COSMO module interface of COLUMBUS

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Marian Lamb
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1 COSMO module interface of COLUMBUS The implementation follows the scheme given in the appendix. Include File cosinc.h Maximum dimensions for direct allocation of smaller arrays. A description of the parameters is given by the comments in the file. Files Beside the cosmo specific files a filehandle for the COLUMBUS output (warnings, errors, etc.) icolum has to be passed to the cosmo module. Open statements of cosmo specific files: cosmo input file open(icosin,file= cosmo.inp,form='formatted', err=...) The next three files are used to store matrix elements of the interaction with the outer cavity and the not inverted A matrix. Because we need them only once we store them in a file and read them before performing the outlying charge corrections. At the end of this read procedure all three files can be deleted. open(icosa2,file='a2mat.tmp',form='unformatted', status='unknown',err=...) open(icosa3,file='a3mat.tmp',form='unformatted', status='unknown',err=...) open(icosa,file='amat',form='unformatted', status='unknown',err=...) The next two files are used to store the cavity surface and some derivative information. These files persist, because sude might be used by a gradient program. open(icosco,file='cosurf',status='unknown',err=...) open(icossu,file='sude',status='unknown',err=...) The information of the cosmo calculation is summarized in the cosmo file, which can be read by the COSMOtherm and the gradient program: open(icosout,file=out.cosmo, form='formatted', status='unknown',err=...) For the gradient calculation (case=7) the following files have to be opened: open(icosout,file='out.cosmo', form='formatted', status='unknown',err=...) open(icosin,file='cosmo.inp', form='formatted', status='unknown',err=...) open(icossu,file='sude',status='unknown',err=...) Input description cosmo.inp The lines are free format, but should not exceed 80 columns. The is used to introduce a comment. Blanc lines are not allowed.

2 The input file consists of the radii and the parameter definition. The radii can be defined in two ways: 1) radius all <nuc. charge> <radius> defines a radius (Å) for all atoms with the given nuc. charge e.g. radius all will define the radius 1.3 Å for all hydrogen atoms. 2) radius < of atom> <radius> e.g. radius defines a radius of 2.0 Å for atom number eleven. Because settings which are not needed for the calculation will be neglected, the whole set of common radii can be given as a standard input. The example cosmo.inp file contains all optimized radii. For other elements we use the v. der Waals radii multiplied by Parameters can be defined as follows: <parameter name> = <value> You can find a list in the example cosmo.inp. If no parameters are given the default values are used. For standard calculations only the radii have to be given. Example input file: all radii in Angstroem optimized radii radius all H radius all C radius all O radius all N radius all F radius all Cl radius all Br radius all I radius all S radii R_bondi * 1.17 radius all Si radius all P radius all Se default values for parameter nppa = 1082 number of basis grid points per atom nspa = 92 number of segments per (non H) atom the number of seg. per H will be calculated by the program disex = 10.0 for distances smaller than disex*mean atomic diameter the A-matrix element will be calculated using the basis grid points of the segments. routf = 0.85 factor for outer sphere construction rsolv = 1.3 add. radius for SAS construction (Angstroem) cavity = 1 1 -> closed; 0-> open open: intersection of spheres will not be filled with segments phsran = 0.0 phase offset for coordinate randomization in consts.f ampran = amplitude factor for coordinate randomization in consts.f refraction index for excited state calculation choose a reasonable value for the solvent refraction_index = 1.2 if epsilon is not set here, it will be treated as

