General: **INTEGRALS

General-purpose directives are given in the **INTEGRALS   section. This mainly includes requests for different atomic integrals, as well as some directives affecting the outcome of such an integral evaluation. Note that although not explicitly stated, all test options do not work with symmetry.

For all atomic integrals, the proper expression for the integral is given, together with the labels written on the file AOPROPER  , for reference in later stages of a DALTON calculation (like for instance in during the evaluation of dynamic response properties, or for non-DALTON programs).

We also note that as long as any single atomic property integral  is requested in this module, the overlap integrals will also be calculated. Note also, that unless the Huckel starting guess is turned off, this overlap matrix will not only be calculated for the requested basis set, but also for ``ghost'' STO-3G basis set appended to the original set in order to do the Huckel starting guess.

.ANGLON  

Contribution to the one-electron contribution of the magnetic moment  using London orbitalsindexLondon orbitals arising from the differentiation on the London phase factors, see Ref. [68].

• Integral:
• Property label: XANGLON , YANGLON , ZANGLON

.ANGMOM  

Angular momentum  around the molecular origin. This can be adjusted by changing the gauge origin through the use of the .GAUGEO   keyword.

• Integral:
• Property label: XANGMOM , YANGMOM , ZANGMOM

.CARMOM  

READ (LUCMD,*) IORCAR

Cartesian multipole integrals  to order IORCAR. Read one more line specifying order. See also the keyword .SPHMOM  .

• Integral:
• Property label: CMiijjkk

where i+j+k =IORDER.

.CM-1  

READ (LUCMD, '(A7)') FIELD1

First derivative of the electric dipole operator  with respect to an external magnetic field  due to differentiation of the London phase factors, see Ref. [54]. Read one more line giving the direction of the electric field (A7) . These include X-FIELD, Y-FIELD, and Z-FIELD.

• Integral:
• Property label: D-CM1 X , D-CM1 Y , D-CM1 Z

where D is the direction of the applied electric field as specified in the input.

.CM-2  

Second derivative electric dipole  operator with respect to an external magnetic field  due to differentiation of the London phase factors, see Ref. [54]. Read one more line giving the direction of the electric field (A7) . These include X-FIELD, Y-FIELD, and Z-FIELD.

• Integral:
• Property label: D-CM2 XX, D-CM2 XY, D-CM2 XZ, D-CM2 YY, D-CM2 YZ, D-CM2 ZZ

where D is the direction of the applied electric field as specified in the input.

.DARWIN  

One-electron Darwin integrals .

• Integral:
• Property label: DARWIN

.DIASUS  

Diamagnetic magnetizability  integrals, as calculated with London atomic orbitals, see Ref. [68].

• Integral:
• Property label: XXdh/dB2, XYdh/dB2, XZdh/dB2, YYdh/dB2, YZdh/dB2, ZZdh/dB2

.DIPLEN  

Dipole length  integrals.

• Integral:
• Property label: XDIPLEN , YDIPLEN , ZDIPLEN

.DIPORG  

READ (LUCMD, *) (DIPORG(I), I = 1, 3)

Specify the dipole origin  to be used in the calculation. Read one more line containing the three Cartesian components (*). Default is (0,0,0).

.DIPVEL  

Dipole velocity  integrals.

• Integral:
• Property label: XDIPVEL , YDIPVEL , ZDIPVEL

.DSO  

Diamagnetic spin-orbitindexdiamagnetic spin-orbit integrals. These are calculated using Gaussian quadrature  as described in Ref. [69]. The number of quadrature point is controled by the keyword .POINTS  .

• Integral:
• Property label: DSO abcd where ab is the symmetry coordinate of a given component for the symmetry-adapted nucleus K, and cd is in a similar fashion the symmetry coordinate for the symmetry-adapted nucleus L.

.DSUSLH  

The contribution to diamagnetic magnetizability  integrals from the differentiation of the London orbital  phase-factors, see Ref. [68].

• Integral:
• Property label: XXDSUSLH, XYDSUSLH, XZDSUSLH, YYDSUSLH, YZDSUSLH, ZZDSUSLH

.DSUSLL  

The contribution to the diamagnetic magnetizability  integrals from mixed differentiation on the Hamiltonian and the London orbital phase factors , see Ref. [68].

