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, none of the test options 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 Hückel starting guess is turned off, this overlap matrix will not only be calculated for the requested basis set, but also for a ``ghost'' ano-4 basis set appended to the original set in order to do the Hückel starting guess.

.1ELPOT

One-electron potential energy integrals.

• Integral: $\sum_K\left<\chi_{\mu}\left\vert\frac{Z_K}{r_{K}}\right\vert\chi_{\nu}\right>$
• Property label: POTENERG

.AD2DAR

READ (LUCMD,*) DARFAC

• Integral: $\frac{\alpha^2}{4}\left<\chi_{\mu}\chi_{\nu}\left\vert\delta\left({\mathbf r}_{12}\right)\right\vert\chi_{\rho}\chi_\sigma\right>$

Add two-electron Darwin integrals to the standard electron-repulsion integrals with a perturbation factor DARFAC.

.ANGLON

Contribution to the one-electron contribution of the magnetic moment using London orbitals arising from the differentiation of London-orbital transformed Hamiltonian, see Ref. [115].

• Integral: $\left<\chi_{\mu}\left\vert{\bf L}_N\right\vert\chi_{\nu}\right>$
• Property labels: 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: $\left<\chi_{\mu}\left\vert{\bf L}_{O}\right\vert\chi_{\nu}\right>$
• Property labels: XANGMOM , YANGMOM , ZANGMOM

.AUXBAS

An auxiliary basis is used. Basis sets must be identified as orbital basis and auxiliary basis in the MOLECULE.INP file (line 5).

.CARMOM

READ (LUCMD,*) IORCAR

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

• Integral: $\left<\chi_{\mu}\left\vert x^{i}y^{j}z^{k}\right\vert\chi_{\nu}\right>$
• Property labels: CMiijjkk

where $ii+jj+kk =$IORDER, and where ii = (i/10)*10+mod(i,10).

.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. [92]. Read one more line giving the direction of the electric field (A7). These include X-FIELD, Y-FIELD, and Z-FIELD.

• Integral: $Q_{MN}\left<\chi_{\mu}\left\vert{\bf r}D\right\vert\chi_{\nu}\right>$
• Property labels: 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

READ (LUCMD, '(A7)') FIELD2

Second derivative electric dipole operator with respect to an external magnetic field due to differentiation of the London phase factors, see Ref. [92]. Read one more line giving the direction of the electric field (A7). These include X-FIELD, Y-FIELD, and Z-FIELD.

• Integral: $Q_{MN}\left<\chi_{\mu}\left\vert{\bf rr}^{T}D\right\vert\chi_{\nu}\right>Q_{MN}$
• Property labels: 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 [116].

• Integral: $\frac{\pi\alpha^{2}}{2}\left<\chi_{\mu}\left\vert\delta\left({\bf r}\right)\right\vert\chi_{\nu}\right>$
• Property label: DARWIN

.DCCR12

Only required for interfaces to other implementations of the R12 approach. Obsolete, do not use.

.DEROVL

Geometrical first derivatives of overlap integrals.

• Integral: $\frac{\partial}{\partial {\mathbf R}_K}\left<\chi_{\mu}\mid\chi_{\nu}\right>$
• Property labels: 1DOVLxyz

where $xyz$ is the symmetry adapted nuclear coordinate.

.DERHAM

Geometrical first derivatives of the one-electron Hamiltonian matrix.

• Integral: $\frac{\partial}{\partial {\mathbf R}_K}\left<\chi_{\mu}\left\vert\sum_K\frac{Z_K}{r_K}-\frac{1}{2}\nabla^2\right\vert\chi_{\nu}\right>$
• Property labels: 1DHAMxyz

where $xyz$ is the symmetry adapted nuclear coordinate.

.DIASUS

Diamagnetic magnetizability integrals, as calculated with London atomic orbitals, see Ref. [115]. It is calculated as the sum of the three contributions DSUSLH, DSUSLL, and DSUSNL.

• Integral: $\frac{1}{4}\left[\left<\chi_{\mu}\left\vert r^{2}_{N}I - {\bf r}_{N} {\bf r}_{N... ...chi_{\mu}\left\vert{\bf r}{\bf r}^{T}h\right\vert\chi_{\nu}\right>Q_{MN}\right]$
• Property label: XXdh/dB2, XYdh/dB2, XZdh/dB2, YYdh/dB2, YZdh/dB2, ZZdh/dB2

.DIPGRA

Calculate dipole gradient integrals, that is, the geometrical first derivatives of the dipole length integrals.

