TAPE21¶

Contents of TAPE21¶

Follows a survey of the sections and variables on TAPE21. Details may differ between different run types (SinglePoint, Frequencies...). Most items should be self-explanatory. Some are only significant for internal proceedings of the program and will not be explained in detail. The sections are described in an order that corresponds to the order in which they are generated and hence printed by the KF utility programs. However, the order of generation depends somewhat on the type of application, so some difference may be found when comparing to your own TAPE21 printout.

Note that variable and section names may contain spaces: these are significant.

A special section is the ‘SUPERINDEX’ section, which is in fact a table-of-contents that lists all the sections in the file, with technical information regarding their position on the file, the amount of data corresponding to that section and similar items. The SUPERINDEX section is not discussed further here. See the KF documentation for more details.

Section General

General information about the calculation and the file

fileident

Name of the file. Here: TAPE21

jobid

ADF release number with date and time of the calculation

title

Title of the calculation. This may have been set in the input file, or be internally generated. In a create run it is picked up from the Create basis set file (if no input value for the title key has been given).

runtype

The type of calculation, for instance SinglePoint or Frequencies

nspin

1 for a spin-restricted calculation, 2 for spin-unrestricted

nspinf

Similar for the fragment occupation numbers as they are used in the calculation, See the key FRAGOCCUPATIONS

ldapot

An integer code for the applied LDA part of the XC potential functional used in the SCF. 1 for VWN, 2 for VWN+Stoll ...

xcparv

X-alpha parameter value. Only relevant for the X-alpha LDA potential, meaningless if another LDA potential functional has been selected.

ldaen

As for ldapot: integer code for the LDA part of the Density Functional, now however pertaining to the (post-SCF) energy evaluation. Usually ldaen and ldapot are identical. See the key XC for details.

xcpare

As xcparv, but now for the energy evaluation.

ggapot

Specification (string) of the GGA part of the XC potential used in the SCF, for instance ‘Becke Perdew’. If no GGA potential is applied, the string ggapot is empty.

ggaen

Similar for the GGA part of the XC energy evaluation

iopcor

Code for usage of frozen core: 1=use frozen cores, 0=pseudopotentials. Pseudopotentials are not supported anymore in ADF, so this variable must always be 1.

electrons

The number of valence electrons Note that this is not necessarily the same as what may consider, chemically, as the valence space. Rather, it equals the total number of electrons in the calculation minus the electrons in the frozen core orbitals.

unit of length

Transformation factor between input-used geometrical units (for distances) and atomic units (bohr). If input of, say, the atomic coordinates is in Angstrom, the unit of length is approximately 1.89

unit of angle

Similar for angles. Internal units in the program are radians. Input (bond and dihedral angles) may be in degrees, in which case the unit of angle equals approximately 0.017

Section Geometry

Geometrical data such as number of atoms, coordinates, etc: Most variable names should be self-explanatory

grouplabel

Point group symmetry (string) used in the calculation, for instance O(H). This may be set in the input file.

Geometric Symmetry

Auto-determined (‘true’) symmetry (considering the nuclear frame and any external fields, but not taking into account any user-defined MO occupation numbers and hence the electronic charge distribution.

symmetry tolerance

Threshold for allowed deviation of input atomic coordinates from symmetry to be detected or verified.

orient

Affine transformation (3,4 matrix: rotation and translation) between the input coordinates and the frame in which the program processes the atoms. ADF has certain orientation requirements for all supported point group symmetries and may rotate and translate the input coordinates accordingly.

oinver

The inverse transformation of orient

lrotat

A logical flag to signal whether or not a rotation has been applied between the input frame and the internally used frame.

nr of fragmenttypes

The number of distinct types of fragments

nr of dummy fragmenttypes

Idem, but counting only dummy atom fragments. A dummy fragment, if it exists, must consist of one single (dummy) atom.

fragmenttype

Names (string) of the fragment types.

fragment mass

Sum of atomic masses in the fragment.

fragment charge

An array with 3 values per fragment type (nftypes,3): 1=sum of nuclear charges, 2=sum of effective nuclear charges (discounting for the frozen core shells), 3=nr of valence electrons

fframe

Signals whether or not special local coordinate frames are used for the atoms. Usually this is not so, in which case the variable has the value DEFAULT. fframe is an array that runs over the atoms. See the ‘z=’ option to the data in the ATOMS input key block.

cum nr of fragments

An array (0:nftyps) that gives the total number of fragments for the fragment types up to and including the indexed one. The ordering of fragments and fragment types is printed in the standard output file.

nr of fragments

The total number of fragments in the calculation This equals the last element of the previous variable ‘cum nr of fragments’

nr of dummy fragments

The total number of fragments that each consist of a single dummy atom.

fragment mapping

Affine transformation matrices (3,4: rotation and translation), one for each fragment in the molecule, that transform the fragment coordinates as they are on the fragment file(s), to the actual position of the fragments in the molecule.

cum nr of atomtypes

An array (0:fragmenttypes) that counts the number of atom types up to and including the indexed fragment type.

nr of atomtypes

Total number of atom types in the molecule. Must equal the last element of the ‘cum nr of atomtypes’ array

nr of dummy atomtypes

Similar, now counting only the atom types consisting of a dummy atom.

atomtype

Names (strings) of the atom types

mass

Atomic masses: array running over the atom types. Compare ‘fragment mass’.

charge

Similar as for ‘fragment charge’, but now the values per atom type.

cum nr of atoms

An array (0:atomtypes) that counts the number of atoms up to and including the indexed atom type.

nr of atoms

Total number of atoms. Must equal the last element of the array ‘cum nr of atoms’.

nr of dummy atoms

Total number of dummy atoms

atmcrd

Type of atomic coordinates in input: CART (Cartesian) or ZMAT (Internal).

kmatrix InputOrder

The connection matrix listing (and referencing) the atoms in the order as they were in the input file. This ordering aspect is significant because internally the program reorders the atoms and groups them together by atom type and fragment type. Hence it is relevant to know what ordering (input- or internal-) is assumed in data arrays.

zaxis

For each atom the direction of the local z-axis. Normally this is identical to the standard (0,0,1), but it may be different for analysis purposes. See the ‘z=’ option to the data records in the ATOMS block.

fragment and atomtype index

An integer array (natoms,2) that specifies for each atom the fragment and the atom type it belongs to.

