, (92, 90): 1, (92, 91): 2, (93, -2): 8, (93, -1): 7, (93, 0): 6, (93, 1): 7, (93, 2): 6, (93, 3): 5, (93, 4): 4, (93, 5): 3, (93, 6): 2, (93, 11): 3, (93, 12): 2, (93, 13): 1, (93, 14): 2, (93, 15): 1, (93, 16): 2, (93, 17): 3, (93, 18): 4, (93, 19): 5, (93, 20): 6, (93, 21): 5, (93, 22): 4, (93, 23): 3, (93, 24): 2, (93, 25): 1, (93, 26): 2, (93, 27): 3, (93, 28): 2, (93, 29): 3, (93, 30): 2, (93, 31): 1, (93, 32): 2, (93, 33): 1, (93, 34): 2, (93, 36): 4, (93, 37): 5, (93, 38): 6, (93, 39): 7, (93, 40): 8, (93, 41): 7, (93, 42): 6, (93, 43): 5, (93, 44): 4, (93, 45): 3, (93, 46): 2, (93, 47): 1, (93, 48): 2, (93, 49): 3, (93, 50): 4, (93, 51): 5, (93, 53): 5, (93, 54): 4, (93, 55): 3, (93, 56): 2, (93, 57): 1, (93, 58): 2, (93, 59): 3, (93, 61): 3, (93, 62): 2, (93, 63): 1, (93, 64): 2, (93, 65): 1, (93, 66): 2, (93, 67): 3, (93, 68): 4, (93, 71): 5, (93, 72): 4, (93, 73): 3, (93, 74): 2, (93, 75): 1, (93, 76): 2, (93, 77): 3, (93, 78): 2, (93, 79): 3, (93, 80): 2, (93, 81): 1, (93, 82): 2, (93, 83): 1, (93, 84): 2, (93, 85): 3, (93, 87): 3, (93, 88): 2, (93, 89): 1, (93, 90): 2, (93, 91): 1, (93, 92): 2, (94, -2): 9, (94, -1): 8, (94, 0): 7, (94, 1): 8, (94, 2): 7, (94, 3): 6, (94, 4): 5, (94, 5): 4, (94, 12): 3, (94, 13): 2, (94, 14): 1, (94, 15): 2, (94, 16): 1, (94, 17): 2, (94, 18): 3, (94, 19): 4, (94, 20): 5, (94, 21): 6, (94, 22): 5, (94, 23): 4, (94, 24): 3, (94, 25): 2, (94, 26): 1, (94, 27): 2, (94, 28): 3, (94, 29): 2, (94, 30): 3, (94, 31): 2, (94, 32): 1, (94, 33): 2, (94, 34): 1, (94, 35): 2, (94, 37): 4, (94, 38): 5, (94, 39): 6, (94, 40): 7, (94, 41): 8, (94, 42): 7, (94, 43): 6, (94, 44): 5, (94, 45): 4, (94, 46): 3, (94, 47): 2, (94, 48): 1, (94, 49): 2, (94, 50): 3, (94, 51): 4, (94, 52): 5, (94, 54): 5, (94, 55): 4, (94, 56): 3, (94, 57): 2, (94, 58): 1, (94, 59): 2, (94, 60): 3, (94, 62): 3, (94, 63): 2, (94, 64): 1, (94, 65): 2, (94, 66): 1, (94, 67): 2, (94, 68): 3, (94, 69): 4, (94, 72): 5, (94, 73): 4, (94, 74): 3, (94, 75): 2, (94, 76): 1, (94, 77): 2, (94, 78): 3, (94, 79): 2, (94, 80): 3, (94, 81): 2, (94, 82): 1, (94, 83): 2, (94, 84): 1, (94, 85): 2, (94, 86): 3, (94, 88): 3, (94, 89): 2, (94, 90): 1, (94, 91): 2, (94, 92): 1, (94, 93): 2, (95, -2): 6, (95, -1): 9, (95, 0): 8, (95, 1): 9, (95, 2): 8, (95, 3): 7, (95, 4): 6, (95, 5): 5, (95, 6): 4, (95, 13): 3, (95, 14): 2, (95, 15): 1, (95, 16): 2, (95, 17): 1, (95, 18): 