• Integral: $\frac{\partial}{\partial {\mathbf R}_K}\left<\chi_{\mu}\left\vert{\mathbf r}\right\vert\chi_{\nu}\right>$
• Property labels: abcDPG d

where $abc$ is the symmetry adapted nuclear coordinate, and $d$ the direction (x/y/z) of the dipole moment.

.DIPLEN

Dipole length integrals.

• Integral: $\left<\chi_{\mu}\left\vert{\bf r}\right\vert\chi_{\nu}\right>$
• Property labels: 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: $\left<\chi_{\mu}\left\vert{\bf\nabla}\right\vert\chi_{\nu}\right>$
• Property label: XDIPVEL , YDIPVEL , ZDIPVEL

.DNS-KE

Kinetic-energy correction to the diamagnetic contribution to nuclear shielding constants with a common gauge origin, see Ref. [].

• Integral: $\frac{3}{4}\left<\chi_{\mu}\left\vert\left[\nabla^2,\frac{{\bf r}_O^T{\bf r}_K - {\bf r}_O{\bf r}_K^T}{r_{K}^3}\right]_+\right\vert\chi_{\nu}\right>$
• Property label: abcNSKEd, where abc is the number of the symmetry-adapted nuclear magnetic moment coordinate, and d refers to the x, y, or z component of the magnetic field. O is the gauge origin.

.DPTOVL

DPT (Direct Perturbation Theory) integrals: Small-component one-electron overlap integrals.

• Integral: $\left<\chi_{\mu}\left\vert\frac{\partial^2}{\partial {\mathbf r}^2}\right\vert\chi_{\nu}\right>$
• Property labels: dd/dxdx, dd/dxdy, dd/dxdz, dd/dydy, dd/dydz, dd/dzdz

.DPTPOT

DPT (Direct Perturbation Theory) integrals: Small-component one-electron potential energy integrals.

• Integral: $\left<\chi_{\mu}\left\vert\frac{\partial}{\partial {\mathbf r}}\frac{1}{\mathbf{R}_K}\frac{\partial}{\partial {\mathbf r}}\right\vert\chi_{\nu}\right>$
• Property labels: DERXXPVP, DERXY+YX, DERXZ+ZX, DERYY, DERYZ+ZY, DERZZ

.DPTPXP

DPT (Direct Perturbation Theory) integrals: Small-component dipole length integrals for Direct Perturbation Theory.

• Integral: $\frac{1}{4}\left<\nabla\chi_{\mu}\left\vert{\mathbf r}\right\vert\nabla\chi_{\nu}\right>$
• Property labels: PXPDIPOL, PYPDIPOL, PZPDIPOL.

.DSO

Diamagnetic spin-orbit integrals. These are calculated using Gaussian quadrature as described in Ref. [117]. The number of quadrature point is controlled by the keyword .POINTS.

• Integral: $\left<\chi_{\mu}\left\vert\frac{{\bf r}_K^T{\bf r}_LI - {\bf r}_K{\bf r}_L^T}{r_K^3r_L^3}\right\vert\chi_{\nu}\right>$
• Property labels: 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.

.DSO-KE

Kinetic energy correction to the diamagnetic spin-orbit integrals. These are calculated using Gaussian quadrature as described in Ref. [117]. The number of quadrature point is controlled by the keyword .POINTS. Please note that this integral has not been extensively tested, and the use of this integral is at the risk of the user.

• Integral: $\left<\chi_{\mu}\left\vert\left[\nabla^2,\frac{{\bf r}_K^T{\bf r}_LI - {\bf r}_K{\bf r}_L^T}{r_K^3r_L^3}\right]_+\right\vert\chi_{\nu}\right>$
• Property labels: DSOKabcd 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. [115].

• Integral: $\frac{1}{4}Q_{MN}\left<\chi_{\mu}\left\vert{\bf r}{\bf r}^{T}h\right\vert\chi_{\nu}\right>Q_{MN}$
• Property labels: 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. [115].

• Integral: $\frac{1}{4}\overline{Q_{MN}\left<\chi_{\mu}\left\vert{\bf r}{\bf L}_{N}^{T}\right\vert\chi_{\nu}\right>}$
• Property labels: 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. [115].