atom order index

An integer array (natoms,2) that defines the re-ordering of atoms between the list in the input file and the internally used list (which is driven by fragment types, fragments, atom types; dummies come last). The internally used list can be derived from the printout of the fragments, early in the standard output.

kmatrix

The connection matrix using the internally applied ordering of atoms

xyz

Cartesian coordinates of the atoms, in the internally used ordering of atoms

xyz Inputorder

Similar, but now for the ordering of atoms as in the input file.

zmatrix

Internal (Z-matrix) atomic coordinates

zmatrix Inputorder

Internal coordinates in the input-order of atoms

Atomic Distances

Inter atomic distance matrix

ntyp

Number of atom types, not counting dummy atoms,

nqptr

A cumulative counting array, very similar to ‘cum nr of atoms’ Differences: it runs only over ‘ntyp’ atom types (not including dummy atoms) and its indexing as well as its values are shifted by one: nqptr(k) is the total number of atoms plus one, counting the atom types up to and including #(k-1)

nnuc

Total number of non-dummy atoms

qtch

Nuclear charges of the non-dummy atoms

qeff

Effective nuclear charges (subtracting charge for the frozen core shells) of the non-dummy atoms

nfragm

Total number of non-dummy fragments

nofrag_1

Integer array specifying for each non-dummy atom the fragment it belongs to.

nofrag_2

Integer array specifying for each non-dummy atom the fragment type it belongs to

nuclab

Names of the non-dummy atom types.

Section Fragments

(To be completed)

FragmentFile

Names of all used fragment files

FragRun Ident,Title

Job identification and title of each fragment run that is used in the current molecule

Section AtomTypes

(To be completed)

Section Properties

AtomCharge Mulliken

Atomic charges derived from Mulliken population analysis.

Dipole

Dipole moment in atomic units.

FragmentCharge Hirshfeld

Fragment charges derived from Hirshfeld analysis

AtomCharge_initial Voronoi

Atomic charges derived from Voronoi analysis for the initial (sum-of-fragments) charge density

AtomCharge_SCF Voronoi

Similar as the previous item, but now for the SCF density

Electrostatic Pot. at Nuclei

Coulomb potentials at the positions of the atoms, not including the contribution from the nucleus itself

Section Basis

Information about the (valence) basis set

nbset

The total number of basis ‘sets’, where a ‘set’ here means a Cartesian function set (3 for a p-type function, 6 for a d-type function, and so on), given by an entry in the ‘list-of-basis-functions’ in the data base file.

nbaspt

Cumulative number of basis sets (see previous variable, for ‘set’), on a per atom type basis. Only non-dummy atoms (type) are considered. nbaspt(k) is 1+nr-of-basis sets up to, but not including atom type #k

nqbas

Main quantum number of each basis set. A 1s function has nqbas()=1

lqbas

Angular momentum quantum number of each basis set. The current implementation of ADF supports only s, p, d,*and f* basis functions, so the allowed lqbas values are 0, 1, 2, and 3

alfbas

The exponential decay parameters of the STO functions in the basis set

basnrm

Normalization coefficients for the basis sets

naos

The total number of basis functions, counting all Cartesian polynomials and all copies of the functions on the atoms of the pertaining atom type

nbos

The total number of Cartesian basis functions, not counting the copies of the functions on the different atoms of the atom type: the functions are defined per atom type and are (for nbos) counted only once. The next few variables relate to lists of basis functions that run from 1 to nbos: all the Cartesian polynomials, but counting the function only once per atom type. Essentially, this means counting all functions with distinct characteristics (apart from their geometrical center).

nbptr

Index array of the nbos functions, where the entries are the cumulative numbers of functions (+1) up to, but not including the atom type. The size of the array is (ntyp+1): one plus the number of (non-dummy) atom types.

kx

Powers of x of the nbos Cartesian STO basis functions

ky

Powers of y of the nbos Cartesian STO basis functions

kz

Powers of z of the nbos Cartesian STO basis functions

kr

Powers of r of the nbos Cartesian STO basis functions

alf

Exponential decay factors of the nbos Cartesian STO basis functions

bnorm

Normalization factors for the nbos Cartesian STO basis functions

nprta

Consider a list of all (naos) Cartesian STO basis functions, including copies of the functions on all atoms of the same atom type. Build that list by first taking all true valence functions on all atoms (loop over atom types, inner loops over atoms, inner loop over basis sets of the atom type, inner loop over Cartesian polynomials for the function set), then all auxiliary core-orthogonalization functions (similar loop structure). nprta(i) gives the index in that list of function #*i*, where i corresponds to a similar list of all naos functions in which the core and valence subsets are not separated.

norde

An array that runs over the non-dummy atom types. Each element gives the maximum of the main quantum number for all STO basis and fit functions corresponding to that atom type.

lorde

As norde, but lorde applies to the angular momentum quantum numbers.

Section Core

Information about frozen core orbitals and the Slater-type exponential functions used to describe them.

nrcset

The number of STO function sets to describe the frozen core orbitals in the calculation. The array is sized (0:llqcor,1:ntyp). llqcor is the maximum l-value in core orbitals (3), ntyp is the number of non-dummy atom types.

nrcorb

An array (0:llqcor, 1:ntyp) specifying the number of frozen core orbitals per l-value and per non-dummy atom type.

ncset

The total number of core expansion STO function sets, not counting copies on all atoms, and not counting the Cartesian polynomials (1 value per p-set, et cetera)

ncorpt

Index array: 1 + cumulative number of core expansion sets up to, but not including, the indexed atom type. The array runs from 1 to ntyp+1

nqcor

Main quantum numbers for the core expansion sets

lqcor

Angular momentum quantum numbers for the core expansion sets.

alfcor

Exponential decay factors for the core expansion sets.

cornrm

Normalization factors for the core expansion sets.

ncos

Total number of core expansion functions, counting all copies on different atoms of each atom type, and counting all Cartesian polynomials.

nccpt

Index array: 1 + cumulative number of core orbitals, counting all copies on different atoms and all Cartesian (sub) functions.

ncptr

Similar, but applying to the STO core expansion functions.

ccor

All core expansion coefficients, which express the core orbitals in the core expansion functions. The array stores the expansion coefficient sequence for each core orbital shell (not for each Cartesian sub function) and only one sequence per orbital per atom type (no duplication for the different atoms of the atom type).

