PROAIMV MANUAL Version 94 Revision B THIS PROGRAM DETERMINES PROPERTIES OF ATOMS IN MOLECULES FROM AB-INITIO MOLECULAR WAVEFUNCTIONS. THIS IS DONE BY INTEGRATING CORRESPONDING PROPERTY DENSITIES OVER THE ATOMIC BASINS, THE BOUNDARIES OF WHICH ARE SURFACES HAVING LOCAL ZERO-FLUX OF THE GRADIENT OF THE ELECTRON DENSITY (GRADRHO). THE ATOMIC SURFACES ARE FOUND EITHER BY WALKING ALONG TRAJECTORIES OF GRADRHO FROM THE (3,-1) BOND CRITICAL POINTS OF RHO WHICH ARE IN THE ATOMIC SURFACE ("PROAIM") OR BY FINDING THE POINTS ALONG EACH INTEGRATION RAY WHERE THE ATTRACTOR OF THE GRADRHO TRAJECTORIES INTERSECTING THE RAY CHANGES FROM THE NUCLEUS OF THE INTEGRATED ATOM TO ANOTHER NUCLEUS, OR VICE VERSA. THE LATTER SURFACE ALGORITHM IS CALLED "PROMEGA." For Information on the Original PROAIM program and a description of the output please see: "CALCULATION OF THE AVERAGE PROPERTIES OF ATOMS IN MOLECULES. II"; F.W. Biegler Konig, R.F.W. Bader, T. Tang; Journal of Computational Chemistry; Volume 13 (No. 2); 1982 QUESTIONS AND SUGGESTIONS SHOULD BE DIRECTED TO: Richard Bader McMASTER UNIVERSITY, DEPT. OF CHEMISTRY, HAMILTON, ONTARIO CANADA EMAIL ADDRESS: bader@mcmaster.ca JANUARY-MARCH 1981: PROAIM WRITTEN BY F.W. BIEGLER-KOENIG AND J.A. DUKE MCMASTER UNIV. NOVEMBER 1988-FEBRUARY 1989: PROAIM MODIFIED AND STREAMLINED KEITH E LAIDIG MCMASTER UNIV. INTEGRATION STRUCTURE HEAVILY MODIFIED,VECTORIZED --> "PROAIMV" TODD A. KEITH: McMASTER UNIVERSITY, HAMILTON ONTARIO 1991 PRIMITIVE CUTOFF ALGORITHM INCORPORATED TAK JUNE 1, 1992 SEPARATION OF BETA SPHERE INTEGRATION FROM OUTER INTEGRATION INCORPORATED. TAK JUNE 10 1992 ADDITION OF F FUNCTIONS RICHARD BONE 1993 MAJOR CLEANUP AND ALLOWANCE OF ARBITRARY EVEN-ORDER QUADRATURE FOR THETA, PHI AND RADIAL INTEGRATIONS. ADDITION OF PROMEGA SURFACE ALGORITHM AND CHANGE OF INPUT/OUTPUT FORMAT. (PROMEGA SURFACE ALGORITHM DEVELOPED BY Todd A. Keith and James R. Cheeseman.) TAK 12/93 INCORPORATION OF MAGNETIC PROPERTIES CAPABILITY TAK 3/94 Generalization of Atomic Overlap Matrix (AOM) and AOM derived properties to ROHF, UHF and natural orbital wavefunctions. JRC and TAK 3/94 Fixed bug for F-functions in "gauscheck". TAK 3/94 PROAIMV CAN HANDLE S,P,D(6) and F(10) TYPE GAUSSIAN FUNCTIONS The maximum number of Theta, Phi and Radial points are determined by the parameters MaxTht, MaxPhi and MaxRad. Presently, they are set at 200, which is larger than anyone will probably ever want ... The maximum number of nuclei, molecular orbitals and primitives are determined by the parameters Mcent, MMO and MPRIMS. Presently they are set at 50, 100 and 500 respectively. ********************************************************************** TO LOWER MEMORY REQUIREMENTS, LOWER THE PARAMETER MPTS IN GAUS3, FUNC3, INTARC and TRUDGE3 - BUT THE LOWER MPTS, THE SLOWER THE JOB. DO NOT CHANGE THE PARAMETERS MPTS0 AND MPTSX IN GAUSCHECK UNLESS THE CUTOFF ALGORITHM IS MODIFIED. ********************************************************************** To Run PROAIMV, two files are needed: the AIMPAC wavefunction file (with the extension ".wfn") and the integration input file (with the extension ".inp"). PROAIMV produces an output file with the extension ".int". For example, to run PROAIMV on a carbon atom of c4h4 (with the executable "proaimv"): proaimv c4h4_c1 c4h4 where c4h4_c1 refers to the file "c4h4_c1.inp" and c4h4 refers to the wavefunction file "c4h4.wfn". The input for PROAIMV is dependent upon which Surface Algorithm is to be used. The first surface algorithm (PROAIM) is usually faster but requires more user input and may sometimes seriously fail. The second surface algorithm (PROMEGA) is slower but rarely fails. As an Example, an Input File for a PROAIM Job is given below within the Starred (*) box for a carbon atom of tetrahedrane (C4H4): ************************************************* CARD1 *C4H4_C1 RHF/6-31G** * CARD2 * C 1 * CARD3 *PROAIM * CARD4 * 4 3 1 * CARD5 *9.71207959E-10 1.98184301E-09 1.15576886E+00 * (C1-C2 bcp) CARD6 *1.15576886E+00 -4.37939987E-09 -2.58361695E-09 * (C1-C3 bcp) CARD7 *-8.22575222E-10 1.15576886E+00 5.95489085E-09* (C1-C4 bcp) CARD8 *1.72948569E+00 1.72948569E+00 