• Integral:
• Property label: XXDSUSLL, XYDSUSLL, XZDSUSLL, YYDSUSLL, YZDSUSLL, ZZDSUSLL

.DSUSNL  

The contribution to the diamagnetic magnetizability  integrals using London orbitals  but with contributions from the differentiation of the Hamiltonian only, see Ref. [68].

• Integral:
• Property label: XXDSUSNL, XYDSUSNL, XZDSUSNL, YYDSUSNL, YZDSUSNL, ZZDSUSNL

.DSUTST  

Test of the diamagnetic magnetizability integrals  with London atomic orbitals . Mainly for debugging purposes.

.EFGCAR  

Cartesian electric field gradient integrals .

• Integral:
• Property label: xyEFGabc, where x and y are the cartesian directions, ab the number of the symmetry independent center, and c that centers c'th symmetry-generated atom.

.EFGSPH  

Spherical electric field gradient  integrals. Obtained by transforming the Cartesian electric-field gradient integrals (see .EFGCAR  ) to spherical basis.

.EXPIKR  

READ (LUCMD, *) (EXPKR(I), I = 1, 3)

Cosine and sine   integrals. Read one more line containing the wave numbers in the three Cartesian directions. The center of expansion is always (0,0,0).

.FC  

Fermi-contact  integrals, see Ref. [33].

• Integral:
• Property label: FC NAMab, where NAM is the three first letters in the name of this atom, as given in the MOLECULE.INP file, and ab is the number of the symmetry-adapted nucleus.

.GAUGEO  

READ (LUCMD, *) (GAGORG(I), I = 1, 3)

Specify the gauge origin  to be used in the calculation. Read one more line containing the three Cartesian components (*). Default is (0,0,0).

.HBDO  

Geometric half-differentiated overlap matrix  differentiated once more with respect to magnetic field as given in Eq. (59) in Ref. [48].

.HDO  

Symmetrized, half-differentiated overlap integrals with respect to geometric distortions , see Ref. [70]. Differentiation on the ket-vector.

• Integral:
• Property label: HDO ab , where ab is the number of the symmetry-adapted coordinate being differentiated.

.HDOBR  

Geometric half-differentiated overlap matrix  differentiated once more on the ket-vector with respect to external magnetic field as given in Eq. (60) of Ref. [48].

.HDOBRT  

Test the calculation of the .HDOBR   integral. Mainly for debugging purposes.

.INPTES  

Test the correctness of the **INTEGRALS  -input. Mainly for debugging purposes, but also a good option to check if the MOLECULE  input has been typed in correctly.

.KINENE  

Kinetic energy integrals . Note however, that the kinetic energy integrals used in the wave function optimization is generated in the *ONEINT   section.

• Integral:
• Property label: KINENERG, where ab is the number of the symmetry-adapted nuclear coordinate.

.LONMOM  

Contribution to the London magnetic moment  from the differentiation with respect to magnetic field on the London orbital  phase factors, see Ref. [68].

• Integral:
• Property label: XLONMOM , YLONMOM , ZLONMOM .

.MAGMOM  

One-electron contribution to the magnetic moment  around the nuclei to which the atomic orbitals are attached. This is the London atomic orbital  magnetic moment  as defined in Eq. (35) of Ref. [31].

• Integral:
• Property label: dh/dBX , dh/dBY , dh/dBZ .

.MASSVE  

Mass-velocity  integrals.

• Integral:
• Property label: MASSVELO, where ab is the number of the symmetry-adapted nuclear coordinate.

.MGMO2T  

Test of two-electron integral contribution to magnetic moment.

.MGMOMT  

Test the calculation of the .MAGMOM   integrals.

.MGMTHR  

READ (LUCMD, *) PRTHRS

Set the threshold for which two-electron integrals should be tested with the keyword .MGMO2T  . Default is 10 .

.NELFLD  

Nuclear electric field integrals .

• Integral: where K is the nucleus of interest.
• Property label: NEF ab , where ab is the number of the symmetry-adapted nuclear coordinate.

.NO HAM  

Do not calculate ordinary Hamiltonian integrals.

.NOSUP  

Do not calculate the supermatrix  integral file. This may be required in order to reduce the amount of disc space used in the calculation (to approximately one-third before entering the evaluation of molecular properties). Note however, that this will increase the time used for the evaluation of the wave function significantly in ordinary Hartree-Fock runs. It is default for direct and parallel calculations.

.NOTWO  

Only calculate the one-electron part of the Hamiltonian integrals. It is default for direct and parallel calculations.