npos

An index array. For each atom type: the index where its data are stored on the TAPE12 core data file. npos(k) may be zero if no data for atom type #k are available on TAPE12.

kcos

The total number of core expansion functions, like ncos, but now counting only the truly independent functions. For instance: 5 functions per d-set, while in ncos there are 6 functions per d-set. The s-type combination in the 6-membered d-set is in the calculation projected out and does not represent a degree of freedom.

s

The (kcos,kcos) overlap matrix of the core expansion functions. Note that, since the dimension is (kcos,kcos), the s-type combination has been eliminated, and likewise for the 3 p-type functions in each f-set.

idfcor

Integer that indicates whether or not the core set contains d- and/or f-type functions. 1=yes, 0=no

nd

Total number of d-type core orbital sets (not counting the Cartesian sub functions)

nf

Total number of f-type core orbital sets (not counting the Cartesian sub functions)

ndorb

An array running over the d-type core orbital sets (loop over atom types, loop over atoms, loop over core orbitals with l*=2). It gives for each the index of the orbital (the first of the Cartesian subset) in the overall list of all core orbitals in the molecule (including the spurious *s-type functions in the d-sets, and so on)

nforb

Similar as ndorb, but now for the f-type core orbitals.

cmat

Overlap matrix between core-orbitals (ncos, counting all Cartesian functions including the s-type function in each d-set, et cetera), and the basis functions. In the list of basis functions, all core functions (the auxiliary orthogonalization functions) come before all true valence basis functions, see array NPRTA.

Section Fit

This section stores information about the fit functions, which are used for the Coulomb potential evaluation.

Unrestr.SumFrag

A logical that flags whether or not the fit coefficients have been set and stored for the sum-of-fragments, but adjusted for the unrestricted fragments option (see the keys UnrestrictedFragments, ModifyStartPotential).

coef_SumFrag

Fit coefficients pertaining to the sum-of-fragments charge density.

coef_SCF

SCF fit coefficients.

nfset

Total number of fit function sets (not counting the Cartesian sub functions, not counting the copies of the functions on the atoms of an atom type)

nfitpt

Index array: 1+the total number of fit function sets up to, but not including, the indicated atom type.

nqfit

Main quantum numbers of the fit sets

lqfit

Angular momentum quantum numbers of the fit sets

alffit

Exponential decay factors of the STO fit sets.

fitnmr

Normalization factors for the STO fit sets.

nfos

Total number of Cartesian fit functions, not counting copies on all atoms of an atom type, but including all (for instance, 6 for a d-set) Cartesian sub functions.

nfptr

Index array: 1+ total number of Cartesian (see variable nfos) fit functions, up to but not including the indicated atom type.

nprimf

Total number of Cartesian (‘primitive’) fit functions, counting also the copies on all atoms of each atom type.

nsfos

The total number of fully symmetric (A1 symmetry) fit function combinations that represent the true dimension (variational freedom) of the space of fit functions in the calculation.

na1ptr

Index array, like nfptr, but applying to the nsfos symmetric function combinations.

niskf

This refers to an atom-limited symmetry combination of primitive fit functions, in the code and some documentation indicated as a ‘g’. A ‘g’ is the specific part of a molecule-wide A1 fit function combination (see nsfos) that consists of all the terms that are centered on one particular atom. The number niskf gives the total number of such ‘g’ function combinations. To clarify this, consider an A1 fit function combination in the molecule. Assume, that it consists of a specific linear combination the following functions: a p-x function on atom A, its partner p-y function, and the corresponding p-x and p-y functions on atom B. (Atoms A and B must be symmetry equivalent). In this example we have one A1 function (in the list of nsfos such functions) and two ‘g’’s. Each ‘g’ consists of a p-x and a p-y function combination on a specific atom.

iskf

Compound index array. It runs over the niskf ‘g’ fit function combinations and has 4 entries for each function (1:4,1:niskf). The meaning of the entries is as follows. #1=number of the fit set (not counting the copies of fit functions on different atoms of an atom type, and not counting the Cartesian sub functions) this ‘g’ belongs to. #2=index where the combination coefficients for this ‘g’ start in the arrays cofcom and numcom (see next). #3=number of terms in the expansion of this ‘g’. #4=number of the molecular fit A1 function combination this ‘g’ belongs to.

na1cof

Length of the arrays numcom and cofcom, see next

numcom

Numcom (and cofcom) consists of a sequence of smaller sub arrays. Each sub array gives the expansion of a ‘g’ function in terms of the Cartesian functions in the pertaining fit function set. The elements of numcom specify the particular Cartesian sub functions that participate in the expansion. Its values are therefore limited to lie between 1 and (L+1)(L+2)/2, where L is the maximum l-value occurring in the fit function sets.

cofcom

Compare numcom: cofcom gives the actual expansion coefficients for the expression of a ‘g’ function in primitive Cartesian fit functions.

Section Num Int Params

Numerical integration parameters: the general precision parameter, but also more technical parameters used by the grid-generating modules.

method

Label of the method used to generate the grid. Usually: ‘polyhedra’

accint min

Minimum integration precision parameter. It is the lower bound of the range in which the value of the actual numerical integration precision parameter may vary.

accint max

Maximum value of the precision general parameter

accint

Actual value of the precision parameter. This variable governs by default almost all other integration parameters.

ldim

In fact, this a geometric parameter: the number of dimensions in which the system is periodic. For molecules this is zero.

PointChargeTypes

The number of point charges types used in the calculation. Point charges belong to a different point charge type if, and only if, their strengths are not equal.

accsph

The precision parameter that determines the (radial) integration grid in the atomic spheres

accpyr

The precision parameter that determines the general precision level of the grid in the atomic polyhedra

accout

The precision parameter that determines the general precision level of the grid in the outer region

accpyu

The precision parameter that determines the 1D grid along the first direction in the quadrangles and triangles of the bases of the atomic pyramids

accpyv

The precision parameter that determines the 1D grid along the second direction in the quadrangles and triangles of the bases of the atomic pyramids

accpyw

The precision parameter that determines the 1D radial integration in the atomic pyramids, between the atomic sphere surfaces and the pyramid basis

frange

Estimated maximum range of functions, to determine how far the integration grid has to extend outwards, away from the molecule

rspher

An array with the radii of the atomic sphere (a value per atom type)

rsph0

The smallest sphere radius

rsphx

The largest sphere radius

dishul

The distance between the innermost boundary planes, which separate the atomic pyramids from the outer region, and the surfaces of the outermost atoms

nouter

The number of intervals in which the outward (radial) integration in the outer region is broken up

outrad

The precision parameter that determines the outward radial integration in the outer region

outpar

The precision parameter that determines the 2D integrals in the outer region parallel to the boundary planes

linteg

An array with maximum angular momentum quantum numbers (one value per atom type), to determine the angular integration grid in the atomic spheres

lintgx

Maximum of linteg()

linrot

Angular momentum quantum number to determine the rotational integration parameter around the molecular axis (in linear molecules only)

ntyps

The number of atom types as seen by the numerical integration grid generator. This means in practice: the number of non-dummy atom types plus the number of point charge types.