1.72948568E+00 * (C1-H5 bcp) CARD9 *3.99523990E-01 -3.99523987E-01 3.99523978E-01 * (C1-C2-C3 rcp) CARD10 *-3.99523982E-01 3.99523994E-01 3.99523989E-01* (C1-C2-C4 rcp) CARD11 *3.99523989E-01 3.99523987E-01 -3.99523978E-01 * (C1-C3-C4 rcp) CARD12 *1.14033776E-08 2.52500697E-09 -3.50325120E-10 * (C1-C2-C3-C4 ccp) CARD13 *1 2 8 0 * CARD14 *1 3 8 0 * CARD15 *2 3 8 0 * CARD16 *64 48 96 * CARD17 *OPTIONS * CARD18 *INTEGER 1 * CARD19 *6 1 * CARD20 *REAL 2 * CARD21 *1 9.0 * CARD22 *4 1.0D-8 * ************************************************* Card1 is the job title (up to 80 characters) Card2 is the Atom Name in A4I4 Format Card3 specifies that the PROAIM surface algorithm is to be used Card4 specifies the number of bond critical points (bcp), ring critical points (rcp) and cage critical points lying within the surface of the carbon atom Cards5-8 specify the coordinates of the bond critical points (in au). cards9-11 specify the coordinates of the ring critical points (in au). card12 specifies the coordinates of the cage critical point (in au). Cards13-15 specify how the ring critical points are linked to the bond critical points and the cage critical points. Thus, Card13 says that the first rcp is connected to the first two bcp's and to the cage critical point. THE INFORMATION ABOUT THE CRITICAL POINTS MUST BE DETERMINED BY THE PROGRAM "EXTREME". Card16 Specifies three numerical integration parameters: the number of Phi planes, the number of theta planes and the number of radial points to be used per integration ray within the Beta Sphere. Card17 Specifies whether the user wishes to change the default parameters of the program. If only defualt values are to be used then the OPTIONS card should be absent. Card18 Specifies that one integer parameter is to be specified in the following cards. Card19 specifies that integer parameter 6 is to be set to the value 1 Card20 Specifies that two real parameters are to be specified in the following cards. Card21 Specifies that the real parameter 1 is set to the value 9.0 Card22 Specifies that the real parameter 4 is set to the value 1.0D-8 A description of the parameters and their default values is as follows if PROAIM is specified: INTEGER OPTIONS: (1) = whether pre-job primitive cutoffs are to be used: 0/1 = No/Yes Default is 1. (2) = Number of points per gradrho path in the surface tracing Default is 140 (3) = Number of basic gradrho paths used in the surface tracing Default is 80 (4) = Multiple of the default number of radial points to be used for integration outside the BEta sphere and the default number of theta and phi planes to be used inside the Beta Sphere. Default is 1. (5) = Maximum number of gradrho paths which can be inserted between adjacent basic paths. Default is 6 (6) = Whether to calculate the atomic overlap matrix: 0/1 = No/Yes Default is 0. For correlated wavefunctions, where there are a relatively large number of Molecular orbitals, the computation of the AOM can become dominant in terms of CPU time. (7) = Whether to calculate second-order magnetic properties - namely the atomic contribution to the shielding tensors of the nuclei and the atomic magnetic susceptibility tensor and the atomic "net current tensor". Note that for magnetic properties, the first-order wavefunctions for the Lx, Ly, Lz Px, Py and Pz perturbations are required in addition to the unperturbed wavefunction. Default is no (0). (8) = Type of Gauge Transformations to perform to calculate the Current Distribution Within the atom, and hence the atom's other magnetic properties. 