.NPOTST  

Test of the nuclear potential integrals calculated with the keyword .NUCPOT  . Mainly for debugging purposes.

.NSLTST  

Test of the integrals calculated with the keyword .NSTLON  . Mainly for debugging purposes.

.NSNLTS  

Test of the integrals calculated with the keyword .NSTNOL  . Mainly for debugging purposes.

.NST  

Calculate the one-electron contribution to the diamagnetic nuclear shielding  tensor integrals using London atomic orbitals , see Ref. [68].

• Integral: where K is the nucleus of interest.
• Property label: NST ab c, where ab is the number of the symmetry-adapted nuclear magnetic moment coordinate, and c refers to the x, y, or z component of the magnetic field.

.NSTCGO  

Calculate the diamagnetic nuclear shielding  ytensor integrals without using London atomic orbitals . Note that the gauge origin is controled by the keyword .GAUGEO  .

• Integral: where K is the nucleus of interest.
• Property label: NSCOab c, where ab is the number of the symmetry-adapted nuclear magnetic moment coordinate, and c refers to the x, y, or z component of the magnetic field. O is the gauge origin.

.NSTLON  

Calculate the contribution to the nuclear shielding tensor  from the differentiation of the London orbital phase-factors , see Ref. [68].

• Integral: where K is the nucleus of interest.
• Property label: NSLOab c, where ab is the number of the symmetry-adapted nuclear magnetic moment coordinate, and c refers to the x, y, or z component of the magnetic field.

.NSTNOL  

Calculate the contribution to the nuclear shielding tensor  from the differentiation of the Hamiltonian alone , see Ref. [68].

• Integral: where K is the nucleus of interest.
• Property label: NSNLab c, where ab is the number of the symmetry-adapted nuclear magnetic moment coordinate, and c refers to the x, y, or z component of the magnetic field.

.NSTTST  

Test the calculation of the one-electron diamagnetic nuclear shielding  tensor using London atomic orbitals .

.NUCMOD  

READ (LUCMD, *) INUC

Choose nuclear model. A 1 corresponds to a point nucleus (which is the default), and 2 corresponds to a Gaussian distribution model.

.NUCPOT  

Calculate the nuclear potential energy. Currently this keyword can only be used in calculations not employing symmetry. 

• Integral: where K is the nucleus of interest.
• Property label: POT.E ab, where ab is the two first letters in the name of this nuclei. Thus note that in order to distinguish between integrals, the fisrt to letters in an atoms name must be unique.

.PHASEO  

READ (LUCMD, *) (ORIGIN(I), I = 1, 3)

Set the origin appearing in the London atomic orbital phase-factors. Read one more line containing the Cartesian components of this origin (*). Default is (0,0,0).

.POINTS  

READ (LUCMD,*) NPQUAD

Read the number of quadrature points  to be used in the evaluation of the diamagnetic spin-orbit  integrals, as requested by the keyword .DSO  . Read one more line containing the number of quadrature points. Default is 40.

.PRINT  

READ (LUCMD,*) IPRDEF

Set default print level during the integral evaluation. Read one more line containing print level. Default is the value of IPRDEF from the general input module for DALTON .

.PROPRI  

Print all one-electron property integrals requested.

.PSO  

Paramagnetic spin-orbit integrals , see Ref. [33].

• Integral: where K is the nucleus of interest.
• Property label: PSO ab , where ab is the number of the symmetry-adapted nuclear magnetic moment coordinate.

.QUADRU  

Quadrupole moment  integrals. For traceless quadrupole moment integrals as defined by Buckingham [23], see the keyword .THETA  .

• Integral:
• Property label: XXQUADRU, XYQUADRU, XZQUADRU, YYQUADRU, YZQUADRU, ZZQUADRU

.QUASUM  

Calculate all atomic integrals as square matrices, irrespective of their inherent Hermiticity or anti-Hermiticity.

.S1MAG  

Calculate the first derivative overlap matrix  with respect to an external magnetic field by differentiation of the London phase factors , see Ref. [68].

• Integral:
• Property label: dS/dBX , dS/dBY , dS/dBZ

.S1MAGL  

Calculate the first magnetic half-differentiated overlap matrix  with respect to an external magnetic field as needed with the natural connection , see Ref. [32]. Differentiated on the bra-vector.