nnucs

The number of atoms as seen by the numerical integration grid generator. This means in practice: the number of non-dummy atoms plus the number of point charges.

qatm

Nuclear charges for all ntyps atom types

nratst1

The numerical integration grid generator automatically determines the symmetry of the nuclear (nnucs atoms!) frame and then puts the atoms in sets of symmetry equivalent ones. nratst1() is an array (0:ntyps) that contains the cumulative number of atoms in the symmetry sets. nratst1(k) is the total number of atoms in the sets up to and including set #k

xyzatm

Cartesian coordinates of the atoms.

linteg all

Similar to array linteg(), extended to include also the point charge types

npowx

Maximum power of the radial variable r, in the set of test functions that the grid generator uses to tune the grid

alfas

An array that stores the exponential decay factors of all test functions, ordered by atom type and by the power of the radial variable r.

Section Symmetry

Symmetry related data.

nogr

The number of symmetry operators in the point group used in the calculation. NB, for the special cases of infinite symmetries, only the operators corresponding to finite elements are counted. Therefore, ATOM has nogr=1 (only the unit operator); C(LIN) has nogr=1, D(LIN) has nogr=2.

faith

An array that stores all the (3,3) symmetry operator matrices in the real space representation

nsetat

The number of sets of symmetry equivalent atoms under the used symmetry

napp

An array that stores for each atom the number of the symmetry set it belongs to

notyps

An array that stores for each set of symmetry equivalent atoms, the atom type to which the set belongs

noat

Map between the normal list of atoms and the symmetry sets. When you loop over the symmetry sets and, inside, loop over the atoms in each set, you thereby run over the index of noat(). The value points to the position of that atom in the original (not set-ordered) list.

ntr

An array (nogr,nnuc) that stores for the each atom A and each symmetry operator R, the atom onto with A is mapped by R. The row index runs over all symmetry operators, the column index over the atoms.

npeq

The number of symmetry unique pairs of atoms

jjsym

An array that runs over the npeq sets of symmetry equivalent atom pairs. Its value gives for the indicated set the index of a (c.f. the first) atom pair in that set.

jasym

An array that runs over the npeq sets of equivalent atom pairs. Its value gives for the indicated the set the number of pairs in that set.

ja1ok

An array (1:npeq), with values 0 or 1. 1=the pair density can be fitted using A1 fit functions only. 0=all fit functions (on the involved atoms) are to be used. The value 1 may arise because of symmetry properties, or because the distance between the atoms is so large that the inaccuracy from using only A1 fit functions can be neglected.

ntr_setat

A condensed variety of array ntr: the columns are not the atoms, but the nsetat sets of symmetry equivalent atoms. The value is the index of the atom, onto which a representative (c.f. the first) atom of the indicated symmetry set is mapped by the given symmetry operator.

igr

A code that fixes, together with nogr and ngr, the point group symmetry. See the header of routine adf/maisya for a list

ngr

One of the code components that fix the symmetry group. See routine adf/maisya

grouplabel

Schönfliess symbol as used in ADF

nsym

The number of symmetry representation (including subspecies) used in the calculation.

norb

For each of the nsym representations the number of basis function combinations (SFOs) that belong to it.

nfcn

For each of the nsym representations the number of primitive atom centered basis functions that participate in the representation.

ncbs

For each of the nsym representations the number of core orthogonalization functions that participate in the representation.

jsyml

For each of the nsym representations: if it belongs to a one-dimensional irrep, the value is 1, otherwise: for the first subspecies in the irrep the value is the dimension of the irrep, for the other subspecies in the same irrep the value is 0

symlab

For each of the nsym representations the label (string) of the representation

norboc

An array (-2:2,nsym). The column runs over the symmetry representations. The positive row indices (1,2) specify for spin-A and spin-B (the latter only if the calculation is spin-unrestricted), the highest non-empty orbital. The negative indices (-1,-2) specify for spin-A and spin-B (if the unrestricted fragment option is used) the total number of non-empty SFOs. The zero row index specifies the number of non-empty SFOs, before applying any fragment occupation changes.

Section Spin_orbit

(To be completed)

Section Energy

XC energies

16 elements of an array enxc(2,2,4): exchange-correlation energies of various charge densities: first index: 1=exchange term, 2=correlation term second index: 1=lda tern, 2=gga term third index: 1=energy of fragments (summed over fragments), 2=energy of sum-of-fragments density, 3=energy of orthogonalized fragments, 4=SCF.

Pauli TS Correction (LDA)

Correction to the ‘Transition State’ method to compute terms in the bonding energy, in this case the Pauli exchange energy term. The Pauli TS Correction is not separately printed in the standard output file, but included in the Pauli interaction term.

Pauli FitCorrection

The first-order correction to the Pauli exchange interaction term, for the error in the Coulomb energy due to the fit incompleteness. This correction term is not printed in the output file but included in the Pauli interaction term

Elstat Core terms

An obsolete variable, not used in the energy computation

Elstat Fitcorrection

The first-order correction to the electrostatic interaction term (putting the fragments together, without any relaxation of Pauli orthogonalization), for the error in the Coulomb energy due to the fit incompleteness

Orb.Int. FitCorrection

The first-order correction to the electrostatic interaction term in the SCF relaxation energy (Orbital Interactions), for the error in the Coulomb energy due to the fit incompleteness. This term is not printed (anymore) separately, but incorporated in the symmetry-specific interaction terms.

Orb.Int. TSCorrection (LDA)

The difference between the representation-specific orbital interaction terms added, and a straightforward computation of the SCF relaxation energy is the result of the neglect of higher order terms in the Taylor expansion that underlies the ‘Transition State’ method. This difference, therefore, corrects exactly this neglect. It is not printed separately anymore in the output, but incorporated in (distributed over) the representation-specific orbital interaction terms.