2, (95, 19): 3, (95, 20): 4, (95, 21): 5, (95, 22): 6, (95, 23): 5, (95, 24): 4, (95, 25): 3, (95, 26): 2, (95, 27): 1, (95, 28): 2, (95, 29): 3, (95, 30): 2, (95, 31): 3, (95, 32): 2, (95, 33): 1, (95, 34): 2, (95, 35): 1, (95, 36): 2, (95, 38): 4, (95, 39): 5, (95, 40): 6, (95, 41): 7, (95, 42): 8, (95, 43): 7, (95, 44): 6, (95, 45): 5, (95, 46): 4, (95, 47): 3, (95, 48): 2, (95, 49): 1, (95, 50): 2, (95, 51): 3, (95, 52): 4, (95, 53): 5, (95, 55): 5, (95, 56): 4, (95, 57): 3, (95, 58): 2, (95, 59): 1, (95, 60): 2, (95, 61): 3, (95, 63): 3, (95, 64): 2, (95, 65): 1, (95, 66): 2, (95, 67): 1, (95, 68): 2, (95, 69): 3, (95, 70): 4, (95, 73): 5, (95, 74): 4, (95, 75): 3, (95, 76): 2, (95, 77): 1, (95, 78): 2, (95, 79): 3, (95, 80): 2, (95, 81): 3, (95, 82): 2, (95, 83): 1, (95, 84): 2, (95, 85): 1, (95, 86): 2, (95, 87): 3, (95, 89): 3, (95, 90): 2, (95, 91): 1, (95, 92): 2, (95, 93): 1, (95, 94): 2, (96, -2): 5, (96, -1): 6, (96, 0): 9, (96, 1): 8, (96, 2): 7, (96, 3): 8, (96, 4): 7, (96, 5): 6, (96, 6): 5, (96, 15): 2, (96, 16): 1, (96, 17): 2, (96, 18): 1, (96, 19): 2, (96, 20): 3, (96, 21): 4, (96, 22): 5, (96, 23): 6, (96, 24): 5, (96, 25): 4, (96, 26): 3, (96, 27): 2, (96, 28): 1, (96, 29): 2, (96, 30): 3, (96, 31): 2, (96, 32): 3, (96, 33): 2, (96, 34): 1, (96, 35): 2, (96, 36): 1, (96, 37): 2, (96, 39): 4, (96, 40): 5, (96, 41): 6, (96, 42): 7, (96, 43): 8, (96, 44): 7, (96, 45): 6, (96, 46): 5, (96, 47): 4, (96, 48): 3, (96, 49): 2, (96, 50): 1, (96, 51): 2, (96, 52): 3, (96, 53): 4, (96, 54): 5, (96, 56): 5, (96, 57): 4, (96, 58): 3, (96, 59): 2, (96, 60): 1, (96, 61): 2, (96, 62): 3, (96, 64): 3, (96, 65): 2, (96, 66): 1, (96, 67): 2, (96, 68): 1, (96, 69): 2, (96, 70): 3, (96, 71): 4, (96, 74): 5, (96, 75): 4, (96, 76): 3, (96, 77): 2, (96, 78): 1, (96, 79): 2, (96, 80): 3, (96, 81): 2, (96, 82): 3, (96, 83): 2, (96, 84): 1, (96, 85): 2, (96, 86): 1, (96, 87): 2, (96, 88): 3, (96, 90): 3, (96, 91): 2, (96, 92): 1, (96, 93): 2, (96, 94): 1, (96, 95): 2, (97, -2): 4, (97, -1): 5, (97, 0): 6, (97, 1): 7, (97, 2): 6, (97, 3): 7, (97, 4): 8, (97, 5): 7, (97, 6): 6, (97, 7): 5, (97, 16): 2, (97, 17): 1, (97, 18): 2, (97, 19): 1, (97, 20): 2, (97, 21): 3, (97, 22): 4, (97, 23): 5, (97, 24): 6, (97, 25): 5, (97, 26): 4, (97, 27): 3, (97, 28): 2, (97, 29): 1, (97, 30): 2, (97, 31): 3, (97, 32): 2, (97, 33): 3, (97, 34): 2, (97, 35): 1, (97, 36): 2, (97, 