• Integral: $\frac{1}{4}\left<\chi_{\mu}\left\vert r^{2}_{N}I - {\bf r}_{N} {\bf r}_{N}^{T}\right\vert\chi_{\nu}\right>$
• Property labels: 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: $\frac{1}{3}\left<\chi_{\mu}\left\vert\frac{3{\bf r}_K{\bf r}_K^T - {\bf r}_K^T{\bf r}_KI}{r_K^5}\right\vert\chi_{\nu}\right>$
• Property labels: xyEFGabc, where x and y are the Cartesian directions, abc 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.

.ELGDIA

Diamagnetic one-electron spin-orbit integrals without London orbitals.

• Integral:
• Property labels: D1-SO XX, D1-SO XY, D1-SO XZ, D1-SO YX, D1-SO YY, D1-SO YZ, D1-SO ZX, D1-SO ZY, D1-SO ZZ

.ELGDIL

Diamagnetic one-electron spin-orbit integrals with London orbitals.

• Integral:
• Property labels: D1-SOLXX, D1-SOLXY, D1-SOLXZ, D1-SOLYX, D1-SOLYY, D1-SOLYZ, D1-SOLZX, D1-SOLZY, D1-SOLZZ

.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).

• Integral:
• Property labels: COS KX/K, COS KY/K, COS KZ/K, SIN KX/K, SIN KY/K, SIN KZ/K.

.FC

Fermi-contact integrals, see Ref. [61].

• Integral: $\frac{4\pi g_e}{3}\left<\chi_{\mu}\left\vert\delta\left({\bf r}_K\right)\right\vert\chi_{\nu}\right>$
• Property labels: 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.

.FC-KE

Kinetic energy correction to Fermi-contact integrals, see Ref. [].

• Integral: $\frac{2\pi g_e}{3}\left<\chi_{\mu}\left\vert\left[\nabla^2,\delta\left({\bf r}_K\right)\right]_+\right\vert\chi_{\nu}\right>$
• Property labels: FCKEnacd, where na is the two first letters in the name of this atom, as given in the MOLECULE.INP file, and cd is the number of the symmetry-adapted nucleus.

.FINDPT

READ (LUCMD, *) DPTFAC

A direct relativistic perturbation is added to the Hamiltonian and metric with the perturbation parameter DPTFAC, where the actually applied perturbation is DPTFAC*$\alpha_{fs}^2$.

.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

Symmetric combination of half-differentiated overap matrix with respect to an external magnetic field perturbation when London orbitals are used.

• Integral: $-\frac{1}{4}\left(Q_{MO} + Q_{NO}\right)\left<\chi_{\mu}\left\vert{\mathbf r}\right\vert\chi_{\nu}\right>$
• Property labels: HBDO X , HBDO Y , HBDO Z .

.HDO

Symmetrized, half-differentiated overlap integrals with respect to geometric distortions, see Ref. [118]. Differentiation on the ket-vector.

• Integral: $\left<\frac{\partial \chi_{\mu}}{\partial R_{ab}}\mid\chi_{\nu}\right> - \left<\chi_{\mu}\mid\frac{\partial\chi_{\nu}}{\partial R_{ab}}\right>$
• Property label: HDO abc , where abc 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 an external magnetic field, see Ref. [78].

• Integral: $-\frac{1}{2}Q_{NO}\left<\frac{\partial \chi_{\mu}}{\partial R_K}\left\vert{\mathbf r}\right\vert\chi_{\nu}\right>$
• Property labels: abcHBD d, where abc is the symmetry coordinate of the nuclear coordinate being differentiations, and d is the coordinate of the external magnetic field.

.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: $\frac{1}{2}\left<\chi_{\mu}\left\vert\nabla^{2}\right\vert\chi_{\nu}\right>$
• Property label: KINENERG.

.LONMOM

Contribution to the London magnetic moment from the differentiation with respect to magnetic field on the London orbital phase factors, see Ref. [115].

• Integral: $\frac{1}{4}Q_{MN}\left<\chi_{\mu}\left\vert{\bf r}h\right\vert\chi_{\nu}\right>$
• Property labels: 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. [56]. The integral is calculated as the sum of .LONMOM and .ANGLON.

• Integral: $\left<\chi_{\mu}\left\vert{\bf L}_N + \frac{1}{4}Q_{MN}{\bf r}h\right\vert\chi_{\nu}\right>$
• Property label: dh/dBX , dh/dBY , dh/dBZ .