Ebond due to Efield

Bond energy term due to any homogeneous electric field

Corr. due to Orthogonalization

For analysis purposes, the concept of ‘orthogonalized fragments’ has been introduced and the bonding energy is split in a part that describes the difference between the sum-of-fragments situation and the orthogonalized-fragments density at the one hand, and the SCF relaxation (from the orthogonalized fragments density) at the other. Both terms contain a first order fit correction term. The result of adding the two parts is not identical to computing the total bonding energy directly and applying the first order correction to that approach. The difference is given by this term, which therefore corrects for the additional second order fit errors caused by using the orthogonalized fragments split-up

SumFragmentsSCF FitCorrection

The ‘true’ first order fit correction for the complete bonding energy, resulting from a direct calculation that takes the sum-of-fragments as starting point and the SCF as final situation, without the intermediate step of orthogonalized fragments.

Pauli Efield

The contribution to the Pauli interaction energy due to any electric field

Orb.Int. Efield

The contribution to the SCF relaxation energy (orbital interactions) due to any electric field

Electrostatic Interaction

The electrostatic interaction energy including any first order fit correction (if computed from the fit density)

Pauli Total

The Pauli exchange (orbital orthogonalization) interaction energy

Steric Electrostatic

INCORRECT. Do not use. The electrostatic interaction energy including any first order fit correction (if computed from the fit density)

Steric Total

The total steric interaction energy, consisting of the electrostatic and the Pauli interactions

Orb.Int. *Irrep*

Irrep stands for one of the irreps of the point group symmetry. The value gives the orbital interaction (SCF relaxation) term for that symmetry representation

Orb.Int. Total

The total orbital interaction energy

SCF Bond Energy

Total bonding energy

elstat

INCORRECT. Do not use. Electrostatic interaction energy. Same as the ‘Electrostatic Interaction’ variable in this section

Bond Energy

Total bonding energy, same as the ‘SCF Bond Energy’ variable

Pauli Kinetic

Kinetic energy term in the Pauli exchange interaction energy

Pauli Coulomb

Coulomb energy term in the Pauli exchange interaction energy

Pauli Kinetic+Coulomb

Sum of the kinetic and Coulomb terms in the Pauli exchange interaction energy

Section Point_Charges

NumberofPointCharges

The total number of point charges used

PointCharges

The array with point charge values: (4,np), where np is the number of point charges and the 4 components are, respectively, the x y z components and the strength.

Section GeoOpt

Optimization data.

Where references are made to the list of atoms, the atoms are assumed to be in internal order. This may be different from the input-list of atoms.

nfree

number of independent optimization variables

idfree

indices (3,nr-of-atoms) for all atomic coordinates referring to the optimization variables (values 1..nfree) and/or LinearTransit parameters (values nfree+k, k being the k-th LT parameter). A zero value means that the coordinate is frozen.

all freedoms

A logical the flags whether or not all fundamental degrees of freedom in the system are allowed to vary. This is not the case when constraints are applied.

Gradients

The most recent values for the derivatives of the energy with respect to the atomic coordinates (cartesian or z-matrix, depending on the type of optimization variables).

Displacements

The most recent step executed for the atomic coordinates (optimization variables)

kmatrix

The connection matrix.

Hessian_CART

The Hessian matrix (second derivatives) as a n*n matrix, in the Cartesian coordinates representation. Note that the reduced storage mode (typically, Fortran upper-triangular) is not applied.

Hessian_ZMAT

Same, but now in the internal coordinates representation

Hessian inverted_CART

The inverted Hessian, in Cartesian coordinates

Hessian inverted_ZMAT

Likewise, in internal coordinates

Note: in most cases only one, or maybe two of the Hessian cases are present on TAPE13. They can be transformed into each other quite easily. The order of atoms is the same as in the input.

xyz old

cartesian coordinates at previous geometry cycle

zmatrix old

idem for internal coordinates

Section TS

Information about the Transition State search

modtrc

Defines the initial search direction. Positive value n: the n-th Hessian eigenvector (default:1). Negative value n: the Hessian eigenvector with the largest (absolute value) component in the n-th optimization variable

itrace

Index of the Hessian eigenvector that is being followed

neghes

The assumed number of negative eigenvalues of the Hessian at the Transition State. Should be 1: searches for higher-order transition states are not supported.

mode to follow

Direction vector in atomic coordinates (Cartesian or Z-matrix, depending on the variable geocrd) that corresponds to the current estimate of the unique Hessian eigenvector with negative eigenvalue

Section LT

Information about the Linear Transit calculation

nr of points

The total number of LT points to be computed.

current point

Index of point that is currently computed

Energies

Energy values in the LT points

Dipole

Dipole moments in the LT points

Parameters

LT parameters, initial and final values (along the path, the values are obtained by even-spaced linear interpolation)

atmcrd

ZMAT if a Z-matrix structure (connection matrix) is available. CART otherwise. Used for printing

geocrd

Type of coordinates to optimize and scan along the path (CART or ZMAT)

xyz

Cartesian coordinates in the LT points (3,natoms,nlt)

zmatrix

Internal coordinates in the LT points

AtomCharge Mulliken

Mulliken atomic charges in the LT points

FragmentCharge Hirshfeld

Hirshfeld fragment charges in the LT points

AtomCharge_initial Voronoi

Voronoi atomic charges corresponding to the sum-of-fragment densities in the LT points

AtomCharge_SCF Voronoi

Voronoi atomic charges corresponding to the SCF densities in the LT points

Section IRC

This section contains general information about the IRC (Intrinsic Reaction Coordinate) calculation. Details of the computed reaction path are in sections IRC_Forward and IRC_Backward.

atmcrd

ZMAT is a Z-matrix structure (connection matrix) is available. CART otherwise

geocrd

CART or ZMAT: the type of coordinates to change, optimize and trace

PointStatus

A string status variable of the current IRC point. Value can be ‘DONE’ (if the point has been computed), ‘EXEC’ if its computation has not yet finished.

nfree

Number of optimization coordinates that can be varied. See section GeoOpt

idfree

(3,natoms) pointers to the optimization variables for each of the atomic coordinates. A zero means: frozen by constraint

xyz

Cartesian coordinates

kmatrix

Connection matrix, if a Z-matrix structure is available

zmatrix

Internal coordinates

Energies

Energy at the Transition State

Dipole

Dipole moment at the Transition State

Gradients

Computed energy gradients at the (assumed) Transition State (should be very small)