3 infinit -> f(eps)=1. For non default settings, give epsilon as follows epsilon = 80.0 if an item is defined twice, the last item is used! common block common /cosmovar/ icosin, icosa2, icosa3, icosa, icosco, icossu, icosout, icolum common /cos/ eps, fepsi, disex, disex2, rsolv, routf, nspa, nsph, nppa, area, refind, fn2, lcavity, srad(maxat), tm(3,3,maxat), nn(3,maxat), volume, phsran, ampran Signature of the cosmo routine cosmo(case, xyz, mtype, natoms, sym, cosurf, nps, npspher, phi, qcos, e, elast, a1mat, a2mat, a3mat, dcos) Dimensions: These are the exact dimensions: xyz(3,natoms), real*8 (first dimension for x,y,z coordinates) mtype(natoms), integer cosurf(3,nps+npspher), real*8 (first dimension for x,y,z coordinates) phi(nps), real*8 qcos(nps), real*8 a1mat(nps*(nps+1)/2), real*8 a2mat(npspher,nps), real*8 a3mat(npspher*(npspher+1)/2), real*8 dcos(3,natoms), real*8 Because nps (number of segments of the cavity) is not known before the cavity construction, we use maxnps for the arrays, which have to be allocated before the cavity construction. cosurf(3,2*maxnps) a1mat(maxnps*(maxnps+1)/2) Parameter description: case: integer, determines the case xyz: array of atomic coordinates mtype: array of atom charges without dummies in the same order than xyz. natoms: integer: number of atoms sym: interger or character specifying symmetry cosurf: COSMO surface (coordinates of segments/charges) containing the coordinates for the "normal" cavity used in case = 2 and the outer cavity used in case = 4.

4 nps, npspher: integer: numbers of segments, needed for the potential calculations for step 3/5 and 4/6. phi: array of potential at the given coordinates. qcos: array of charges e: ectric energy elast: last SCF energy (for final output) dcos: A-matrix contribution of the cart. gradient Variables only included for allocation: a1mat: A matrix, has to be kept during the whole procedure a2mat: Interaction of segments on the cavity with segments on the outer cavity. Only used with case=4/6 a3mat: A matrix for segments on the outer cavity. Only used with case=4/6 Functionality -> cosmo: updated by COLUMBUS <- cosmo: updated by the cosmo routine case = 1 -> cosmo: mtype und natoms <- cosmo: Initialization: The routine will read the input file (icosin). The parameters are kept inside the cosmo routine using SAVE, so COLUMBUS just has to call the cosmo(1,...) routine. case = 2 -> cosmo: xyz, mtype, natoms, a1mat (memory), cosurf, isym <- cosmo: cosurf, nps, npspher As in the first passage the cosmo internals will be saved by SAVE. Additionally some files are written: icosa2: file for A2 matrix (interaction of segments on the cavity with segments on the outer cavity) icosa3: file for A3 matrix (A matrix for segments on the outer cavity) icosa: file for the original, non inverted A matrix icosa2,icosa3, and icosa can be deleted after step case=4 icosco: file containing information about the surface (for debug) icossu: file containing information about surface derivatives (for gradient program) The cosurf array, which contains the coordinates of the cavity segments/charges and the two parameters defining the number of segments are given by cosmo. case = 3 -> cosmo: phi, nps <- cosmo: qcos, e The array of the potentials for the cavity segments has to be

5 given by COLUMBUS (Potential for nps points starting with cosurf(1,1) ). cosmo will return the corresponding screening charges qcos and the ectric energy e. Please note: The charges have to be multiplied by f(ε) (fepsi) before they are used to calculate the solvent modified one-electron integrals. Substract e from the energy calculated with the scaled screening charges to gain elast, the energy of the SCF step. * ( q = f (ε )q Sceening charges outside the module, passed by the interface or written to out.cosmo are always unscaled (q*). Because qcos is also used in case=4, the values in the array should not be changed) case = 4 -> cosmo: xyz, mtype, natoms, cosurf, nps, npspher, qcos, phi (outer cavity), elast, e, a1mat(memory), a2mat (memory), a3mat (memory) <- cosmo: Phi now contains the potential on the outer cavity. ( The potential has to be calculated for npspher points starting at cosurf(1,nps+1)) cosmo performs the outlying charge correction and writes the output file out.cosmo containing the coordinates, energies, charges... Please note: qcos contains the unscaled screening charges q*. case = 5 -> cosmo: phi( ), nps <- cosmo: qcos( ), e case=3 equivalent for excited states. phi( ) is defined as the difference between the ground state potential phi(p0) (from the ground state cosmo file) and the current potential. The module calculates e with respect to the potential difference ( E ( ) ), using the scaling factor f(n 2 ). The refraction index has to be defined in the cosmo.inp file (see example). Analogous to case=3 the screening charges qcos( ) have to be multiplied by f(n 2 ) (fn2). The total charges for the calculation of the solvent-modified one-electron integrals are given by: qcos(p0)*fepsi + qcos( )*fn2 qcos(p0) denotes the corrected (outlying charge correction) screening charges, which can be read from the ground state cosmo file (section $segment_information). Note: As in case=3 The energy has to be reduced by the ectric energy: corr E = ECI E ( P 0 ) E ( ) E CI is the Energy including the screening charges in the one elec. part of the operator. case = 6 -> cosmo: xyz, mtype, natoms, cosurf, nps, npspher, qcos, phi (outer cavity), elast, e, a1mat(memory), a2mat (memory), a3mat (memory) <- cosmo: phi = Φ ( ) on the outer cavity qcos = q ( ) corr elast = E E E ( P 0 ) E ( ) = CI (E CI is the Energy including the ext. pot. in the one elec. part of the operator.)