.MASSVE

Mass-velocity integrals.

• Integral: $\frac{\alpha^2}{8}\left<\chi_{\mu}\left\vert\nabla^{2}\cdot\nabla^2\right\vert\chi_{\nu}\right>$
• Property label: MASSVELO.

.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$^{-10}$.

.MNF-SO

Calculates the atomic mean-field spin-orbit integrals as described in Ref. [103]. As the calculation of these integrals require a proper description of the atomic states, reliable results can only be expected for generally contracted basis sets such as the ANO sets, and in some cases also the correlation-consistent basis sets ((aug-)cc-p(C)VXZ)).

.NELFLD

Nuclear electric field integrals.

• Integral: $\left<\chi_{\mu}\left\vert\frac{{\bf r}_K}{r_{K}^3}\right\vert\chi_{\nu}\right>$ where $K$ is the nucleus of interest.
• Property labels: NEF abc , where abc is the number of the symmetry-adapted nuclear coordinate.

.NO HAM

Do not calculate ordinary one- and two-electron Hamiltonian integrals.

.NO2SO

Do not calculate two-electron contribution to spin-orbit integrals.

.NOPICH

Do not add direct perturbation theory correction to Hamiltonian integral, see keyword  .FINDPT.

.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.

.NOTV12

Obsolete keyword, do not use.

.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. [115]. It is calculated as the sum of NSTLON and NSTNOL.

• Integral: $\frac{1}{2}\left<\chi_{\mu}\left\vert\frac{{\bf r}_N^T{\bf r}_K - {\bf r}_N{\bf... ...{K}^3} + Q_{MN}\frac{{\bf r}_N^T{\bf l}_K}{r_{K}^3}\right\vert\chi_{\nu}\right>$ where $K$ is the nucleus of interest.
• Property label: abcNST d, where abc is the number of the symmetry-adapted nuclear magnetic moment coordinate, and d refers to the x, y, or z component of the magnetic field.

.NSTCGO

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

• Integral: $\frac{1}{2}\left<\chi_{\mu}\left\vert\frac{{\bf r}_O^T{\bf r}_K - {\bf r}_O{\bf r}_K^T}{r_{K}^3}\right\vert\chi_{\nu}\right>$ where $K$ is the nucleus of interest.
• Property label: abcNSCOd, where abc is the number of the symmetry-adapted nuclear magnetic moment coordinate, and d refers to the x, y, or z component of the magnetic field. O is the gauge origin.

.NSTLON

Calculate the contribution to the London orbital nuclear shielding tensor from the differentiation of the London orbital phase-factors, see Ref. [115].

• Integral: $\frac{1}{2}Q_{MN}\left<\chi_{\mu}\left\vert\frac{{\bf r}_N^T{\bf l}_K}{r_{K}^3}\right\vert\chi_{\nu}\right>$ where $K$ is the nucleus of interest.
• Property labels: abcNSLOd, where abc is the number of the symmetry-adapted nuclear magnetic moment coordinate, and d refers to the x, y, or z component of the magnetic field.

.NSTNOL

Calculate the contribution to the nuclear shielding tensor when using London atomic orbitals from the differentiation of the Hamiltonian alone, see Ref. [115].

• Integral: $\frac{1}{2}\left<\chi_{\mu}\left\vert\frac{{\bf r}_N^T{\bf r}_K - {\bf r}_N{\bf r}_K^T}{r_{K}^3}\right\vert\chi_{\nu}\right>$ where $K$ is the nucleus of interest.
• Property label: abcNSNLd, where abc is the number of the symmetry-adapted nuclear magnetic moment coordinate, and d 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: $\left<\chi_{\mu}\left\vert\frac{Z_K}{r_{K}}\right\vert\chi_{\nu}\right>$ where $K$ is the nucleus of interest.
• Property labels: POT.E ab, where ab are the two first letters in the name of this nucleus. Thus note that in order to distinguish between integrals, the first two letters in an atom's name must be unique.

.OCTGRA

Calculate octupole gradient integrals, that is, the geometrical first derivatives of the third moment integrals ( .THIRDM).

• Integral: $\frac{\partial}{\partial {\mathbf R}_K}\left<\chi_{\mu}\left\vert{\mathbf r}^3\right\vert\chi_{\nu}\right>$
• Property labels: abODGcde

where ab is the symmetry adapted nuclear coordinate, and cde the component (x/y/z) of the third moment tensor. Currently, this integral does not work with symmetry.