37): 1, (97, 38): 2, (97, 40): 4, (97, 41): 5, (97, 42): 6, (97, 43): 7, (97, 44): 8, (97, 45): 7, (97, 46): 6, (97, 47): 5, (97, 48): 4, (97, 49): 3, (97, 50): 2, (97, 51): 1, (97, 52): 2, (97, 53): 3, (97, 54): 4, (97, 55): 5, (97, 57): 5, (97, 58): 4, (97, 59): 3, (97, 60): 2, (97, 61): 1, (97, 62): 2, (97, 63): 3, (97, 65): 3, (97, 66): 2, (97, 67): 1, (97, 68): 2, (97, 69): 1, (97, 70): 2, (97, 71): 3, (97, 72): 4, (97, 75): 5, (97, 76): 4, (97, 77): 3, (97, 78): 2, (97, 79): 1, (97, 80): 2, (97, 81): 3, (97, 82): 2, (97, 83): 3, (97, 84): 2, (97, 85): 1, (97, 86): 2, (97, 87): 1, (97, 88): 2, (97, 89): 3, (97, 91): 3, (97, 92): 2, (97, 93): 1, (97, 94): 2, (97, 95): 1, (97, 96): 2, (98, -1): 4, (98, 0): 5, (98, 1): 6, (98, 2): 5, (98, 3): 6, (98, 4): 7, (98, 5): 8, (98, 6): 7, (98, 7): 6, (98, 8): 5, (98, 17): 2, (98, 18): 1, (98, 19): 2, (98, 20): 1, (98, 21): 2, (98, 22): 3, (98, 23): 4, (98, 24): 5, (98, 25): 6, (98, 26): 5, (98, 27): 4, (98, 28): 3, (98, 29): 2, (98, 30): 1, (98, 31): 2, (98, 32): 3, (98, 33): 2, (98, 34): 3, (98, 35): 2, (98, 36): 1, (98, 37): 2, (98, 38): 1, (98, 39): 2, (98, 41): 4, (98, 42): 5, (98, 43): 6, (98, 44): 7, (98, 45): 8, (98, 46): 7, (98, 47): 6, (98, 48): 5, (98, 49): 4, (98, 50): 3, (98, 51): 2, (98, 52): 1, (98, 53): 2, (98, 54): 3, (98, 55): 4, (98, 56): 5, (98, 58): 5, (98, 59): 4, (98, 60): 3, (98, 61): 2, (98, 62): 1, (98, 63): 2, (98, 64): 3, (98, 66): 3, (98, 67): 2, (98, 68): 1, (98, 69): 2, (98, 70): 1, (98, 71): 2, (98, 72): 3, (98, 73): 4, (98, 76): 5, (98, 77): 4, (98, 78): 3, (98, 79): 2, (98, 80): 1, (98, 81): 2, (98, 82): 3, (98, 83): 2, (98, 84): 3, (98, 85): 2, (98, 86): 1, (98, 87): 2, (98, 88): 1, (98, 89): 2, (98, 90): 3, (98, 92): 3, (98, 93): 2, (98, 94): 1, (98, 95): 2, (98, 96): 1, (98, 97): 2, (99, 0): 4, (99, 1): 5, (99, 2): 4, (99, 3): 5, (99, 4): 6, (99, 5): 7, (99, 6): 8, (99, 7): 7, (99, 8): 6, (99, 9): 5, (99, 18): 2, (99, 19): 1, (99, 20): 2, (99, 21): 1, (99, 22): 2, (99, 23): 3, (99, 24): 4, (99, 25): 5, (99, 26): 6, (99, 27): 5, (99, 28): 4, (99, 29): 3, (99, 30): 2, (99, 31): 1, (99, 32): 2, (99, 33): 3, (99, 34): 2, (99, 35): 3, (99, 36): 2, (99, 37): 1, (99, 38): 2, (99, 39): 1, (99, 40): 2, (99, 42): 4, (99, 43): 5, (99, 44): 6, (99, 45): 7, (99, 46): 8, (99, 47): 7, (99, 48): 6, (99, 49): 5, (99, 50): 4, (99, 51): 3, (99, 52): 2, (99, 53): 1, (99, 54): 2, (99, 55): 