AtomCharge Mulliken

Mulliken atomic charges, for the TS geometry

AtomSpinDen Mulliken

Atomic spin densities (Mulliken) at the TS

AtomCharge_initial Voronoi

Voronoi atomic charges at the TS, from the sum-of-fragments density

AtomCharge_SCF Voronoi

Similar, for the SCF density

modtrc

Defines the start direction for the IRC path. A positive value n selects the n-th eigenvector of the Hessian. A value -1 selects the gradient vector (which must then, of course, not be exactly zero). A value -2 specifies that the start direction is specified in the input file.

step

Step length (in mass-weighted metric) between successive points of the IRC path.

stepMin

The minimum value for the step

stepMax

The maximum value for the step

Hessian inverted_ZMAT

Inverse Hessian in internal coordinates.

lfree

The number of independent optimization step directions (for the restricted optimization orthogonal to the IRC path.

vfree

Direction vectors (3,natoms,lfree) for the independent optimization directions

GradientVector

The current gradient vector (during optimization)

Section IRC_Forward

Information about the ‘forward’ IRC path. The choice, which direction down from the Transition State is forward or backward is arbitrary. By definition, in ADF the forward direction is in the positive direction along the first Hessian eigenvector, for which the sign convention is that the largest coefficient is positive.

PathStatus

Status (string) variable for the ‘forward’ half of the IRC path. May be ‘EXEC’, or ‘DONE’, ‘UNKNOWN’, ‘WAIT’, ‘OFF’

PointStatus

Status variable for the current point at the ‘forward’ path. May be ‘DONE’, ‘EXEC’

nset

Size of arrays to store data in the IRC points along the path. Will be increased when too small

pivot

Coordinates of the current pivot point

xyz

Cartesian coordinates of the IRC points (3,natoms,nset)

zmatrix

Internal coordinates of the IRC points (3,natoms,nset)

Path

Lengths measures in mass-weighted metric along the path to the IRC points

Curvature

Local curvature values of the path at the IRC points

Energies

Energy values at the IRC points

Gradients

Energy gradients at the IRC points (one value: the gradient along the path. The orthogonal components are presumably zero)

Dipole

Dipole moments at the IRC points

AtomCharge Mulliken

Mulliken atom charges at the IRC points

FragmentCharge Hishfeld

Hirshfeld fragment charges at the IRC points

AtomCharge_initial Voronoi

Voronoi atomic charges at the IRC points, corresponding to sum-of-fragments densities

AtomCharge_SCF Voronoi

Voronoi atomic charges at the IRC points, corresponding to the SCF densities

CurrentPoint

Integer index of the current IRC point (in the set of nset points)

step

Current step length

Section IRC_Backward

All entries in this section match those in the section IRC_Forward. Of course, here they refer to the other half of the IRC path.

Section Freq

This section contains information about (progress) of the Frequencies calculation and results.

kountf

An integer counter that keeps track of how many geometric displacements have been carried out to scan the potential energy surface around the equilibrium

nraman

Integer to flag whether or not Raman intensities are computed

numdif

Integer to determine the type of numerical differentiation (of gradients, to get the second derivative): 1=one-sided, 2=two-sided displacements.

disrad

Size of displacements of Cartesian coordinates or bond lengths (in case of displacements in internal coordinates)

disang

Size of displacements of angular coordinates

geocrd

Type (string) of coordinates to displace: CART or ZMAT

atmcrd

ZMAT if a z-matrix structure is available. This determines printed output but does not affect the computation. Compare the variable geocrd

nfree

The number of degrees of freedom

idfree

An array (3,natoms) that stores for each atomic coordinates (Cartesian or internal, depending on geocrd) the number of the (1..nfree) variational freedom it corresponds to. If zero, the coordinate is frozen by constraint.

xyz

Cartesian coordinates of the equilibrium geometry

kmatrix

Connection matrix that defines a Z-matrix

zmatrix

The Z-matrix variable values of the equilibrium geometry

all freedoms

Logical: true if all atomic coordinates are allowed to be displaced, not restricted by constraints.

nr of atoms

The total number of atoms, including dummy’s

rigids

Vectors of rigid motion directions, expressed in the atomic coordinates (3,natoms,6)

Dipole previous

The dipole moment of the previous geometry. This is used to compute dipole derivatives by numerical differentiation. The ‘previous’ geometry is the equilibrium geometry in case of one-sided displacements.

Dipole

The dipole moment corresponding to the current geometry

Dipole derivatives

The matrix of dipole derivatives with respect to atomic displacements

Polbty previous

The polarizability tensor (6 elements, triangular representation) of the ‘previous’ geometry. See the remarks about the dipole moment

Polbty

The polarizability tensor corresponding to the current geometry

Polbty derivatives

The matrix of derivatives (w.r.t. the atomic coordinates) of the polarizability tensor

Gradients

The energy gradients corresponding to the current geometry

Gradients previous

The energy gradients of the ‘previous’ geometry. See the remarks about ‘previous’ dipole moment

Force constants

The matrix of force constants (second derivatives), built up during the frequencies calculation.

xyz displaced

The Cartesian coordinates of the current (displaced) geometry

zmatrix displaced

Internal coordinates of the current (displaced) geometry

Dipole derivatives_CART

Dipole derivatives with respect to Cartesian coordinate changes

Hessian_CART

The Hessian matrix in Cartesian coordinates, computed at the end, when the construction of the ‘Force constants’ has been completed.

Frequencies

An array with harmonic frequencies.