.OZ-KE

Calculates the kinetic energy correction to the orbital Zeeman operator, see Ref. [].

• Integral: $\left<\chi_{\mu}\left\vert\left[\nabla^2,{\mathbf l}_O\right]_+\right\vert\chi_{\nu}\right>$
• Property labels: XOZKE , YOZKE , ZOZKE .

.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. [61].

• Integral: $\left<\chi_{\mu}\left\vert\frac{{\bf l}_K}{r_{K}^{3}}\right\vert\chi_{\nu}\right>$ where $K$ is the nucleus of interest.
• Property label: PSO abc , where abc is the number of the symmetry-adapted nuclear magnetic moment coordinate.

.PSO-KE

Kinetic energy correction to the paramagnetic spin-orbit integrals, see Ref. [].

• Integral: $\left<\chi_{\mu}\left\vert\left[\nabla^2,\frac{{\bf l}_K}{r_{K}^{3}}\right]_+\right\vert\chi_{\nu}\right>$ where $K$ is the nucleus of interest.
• Property label: PSOKEabc, where abc is the number of the symmetry-adapted nuclear magnetic moment coordinate.

.PSO-OZ

Orbital-Zeeman correction to the paramagnetic spin-orbit integrals, see Ref. [].

• Integral: $\left<\chi_{\mu}\left\vert\left[{\mathbf l}_O,\frac{{\bf l}_K}{r_{K}^{3}}\right]_+\right\vert\chi_{\nu}\right>$ where $K$ is the nucleus of interest.
• Property label: abcPSOZd, where abc is the number of the symmetry-adapted nuclear magnetic moment coordinate, and $d$ is the direction (x/y/z) of the external magnetic field (corresponding to the component of the orbital Zeeman operator).

.PVP

Calculate the $pVp$ integrals that appear in the Douglas-Kroll-Heß transformation [119].

• Integral: $\left<\chi_{\mu}\left\vert\nabla\left(\sum_K\frac{Z_K}{r_iK}\right)\nabla\right\vert\chi_{\nu}\right>$
• Property labels: pVpINTEG.

.PVIOLA

Parity-violating electroweak interaction.

• Integral:
• Property labels: PVIOLA X, PVIOLA Y, PVIOLA Z.

.QDBINT

READ (LUCMD,'(A7)') FIELD3

London orbital corrections arising from the second-moment of charge operator in finite-perturbation calculations involving an external electric field gradient. Possible values for the perturbation (FIELD3) may be XX/XY/XZ/YY/YZ/ZZ-FGRD.

• Integral:
• Property labels: ab-QDB X, ab-QDB Y, ab-QDB Z, where $ab$ is the component of the electric field gradient operator read in the variable FIELD3.

.QDBTST

Test of the .QDBINT integrals, mainly for debugging purposes.

.QUADRU

Quadrupole moment integrals. For traceless quadrupole moment integrals as defined by Buckingham [43], see the keyword .THETA.

• Integral: $\frac{1}{4}\left<\chi_{\mu}\left\vert r^{2}_{O}I_3 - {\bf r}_{O}{\bf r}_{O}^{T} \right\vert\chi_{\nu}\right>$
• Property label: XXQUADRU, XYQUADRU, XZQUADRU, YYQUADRU, YZQUADRU, ZZQUADRU

.QUAGRA

Calculate quadrupole gradient integrals, that is, the geometrical first derivatives of the second moment integrals (i.e. .SECMOM, note: it is NOT the gradient of the .QUADRU integrals).

• Integral: $\frac{\partial}{\partial {\mathbf R}_K}\left<\chi_{\mu}\left\vert{\mathbf r}{\mathbf r}^T\right\vert\chi_{\nu}\right>$
• Property labels: abcQDGde

where abc is the symmetry adapted nuclear coordinate, and de the component (xx/xy/xz/yy/yz/zz) of the second moment tensor. Currently symmetry can not be used with these integrals.

.QUASUM

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

.RANGMO

Calculate the diamagnetic magnetizability integrals using the CTOCD-DZ method, see Ref. [58,59]. The gauge origin is, as default, in the center of mass.