• Integral:
• Property label: d<S/dBX|, d<S/dBY|, d<S/dBZ|

.S1MAGR  

Calculate the first magnetic half-differentiated overlap matrix  with respect to an external magnetic field as needed with the natural connection , see Ref. [32]. Differentiated on the ket-vector.

• Integral:
• Property label: dS>/dBX|, dS>/dBZ|, dS>/dBZ|

.S1MAGT  

Test the integrals calculated with the keyword .S1MAG  . Mainly for debugging purposes.

.S1MLT  

Test the integrals calculated with the keyword .S1MAGL  . Mainly for debugging purposes.

.S1MRT  

Test the integrals calculated with the keyword .S1MAGR  . Mainly for debugging purposes.

.S2MAG  

Calculate the second derivate of the overlap matrix  with respect to an external magnetic field by differentiation of the London phase factors , see Ref. [68].

• Integral:
• Property label: dS/dB2XX, dS/dB2XY, dS/dB2XZ, dS/dB2YY, dS/dB2YZ, dS/dB2ZZ

.S2MAGT  

Test the integrals calculated with the keyword .S2MAG  . Mainly for debugging purposes.

.SD  

Spin-dipole integrals , see Ref. [33].

• Integral:
• Property label: SD ab c, where ab is the number of the first symmetry-adapted coordinate (corresponding to symmetry-adapted nuclear magnetic moments) and c is the x, y, or z component of the magnetic moment with respect to spin coordinates.

.SD+FC  

Calculate the sum of the spin-dipole  and Fermi-contact integrals .

• Integral:
• Property label: SDC ab c, where ab is the number of the first symmetry-adapted coordinate (corresponding to symmetry-adapted nuclear magnetic moments) and c is the x, y, or z component of the magnetic moment with respect to spin coordinates.

.SECMOM  

Second-moment integrals  .

• Integral:
• Property label: XXSECMOM, XYSECMOM, XZSECMOM, YYSECMOM, YZSECMOM, ZZSECMOM

.SELECT  

READ (LUCMD, *) NPATOM
READ (LUCMD, *) (IPATOM(I), I = 1, NPATOM

Select which atoms for which a given atomic integral is to be calculated. This applies mainly to property integrals for which there exist a set of integrals for each nuclei. Read one more line containing the number of atoms selected, and then another line containing the numbers of the atoms selected. Most useful when calculating diamagnetic spin-orbit  integrals, as this is a rather time-consuming calculation. The numbering is of symmetry-independent nuclei.

.SORT I  

  Requests that the two-electron integrals should be sorted for later use in SIRIUS  . See also keywords .PRESORT   in the **DALTON   and *TRANSFORMATION   input sections.

.SOTEST  

Test the calculation of spin-orbit integrals as requested by the keyword .SPIN-O  .

.SPHMOM  

READ (LUCMD,*) IORSPH

Spherical multipole  integrals to order IORSPH. Read one more line specifying order. See also the keyword .CARMOM  .

• Property label: CMiijjkk

where i+j+k =IORDER.

.SPIN-O  

Spatial spin-orbit  integrals, see Ref. [71]. Both the one- and the two-electron integrals are calculated, the latter stored on the file AO2SOINT.

• One-electron Integral: where is the charge of nucleus A and the summation runs over all nuclei of the molecule.
• Property label: X1SPNORB, Y1SPNORB, Z1SPNORB
• Two-electron Integral:
• Property label: X2SPNORB, Y2SPNORB, Z2SPNORB

.SQHDOR  

Square, non-symmetrized half differentiated overlap integrals with respect to geometric distortions , see Ref. [70]. Differentiation on the ket-vector.

• Integral:
• Property label: SQHDORab, where ab is the number of the symmetry-adapted coordinate being differentiated.

.SUPONL  

Only calculate the supermatrix. Requires the presence of the two-electron integral file  .

.SUSCGO  

Diamagnetic magnetizability  integrals calculated without the use of London atomic orbitals. The choice of gauge origin  can be controled by the keyword .GAUGEO  .

• Integral:
• Property label: XXSUSCGO, XYSUSCGO, XZSUSCGO, YYSUSCGO, YZSUSCGO, ZZSUSCGO

.THETA  

Traceless quadrupole moment  integrals as defined by Buckingham [23].

• Integral:
• Property label: XXTHETA , XYTHETA , XZTHETA , YYTHETA , YZTHETA , ZZTHETA