6 corr e = E ( P 0 ) E ( ) E corr ( P 0 ) + can be read from the out.cosmo file of the ground state calculation (Dielectric energy corr. [a.u.]). case=4 equivalent for excited states. The module calculates the correction for E ( ). Due to the definition of elast and e the out.cosmo files will give the corrected energies for the excited state (the fixed ground state potential inclusive). The charges in the out.cosmo file are corrected (outlying charge correction) qcos( ) values. case=6 should be used in combination with case=5 only. Thus, the cosmo file for the excited sates consists of the total corrected energies E = E E corr CI E corr = E + OC( ) ( P 0 ) E ( ) but the potential and the charges are the corrected q( ) and Φ( ) values. case = 7 -> cosmo: xyz, sym, mtype, qcos(memory), cosurf(memory) (The files that are used by the gradient routine are defined above) <- cosmo: dcos, qcos, cosurf case=7 calculates the gradient contribution arising from the cavity as defined below. qcos and cosurf are filled with data from the out.cosmo file. These data can be used to perform the derivative of the potential. nps and fepsi are also updated with case=7. The program reads the files sude and out.cosmo from the energy calculation. These files contain all information needed, so case=7 can be use as stand alone. An initialization with case=1 is not needed. The full gradient of the additional cosmo energy is given as: * q = f (ε )q For scaled screening charges X E 1 cos = q Aq + q Φ mo 2 f ( ε ) (G1) For unscaled screening charges 1 * * * X Ecos mo = f ( ε) q Aq + q Φ (G2) 2 1 * * case=7 calculates the first term of the sum: q Aq 2 Additional to the formulas mentioned in J. Chem. Soc. Perkin Trans. 2 (1993) a surface derivative term can be included. This term takes the change of the cavity surface into account. Because of the small contribution of the surface derivative term, we neglect it for symmetries higher than C1. The total cosmo gradient contribution (G2) can be calculated as follows: 1 * * 1) get the q Aq part by using the cosmo module with case=7 2 * X 2) calculate q Φ 3) add the two terms and multiply the sum by fepsi (fepsi from common /cos/)