0 = Use IGAIM method - gauge origin coincident with the nucleus of the integrated atom. 1 = use another single gauge origin - the gauge origin should be specified (X,Y,Z) on the following card. 2=Becke-Igaim. Default is 0 (IGAIM). (9) = If this is an unrestricted wfn, the number of the first beta MO. Default = 0. REAL OPTIONS: (1) = Maximum distance from the nucleus of the integrated atom to integrate to. Default is 9.0 au (2) = Value of the first rho isosurface. Default is 0.001 au. (3) = Value of the second rho isosurface. Default is 0.002 au. (4) = Cutoff Value for the primitive cutoff algorithms. Smaller is more accurate but more time-consuming. Default is 1.0D-9. (5) = Maximum Allowable Distance between ends of adjacent gradrho paths. Default is 0.6 au. (6) = Length of Grad Rho Paths in Surface Tracing. Default is 8.0 au. The input file for a PROMEGA job is simpler. An example is given below in the starred (*) box for the same carbon atom: ********************************************** CARD1 *C4H4_C1 RHF/6-31G** * CARD2 * C 1 * CARD3 *PROMEGA * CARD4 *64 48 96 * CARD5 *OPTIONS * CARD6 *INTEGER 1 * CARD7 *3 4 * CARD8 *REAL 2 * CARD9 *6 0.0015 * CARD10 *7 0.03 * ********************************************** Card1 specifies the job title A80 Card2 specifies the atom name A4I4 Card3 specifies that the PROMEGA surface algorithm is to be used Card4 is the number of phi, theta and radial points as in Card 16 above. Card5 specifies whether optional parameters are to be supplied in the following cards. If all default values are to be used, this OPTIONS card should not be specified Card6 Specifies that one integer parameter is to be specified in the following cards. Card7 specifies that integer parameter 3 is to be set to the value 4. Card8 Specifies that two real parameters are to be specified in the following cards. Card9 Specifies that the real parameter 6 is set to the value 0.0015 Card10 Specifies that the real parameter 7 is set to the value 0.03 A description of the parameters and their default values is as follows if PROMEGA is specified: INTEGER OPTIONS: (1) = whether second and third intersections of the integration rays with the atomic surface are searched for 1/0 = No/Yes. Default is 1 (search only for first intersections). (2) = Number of small steps per regular step in tracing the gradrho trajectories. Default is 5 (3) = Order of Adam's Bashforth-Moulton predictor corrector method to be used in calculating the gradrho trajectries. Defualt is 6. (4) = Multiple of the default number of radial points to be used for integration outside the BEta sphere and the default number of Theta and Phi planes to be used inside the Beta Sphere. Default is 1. (6) = Whether to calculate the atomic overlap matrix: 0/1 = No/Yes Default is 0. For correlated wavefunctions, where there are a relatively large number of Molecular orbitals, the computation of the AOM can become dominant in terms of CPU time so this option should be considered for such cases. (7) = Whether to calculate second-order magnetic properties - namely the atomic contribution to the shielding tensors of the nuclei and the atomic magnetic susceptibility tensor and the atomic "net current tensor". Note that for magnetic properties, the first-order wavefunctions for the Lx, Ly, Lz Px, Py and Pz perturbations are required in addition to the unperturbed wavefunction. (8) = Type of Gauge origin to use in order to calculate the Current Distribution Within the atom, and hence the atom's other magnetic properties. 0 = Use IGAIM method - gauge origin coincident with the nucleus of the integrated atom. 1 = use another single gauge origin - the gauge origin should be specified (X,Y,Z) on the following card. 2=Becke- Igaim. Default is 0 (IGAIM). (9) = If this is an unrestricted wfn, the number of the first beta MO. Default = 0. REAL OPTIONS: (1) = Maximum Distance from nucleus of integrated atom to integrate to. Default is 9.0 au (2) = Value of the first rho isosurface. Default is 0.001 au. (3) = Value of the second rho isosurface. Default is 0.002 au. (4) = Value for the primitive cutoff algorithms. Smaller is more accurate but more time-consuming. Default is 1.0D-9. (5) = How far out along the integration rays to search for an intersection. Default is 7.5. (6) = How close to the atomic surface to get in intersections search. Default is 0.001. Smaller is better but more time consuming. (7) = Step Size for tracing the gradrho trajectories. Default is 0.025 au (8) = Initial Step Size along integration rays in search for First intersections. Default is 0.25 au (9) = Initial Step Size along integration rays in search for Second and Third intersections. Default is 0.025 au Atomic Units only are used throughout ...