• Integral: $\left<\chi_{\mu}\left\vert{\bf r}_O{\bf L}_{N}^{T}\right\vert\chi_{\nu}\right>$
• Property label: XXRANG, XYRANG, XZRANG, YXRANG, YYRANG, YZRANG, ZXRANG, ZYRANG, ZZRANG

.R12

Perform integral evaluation as required by the R12 method. One-electron integrals for the R12 method (Cartesian multipole integrals up to order 2) are precomputed and stored on the file AOPROPER. Two-electron integrals are computed in direct mode.

.R12EXP

READ (LUCMD,*) GAMMAC

Same as .R12 but with Gaussian-damped linear $r_{12}$ terms of the form $r_{12}\exp{-\gamma r_{12}^2}$. The value of $\gamma$ is read from the input line.

.R12INT

Calculation of two-electron integrals over r12.

.ROTSTR

Rotational strength integrals in the mixed representation [120].

• Integral: $\left<\chi_{\mu}\left\vert\nabla\;{\mathbf r}^T + {\mathbf r}\nabla^T\right\vert\chi_{\nu}\right>$
• Property labels : XXROTSTR, XYROTSTR, XZROTSTR, YYROTSTR, YZROTSTR, ZZROTSTR.

.RPSO

Calculate the diamagnetic nuclear shielding tensor integrals using the CTOCD-DZ method, see Ref. [58,59,60]. The gauge origin is, as default, at the center of mass. Setting the gauge origin somewhere else will give wrong results in calculations using symmetry.

• Integral: $\left<\chi_{\mu}\left\vert\frac{{\bf r}_O^T{\bf l}_K}{r_{K}^{3}}\right\vert\chi_{\nu}\right>$ where $K$ is the nucleus of interest.
• Property label: abcRPSOd, where abc is the number of the symmetry-adapted nuclear magnetic moment coordinate and d refers to the x, y, z component of the magnetic field

.S1MAG

Calculate the first derivative overlap matrix with respect to an external magnetic field by differentiation of the London phase factors, see Ref. [115].

• Integral: $\frac{1}{2}Q_{MN}\left<\chi_{\mu}\left\vert{\bf r}\right\vert\chi_{\nu}\right>$
• Property labels: 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. [57]. Differentiated on the bra-vector.

• Integral: $\frac{1}{2}Q_{MO}\left<\chi_{\mu}\left\vert{\bf r}\right\vert\chi_{\nu}\right>$
• Property label:

.S1MAGR

Calculate the first magnetic half-differentiated overlap matrix with respect to an external magnetic field as needed with the natural connection, see Ref. [57]. Differentiated on the ket-vector.

• Integral: $\frac{1}{2}Q_{ON}\left<\chi_{\mu}\left\vert{\bf r}\right\vert\chi_{\nu}\right>$
• Property labels:

.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 derivative of the overlap matrix with respect to an external magnetic field by differentiation of the London phase factors, see Ref. [115].

• Integral: $\frac{1}{4}Q_{MN}\left<\chi_{\mu}\left\vert{\bf r}{\bf r}^{T}\right\vert\chi_{\nu}\right>Q_{MN}$
• Property labels: 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. [61].

• Integral: $\frac{g_e}{2}\left<\chi_{\mu}\left\vert\frac{3{\bf r}_K{\bf r}_K^T - r_K^2}{r_{K}^5}\right\vert\chi_{\nu}\right>$
• Property label: SD abc d, where abc is the number of the first symmetry-adapted coordinate (corresponding to symmetry-adapted nuclear magnetic moments) and d 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: $\frac{g_e}{2}\left<\chi_{\mu}\left\vert\frac{3{\bf r}_K{\bf r}_K^T - r_K^2}{r_{... ...ft<\chi_{\mu}\left\vert\delta\left({\bf r}_K\right)\right\vert\chi_{\nu}\right>$
• Property label: SDCabc d, where abc is the number of the first symmetry-adapted coordinate (corresponding to symmetry-adapted nuclear magnetic moments) and d is the x, y, or z component of the magnetic moment with respect to spin coordinates.

.SD-KE

Kinetic energy correction to spin-dipole integrals, see Ref. [].

• Integral: $\frac{g_e}{4}\left<\chi_{\mu}\left\vert\left[\nabla^2,\frac{3{\bf r}_K{\bf r}_K^T - r_K^2}{r_{K}^5}\right]_+\right\vert\chi_{\nu}\right>$
• Property label: SDKEab 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: $\left<\chi_{\mu}\left\vert{\bf r}{\bf r}^{T}\right\vert\chi_{\nu}\right>$
• Property labels: 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 nucleus. 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.