3, (99, 56): 4, (99, 57): 5, (99, 59): 5, (99, 60): 4, (99, 61): 3, (99, 62): 2, (99, 63): 1, (99, 64): 2, (99, 65): 3, (99, 67): 3, (99, 68): 2, (99, 69): 1, (99, 70): 2, (99, 71): 1, (99, 72): 2, (99, 73): 3, (99, 74): 4, (99, 77): 5, (99, 78): 4, (99, 79): 3, (99, 80): 2, (99, 81): 1, (99, 82): 2, (99, 83): 3, (99, 84): 2, (99, 85): 3, (99, 86): 2, (99, 87): 1, (99, 88): 2, (99, 89): 1, (99, 90): 2, (99, 91): 3, (99, 93): 3, (99, 94): 2, (99, 95): 1, (99, 96): 2, (99, 97): 1, (99, 98): 2, (100, 0): 3, (100, 1): 4, (100, 2): 3, (100, 3): 4, (100, 4): 5, (100, 5): 6, (100, 6): 7, (100, 7): 8, (100, 8): 7, (100, 9): 6, (100, 10): 5, (100, 19): 2, (100, 20): 1, (100, 21): 2, (100, 22): 1, (100, 23): 2, (100, 24): 3, (100, 25): 4, (100, 26): 5, (100, 27): 6, (100, 28): 5, (100, 29): 4, (100, 30): 3, (100, 31): 2, (100, 32): 1, (100, 33): 2, (100, 34): 3, (100, 35): 2, (100, 36): 3, (100, 37): 2, (100, 38): 1, (100, 39): 2, (100, 40): 1, (100, 41): 2, (100, 43): 4, (100, 44): 5, (100, 45): 6, (100, 46): 7, (100, 47): 8, (100, 48): 7, (100, 49): 6, (100, 50): 5, (100, 51): 4, (100, 52): 3, (100, 53): 2, (100, 54): 1, (100, 55): 2, (100, 56): 3, (100, 57): 4, (100, 58): 5, (100, 60): 5, (100, 61): 4, (100, 62): 3, (100, 63): 2, (100, 64): 1, (100, 65): 2, (100, 66): 3, (100, 68): 3, (100, 69): 2, (100, 70): 1, (100, 71): 2, (100, 72): 1, (100, 73): 2, (100, 74): 3, (100, 75): 4, (100, 78): 5, (100, 79): 4, (100, 80): 3, (100, 81): 2, (100, 82): 1, (100, 83): 2, (100, 84): 3, (100, 85): 2, (100, 86): 3, (100, 87): 2, (100, 88): 1, (100, 89): 2, (100, 90): 1, (100, 91): 2, (100, 92): 3, (100, 94): 3, (100, 95): 2, (100, 96): 1, (100, 97): 2, (100, 98): 1, (100, 99): 2}

Dictionary of species’ ground state multiplicities.

Has items (atnum, charge): Tuple[int, int].

atomdb.utils.generate_mult_csv(max_atnum=100)

Write a table of multiplicities to a CSV file.

Values retrieved from database_beta_1.3.0.h5 are organized into a table, with rows corresponding to atomic numbers and columns to charges.

The maximum atomic number (max_atnum) must not exceed 100, which is the database’s limit.

The charge range spans from -2 to max_atnum - 1.

Missing entries have multiplicities set to zero.

Parameters

max_atnumint, default=100

Highest atomic number of the elements to be added to the table.

Raises

ValueError

If the maximum allowed atomic number is greater than 100.