Sections Ftyp n

n is an integer. All such sections give general information about fragment type #n, and more specifically about the ADF calculation that produced the corresponding fragment file.

jobid

Job identification of the fragment run

title

Title of that calculation

nsym

Number of symmetry representations (subspecies) used

norb

For each representation the size of the Fock matrix (variational degrees of freedom)

bb

Labels of the subspecies

igr

(Partial) code for the point group symmetry

ngr

(Partial) code for the point group symmetry

grouplabel

Schönfliess symbol of the point group symmetry (of the fragment calculation)

nfcn

An array over the representation: for each subspecies the number of primitive STO basis functions that participate in that subspecies

jsyml

An array (1:nsym). Value 1 means that the corresponding subspecies belongs to a 1D irrep. A value larger than 1 means a correspondingly higher dimensionality of the irrep and indicates that that subspecies is the first in that irrep. A value 0, finally, means that it is not the first subspecies in its irrep.

nfrag

Number of fragments used in that fragment calculation

natom

Number of atoms in the fragment

naos

Number of primitive atomic basis functions

nrat 1

Maps the atoms of this fragment (the ‘1’ signals the first fragment of this type) onto the list of all atoms

rotfrg

Rotation matrix to map the fragment coordinates as they are on the fragment file onto their actual orientation in the molecule

nsot

Total number of MO degrees of freedom, summation over all subspecies

nmis

The number of symmetry representations that could not be spanned by the basis set

mis

Indices of the missing symmetry representations

Sections Ftyp n?

n stands for the n-th fragment type. The ? stands for one of the symmetry representations (of the point group symmetry used in the fragment calculation)

froc

MO occupation numbers for the MOs in this subspecies

eps

Orbital energies When they result from a ZORA calculation, the non-scaled values are stored on file (the scaled values are printed in the standard output file).

eigvf

Fragment MO eigenvectors, expressed in all the primitive atomic orbitals of the fragment.

nsos 1

Total number of MOs in this subspecies: size of variational problem

nbas 1

Number of primitive atomic basis functions that participate in this subspecies

npart 1

Indices that give for each of the nbas functions, the number of the basis function in the list of all basis functions

FO 1

The fragment MOs (nbas*nsos coefficients)

nocc 1

Number of non-empty orbitals

Section Freq Symmetry

Information about the true (possibly input-specified) symmetry of the equilibrium geometry (in a frequencies calculation). The displaced geometries may loose symmetry. Therefore, the program uses NOSYM symmetry, internally, for a frequencies calculation. The ‘true’ symmetry of the system is used for analysis purposes.

nr of operators

Number of symmetry operators used

operators

(3,3) matrices of the operators

nr of symmetries

Number of subspecies

symmetry labels

Names of the subspecies

atom indices

List of indices to map the symmetry-ordered atoms (loop over symmetry sets, loop over atoms in each set) to the ‘normal’ list of all atoms

nr of atomsets

Number of sets of symmetry equivalent atoms

atom mappings

Integer array that provides mapping (back and forth) between the atom list in the input file and the internally used list, which is atom type driven

atomset indices

The number of atoms in each of the sets of symmetry equivalent atoms

nr of displacements_X

(X must be one of the symmetry representations.) The number of symmetry-combined atomic displacements that transform as X

degeneracy_X

Degeneracy of X

displace_X

The actual displacement direction vectors (3,natoms,N). N is the number of symmetry displacements for X.

nr of rigids_X

The number of rigid motion direction vectors that transform as symmetry representation X

displ_InputOrder_X

The displacement vectors, but now expressed in the atomic coordinates using the ordering of atoms in the input file

NormalModes_X

Harmonic frequency normal modes in representation X

Frequencies_X

The harmonic frequency values

IR intensities_X

The infrared intensities

Sections X

X stands here for the label of a subspecies of the point group symmetry, for instance A1. Depending on the point group symmetry, there may be many such sections, each corresponding to one of the subspecies. All such sections have an identical structure.

nmo_A

The number of MOs with spin-A, for which the coefficient vectors are calculated. During the SCF this may be severely reduced, at the end it is usually the complete basis in the pertaining symmetry representation.

nmo_B

Similar for spin b. This variable is not present in a restricted calculation.

SFO

The definition of the SFOs in the representation, consisting of expansion coefficients in terms of the primitive atomic STO basis functions

frocf

The occupation numbers of the SFOs in this representation

npart

A list of indices of the bas functions that are used in this symmetry representation

froc_A

The occupation numbers of the MOs in the representation, for spin-A

froc_B

Similar for spin-B, if a spin-unrestricted calculation is performed

smx

Overlap matrix between core functions and SFOs

frocor

SFO occupation numbers

Orth-Bas

The orthogonalized fragment orbitals in the BAS representation.

Low-Bas

The Lowdin orbitals in the BAS representation: the matrix to transform the MOs from Lowdin representation (orthonormalized SFOs) to the BAS representation

Eigen_Bas_A

mo expansion coefficients in the bas representation for all nmo_A orbitals. The coefficients run over all bas functions indicated by npart

Eigen_Bas_B

Similar for spin-B, if present

eps_A

The orbital energies for the nmo_A orbitals of spin-A When they result from a ZORA relativistic calculations, the non-scaled values are stored on file. (The scaled energies are printed in standard output.

eps_B

Similar for spin-B, if present

Eig-CoreSFO_A

MOs expressed in SFOs, for spin-A MOs

Eig-CoreSFO_B

Similar for spin-B

Sections Atyp n X

Each such section contains the (core- and possibly also valence-) radial density and potential of one particular atom type. X is the atom type label and n is an index running over all atom types in the calculation. The list of all atom types is printed on standard output in the early geometry section.

The radial densities and potentials may be represented as simple tables - a sequence of values for r, the distance to the nucleus, and the corresponding density or potential - or as a piecewise expansion in Chebyshev polynomials over a sequence of intervals (r1,r2).

The core density and potential have been constructed from the Frozen Core orbitals, which are defined in the section Core. If a TAPE12 (corepotentials) file has been attached to the calculation the core data is read off from that TAPE12 and stored also.

rx val

Maximum r-value for which the valence density is non-negligible

nrint val

Number of intervals for piecewise expansion of the valence density in Chebyshev polynomials

rup val

Arrays (1..nrint) of upper bounds of the intervals. The lower bound of the first interval is zero

ncheb val

Array (1..nrint) with the number of expansion coefficients for each interval

ccheb val

Coefficients of the expansion. All coefficients, for all intervals, are stored contiguously in one linear array. The parts pertaining to a particular interval are determined by using the arrays ncheb()

nrad

Number of points used in the direct tabular representation of the atomic densities and potentials

rmin

The first r-value of the table: the radial grid is defined by a first value (rmin), a constant multiplication factor defining rk+1 w.r.t. rk (rfac, see next), and the total nr of points (nrad).

rfac

The multiplication factor of the radial grid

valence den

The valence density, in a table of nrad values.