7 Units: All parameters are used in a.u. inside the module. Symmetry: In the case of symmetry, cosurf, e, phi, qcos, nps, are npspher are defined for the irred.. xyz, mtype, natoms, and elast are needed for whole system. case=2 provides the reduced cosurf, nps, and npspher. These values are used to calculate the potential on the remaining surface. In case =3/5 the screening charges qcos and the ectric energy e is calculated for the irred. These values are given to case=4 together with the total energy elast for the whole system. The cosmofile contains information for the whole molecule like in the C1 symmetry case. Like the cosmo.out, the dcos array in case=7 contains the symmetric cart. gradients for all atoms. Because COLUMBUS is the first program using cosmo routines with symmetry we don t have experience using symmetry along with our grid construction scheme. Results calculated using different symmetries are not exactly the same, but should be in a range of the accuracy of the continuum model. One should avoid to calculate small molecules with high symmetries. Especially cosmo energies of charged molecules should be more sensitive to the choice of the symmetry. It is recommended to perform test calculations for the molecules and symmetries of interest. A comparison of the cosmo energies calculated with C1 and higher symmetries (single point HF) shows the influence of the symmetry used. For excited states the same symmetry is used for the ground state and the excited state of interest. Thus the same cavity surface (grid) is used for both calculations. Literature: COSMO Theory 1) A. Klamt, G. Schüürmann, J. Chem. Soc. Perkin Trans. 1993, 1, ) A. Klamt, Encyclopedia of Computational Chemistry, p.604, Wiley Excited States 3) A. Klamt, J. Phys. Chem 1996, 100, Synopsis of the TURBOMOLE Implementation 4) A. Schäfer, A. Klamt, D. Sattel, J. C. W. Lohrenz, F. Eckert, Phys. Chem. Phys. 2000, 2, Appendix List of most important variables Variable a1mat(nps*(nps+1)/2) a1matmax(maxnps*(maxnps+1)/2) ampran ar(2*maxnps) area cosurf(3*2*maxnps) dcos(3*maxat) dirsm(3*nspa) dirsmh(3*nsph) dirtm(3*nppa) dirvec(3*nppa) disex Description array for the lower triangular of the A-matrix temporary array for the A-matrix amplitude factor for coordinate randomization in consts.f area of segment surface area of the cavity COSMO surface (position of segments): cosurf(3 (xyz),2*maxnps (segments)) segments 1 - nps -> surface of cavity segments nps+1 - nps+npspher -> surface of outer sphere (outlying charge corr.) array of cart. gradient (A-matrix cont.) direction vector for atomic basis grid (non H atoms) direction vector for hydrogen atom basis grid direction vectors after atomic transformation direction vectors before atomic transformation for distances smaller than disex*mean atomic

8 diameter the A-matrix element will be calculated using the basis grid points of the segments. disex2: (disex*mean atomic diameter)**2 eps ε fepsi factor f(ε) fepsi=(eps-1.d0)/(eps+0.5d0) fn2 scaling factor for excited sate calc. f(n 2 ) iatsp(2*maxnps) number of atom the segment belongs to lcavity use closed (1) or open (0) cavity maxat maximal number of atoms maxnppa max. number of nppa maxnps maximum number of nps maxnspa maximum number of nspa maxnsph max. number of nsph maxrepl max. number of replicates (symmetry) mtype(maxat) element type of atoms (integer) nar(2*maxnps) number of basic grid points per segment natoms number of atoms nn(3,maxat) the three next neighbors of atom i nps number of segments of the cavity npsd npsd= nps + npspher npspher number of segmnets of the outersphere (outlying charge correction) nspa number of segments per atom for non hydrogen atoms nsph number of segments per hydrogen atom nppa: nppa total number of basis grid points (default: 1082) phi(nps) potential on the segments phsran phase offset for coordinate randomization in consts.f qcos(nps) screening charge on the segments refind refraction index (for excited states) routf factor for outer sphere construction. The radii on the outer sphere are defined as: ri=ri+routf*rsolv. The outer sphere is used for the outlying charge corrections. rsolv add. radius for SAS construction. smtype(maxat) element type of atoms (lower case symbols) srad(maxat) set of radii of all atoms (after initialization the radii include rsolv: ri+rsolv!!!) tm(3,3,maxat) atomic transformation matrix for the basis grid points tm(3,3, atom) see consts.f volume volume of cavity xsp(3*2*maxnps) array for segment centers (to build cosurf)

9 Scheme: COSMO in SCF case=1 Initialization: -read parameter or set defaults case=2. basis grid construction, cavity and A matrix construction COLUMBUS Determine electrostatic potential Phi on surface grid case=3 Calculate COSMO charges qcos = - A**(-1) * Phi Calculate ectric energy: E = 0.5 * fepsi * qcos * Phi COLUMBUS Add the entire electrostatic potential of the screening charges as an external potential to the one-electron part of the Fock matrix. Substact half of the solute continuum interaction energy (e) from the received SCF energy. no conv. yes case=4 Make outlying charge correction and final printout.

INPUT DESCRIPTION FOR SQM version 2.0

INPUT DESCRIPTION FOR SQM version 2.0 INTRODUCTION SQM is an add-on module for the PQS program which scales force constants to produce a Scaled Quantum Mechanical (SQM) Force Field. This can correct for