.SOFIEL

External magnetic-field dependence of the spin-orbit operator integrals [121].

• Integral: $\frac{1}{2}\sum_KZ_K\left<\chi_{\mu}\left\vert\frac{{\bf r}_O^T{\bf r}_K - {\bf r}_O{\bf r}_K^T}{r_{K}^3}\right\vert\chi_{\nu}\right>$
• Property labels: SOMF XX, SOMF XY, SOMF XZ, SOMF YX, SOMF YY, SOMF YZ, SOMF ZX, SOMF ZY, SOMF ZZ.

.SOMAGM

Nuclear magnetic moment dependence of the spin-orbit operator integrals [122].

• Integral: $\sum_KZ_K\left<\chi_{\mu}\left\vert\frac{{\bf r}_K^T{\bf r}_LI - {\bf r}_K{\bf r}_L^T}{r_K^3r_L^3}\right\vert\chi_{\nu}\right>$
• Property label: abcSOMMd, where abc is the number of the symmetry-adapted nuclear magnetic moment coordinate, and d refers to the x, y, or z component of the spin-orbit operator.

.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, and where ii = (i/10)*10+mod(i,10).

.SPIN-O

Spatial spin-orbit integrals, see Ref. [123]. Both the one- and the two-electron integrals are calculated, the latter is stored on the file AO2SOINT.

• One-electron Integral: $\sum_AZ_A\left<\chi_{\mu}\left\vert\frac{{\bf l}_A}{r_{A}^{3}}\right\vert\chi_{\nu}\right>$ where $Z_A$ is the charge of nucleus $A$ and the summation runs over all nuclei of the molecule.
• Property labels: X1SPNORB, Y1SPNORB, Z1SPNORB
• Two-electron Integral: $\left<\chi_{\mu}\chi_{\nu}\left\vert\frac{{\bf l}_{12}}{r_{12}^{3}}\right\vert\chi_{\rho}\chi_{\sigma}\right>$
• Property labels: X2SPNORB, Y2SPNORB, Z2SPNORB

.SQHDOR

Square, non-symmetrized half-differentiated overlap integrals with respect to geometric distortions, see Ref. [118]. Differentiation on the ket-vector.

• Integral: $\left<\chi_{\mu}\mid\frac{\partial\chi_{\nu}}{\partial R_{ab}}\right>$
• Property label: SQHDRabc, where abc 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 controlled by the keyword .GAUGEO.

• Integral: $\frac{1}{4}\left<\chi_{\mu}\left\vert r^{2}_{O}I - {\bf r}_{O} {\bf r}_{O}^{T}\right\vert\chi_{\nu}\right>$
• Property labels: XXSUSCGO, XYSUSCGO, XZSUSCGO, YYSUSCGO, YZSUSCGO, ZZSUSCGO

.THETA

Traceless quadrupole moment integrals as defined by Buckingham [43].

• Integral: $\frac{1}{2}\left<\chi_{\mu}\left\vert 3{\bf r} {\bf r}^{T} - r^{2}I_3 \right\vert\chi_{\nu}\right>$
• Property labels: XXTHETA , XYTHETA , XZTHETA , YYTHETA , YZTHETA , ZZTHETA

.THIRDM

Third-moment integrals.

• Integral: $\left<\chi_{\mu}\left\vert{\bf r}^3\right\vert\chi_{\nu}\right>$
• Property labels: XXX 3MOM, XXY 3MOM, XXZ 3MOM, XYY 3MOM, XYZ 3MOM, XZZ 3MOM, YYY 3MOM, YYZ 3MOM, YYZ 3MOM, ZZZ 3MOM.

.U12INT

Calculation of two-electron integrals over $\left[T1,r_{12}\right]$.

.U21INT

Calculation of two-electron integrals over $\left[T2,r_{12}\right]$.

.WEINBG

READ (LUCMD,*) BGWEIN
Read in the square of the sin of the Weinberg angle appearing in the definition of parity-violating integrals, see .PVIOLA. The Weinberg angle factor will if this keyword is used be set to [1-4*BGWEIN].

.XDDXR3

Direct perturbation theory paramagnetic spin-orbit like integrals.

• Integral:
• Property labels: ALF abcd, where $a$ is ????.