valence pot

Similar for the Coulomb potential of the density, including a nuclear term Q/r, such that the long-range monopole term in the potential is zero

qval

The number of electrons contained in the valence density

rx core

Maximum r-value for which the core density is non-negligible

nrint core

Number of intervals for piecewise expansion of the core density in Chebyshev polynomials

rup core

Arrays (1..nrint) of upper bounds of the intervals. The lower bound of the first interval is zero

ncheb core

Array (1..nrint) with the number of expansion coefficients for each interval

ccheb core

Coefficients of the expansion. All coefficients, for all intervals, are stored contiguously in one linear array. The parts pertaining to a particular interval are determined by using the arrays ncheb()

qcore

The number of electrons contained in the core density

core den

The core density, in a table of nrad values.

core pot

Similar for the Coulomb potential of the density, including a nuclear term Q/r, such that the long-range monopole term in the potential is zero

Section LqbasxLqfitx_xyznuc

This section will be removed again in the future. Temporarily it serves to transfer data from the calling program to the grid generator.

lqbasx

An array with for each atom type the maximum angular moment quantum number in the basis functions for that type

lqfitx

An array with for each atom type the maximum angular moment quantum number in the fit functions for that type

xyznuc

Cartesian coordinates of the non-dummy atoms

Section GenptData

This section will be removed in the future. It serves, temporarily, to transfer data from the calling program to the numerical integration grid generator. Most of the entries here occur also in other sections but are packed together as replacement for previous common block structure.

numint

Integer code for the type of integration grid. Usual value: 2 (polyhedra method)

iexcit

Integer flag for excitations (response) calculation

lpolar

Integer flag for polarizability (response) calculation

ldim

Number of dimensions of periodicity

mdim

Dimensionality of the molecule, for instance a linear molecule has mdim=1

r0mult

A technical parameter that sets the radius outside which the multipole part of the fit coulomb potential functions is separated (from the exponentially decaying part), for separate treatment in the evaluation of the molecular coulomb potential.

avec

(3,3) matrix with lattice vectors. Only the (ldim,ldim) sub matrix is significant.

bvec

Inverse of avec (apart from a factor of 2 pi): lattice vectors in reciprocal space.

ngimax

Maximum number of geometry optimization iterations

llbloc

Block length determination parameter (maximum)

ipnbl

Number of integration blocks processed by the current process

nbleqv

The number of symmetry equivalent blocks to each symmetry unique block of points. This value is 1 if any equivalent blocks are not constructed and used.

ngmax

The number of integration points, accumulated over all parallel processes

nblock

The number of integration blocks

lblock

The block length

lblx

An upper bound of the block length applied during the computation of the block length

nmax

The number of integration points generated by this process

twopi

Value of the constant 2 \(\pi\)

fourpi

Value of the constant 4 \(\pi\)

Section Multipole matrix elements

Information in a response calculation

dipole elements

The matrix elements of the 3 dipole operator components between occupied and virtual orbitals: outer loop over the operators (in order: y, z, x), loop over virtual MOs, inner loop over occupied MOs

quadrupole elements

Similar as for dipole. Order of operators: \(\sqrt{3}\) *xy \(\sqrt{3}\) *yz z2-(x2+y2)/2 \(\sqrt{3}\) *xz \(\sqrt{3}\) *(x2-y2)/2

octupole elements

Similar as for dipole and quadrupole. Order of operators: \(\sqrt{10}\) *y*(3*x2-y2)/4 \(\sqrt{15}\) *xyz \(\sqrt{6}\) *y*(4*z2-x2-y2)/4 z*(z2-3(x2-y2)/2) \(\sqrt{6}\) *x*(4*z2-x2-y2)/4 \(\sqrt{15}\) *z*(x2-y2)/2 \(\sqrt{10}\) *x*(x2-3y2)/4

hexadecapole elements

Similar as for dipole and quadrupole. Order of operators: \(\sqrt{35}\) *xy*(x2-y2)/2 \(\sqrt{70}\) *z*(3x2y-y3)/4 \(\sqrt{5}\) *xy*(6z2-x2-y2)/2 \(\sqrt{10}\) *(4yz3-3yz*(x2+y2))/4 (8z4-24*z2*(x2+y2)+3(x4+2x2y2+y4))/8 \(\sqrt{10}\) *(4xz3-3xz*(x2+y2))/4 \(\sqrt{5}\) *(x2-y2)*(6z2-x2-y2)/4 \(\sqrt{70}\) *z*(x3-3xy2)/4 \(\sqrt{35}\) (x4-6x2y2+y4)/8

Section Irreducible matrix elements

Information in a response calculation

irreducible dipole elements

The dipole matrix elements between occupied and virtual MOs, as in the section Multipole matrix elements. Here, however, the matrix elements are ordered by symmetry representations and ‘symmetry zeros’ are omitted. The stored arrays, however, have the same size as in the previous section. See the implementation for details about the storage of this data. (Directory $ADFHOME/adf/response/)

irreducible quadrupole elements

Similar as for the dipole elements

irreducible octupole elements

Similar as for the dipole elements

irreducible hexadecapole elements

Similar as for the dipole elements

Section ETS

Technical data used in the ets procedure.

nff

Size of array ncspt (next)

ncspt

Pointer array to find, for each atom type, the first element corresponding to that atom type’s section in the arrays ncsett, alfcst, and cfcset, see below

ncs

Size of the matrices ncsett, alfcst, and cfcset, see below

ncsett

Build a list of products of core orbital expansion functions, taking only the one-center products and looping over the atom types (not the atoms). ncsett stores the powers of the radial variable r for the products (from the main quantum numbers, one subtracted). A product of a 1s and a 2p yields ncsett()=1

alfcst

Similar as ncsett: the sum of the exponential decay factors of the factor functions

cfcset

The density matrix corresponding build from the frozen core orbitals (all atom types, but no copies for the distinct atoms of a type), in the representation of the core orbital expansion functions. Stored are, per atom and per l-value (0..3) the upper-triangles of the corresponding density matrices, one after the other, all in cfcset

nnuc

The number of (non-dummy) nuclei

qcore

For each atom the number of electrons summed over its core orbitals, resulting from analytical integration of the core orbital expansions in STO core expansion functions.

Using Data from TAPE21¶

An ASCII dump of TAPE21 (complete or partial) can be obtained with the kf utility dmpkf, see the utilities document. Alternatively you may build your own small program to extract any required information, using the KF library routines in the ADF package. Consult the KFS documentation for a description of this software.