From ENZO@CHEMNA.DICHI.UNINA.IT Wed Mar 19 05:30:20 1997 Received: from CHEMNA.DICHI.UNINA.IT for ENZO@CHEMNA.DICHI.UNINA.IT by www.ccl.net (8.8.3/950822.1) id EAA09272; Wed, 19 Mar 1997 04:53:12 -0500 (EST) From: Received: from CHEMNA.DICHI.UNINA.IT by CHEMNA.DICHI.UNINA.IT (PMDF V5.0-6 #3559) id <01IGON0XVC3K000AOX@CHEMNA.DICHI.UNINA.IT> for CHEMISTRY@www.ccl.net; Wed, 19 Mar 1997 10:53:45 +0100 (CET) Date: Wed, 19 Mar 1997 10:53:45 +0100 (CET) Subject: ESR anisotropic coupling constants To: CHEMISTRY@www.ccl.net Message-id: <01IGON0XXH9E000AOX@CHEMNA.DICHI.UNINA.IT> X-VMS-To: IN%"CHEMISTRY@www.ccl.net" MIME-version: 1.0 Content-type: TEXT/PLAIN; CHARSET=US-ASCII Content-transfer-encoding: 7BIT I have received several requests about the computation of ESR anisotropic coupling constants by Gaussian94. Since this seems a general question I directly post this message for the whole CCL community. These constants are nothing else than field gradients computed with the spin rather than the total electronic density and not including the nuclear contribution. Furthermore the resulting tensor must be put in the zero-trace form. In gaussian94 it is possible to force these options by setting in the keyword list the following items: PROP IOP(6/17=2,6/26=4) Here follows an input and the relevant part of the output for a STO-3G computation of H2NO ---------------------------------------------------------------------------- #UHF/PROP IOP(6/17=2) IOP(6/26=4) H2NO 0 2 X X 1 1.0 N 2 1.0 1 90.0 H 3 NH 2 90.0 1 THETA H 3 NH 2 90.0 1 -THETA O 3 NO 2 ALPHA 1 180.0 NH=1.0179 NO=1.2778 THETA=58.9235 ALPHA=110.0 ----------------------------------------------------------------------------- Fermi contact analysis (atomic units). 1 1 N .042923 2 H -.005038 3 H -.005038 4 O .098025 ********************************************************************** Electrostatic Properties Using The SCF Density ********************************************************************** Warning! Using spin rather than total density! --- Only the electronic contributions will be computed --- ----------------------------------------------------- Center ---- Electric Field Gradient ---- XX YY ZZ ----------------------------------------------------- 1 Atom .119043 -.295145 -.363285 2 Atom .002506 .031422 .029384 3 Atom .002506 .031422 .029384 4 Atom 2.130337 -1.663300 -1.698867 ----------------------------------------------------- ----------------------------------------------------- Center ---- Electric Field Gradient ---- ( tensor representation ) 3XX-RR 3YY-RR 3ZZ-RR ----------------------------------------------------- 1 Atom .298838 -.115349 -.183489 2 Atom -.018598 .010318 .008280 3 Atom -.018598 .010318 .008280 4 Atom 2.540947 -1.252690 -1.288257 ----------------------------------------------------- these are the principal values of anisotropic coupling constants ------------------------------------------------------------------------------- Since the directions of principal moments are often significant and transforma- tion to more conventional units can be performed once for ever, I have modified the links 601 and 602 of gaussian to obtain the following output for the same input ------------------------------------------------------------------------------- ------------------------------------------------------------------------------ Isotropic Fermi Contact Couplings ------------------------------------------------------------------------------ Atom a.u. MegaHertz Gauss 10(-4) cm-1 1 N(14) .04292 13.86856 4.94865 4.62605 2 H -.00504 -22.51979 -8.03562 -7.51179 3 H -.00504 -22.51979 -8.03562 -7.51179 4 O(17) .09802 -59.42481 -21.20426 -19.82198 ------------------------------------------------------------------------------ ********************************************************************** Electrostatic Properties Using The SCF Density ********************************************************************** Warning! Using spin rather than total density! --- Only the electronic contributions will be computed --- Atomic Center 1 is at -.021142 .543231 .000000 Atomic Center 2 is at .158563 1.036966 .871810 Atomic Center 3 is at .158563 1.036966 -.871810 Atomic Center 4 is at -.021142 -.734569 .000000 ----------------------------------------------------- Center ---- Spin Dipole Couplings ---- 3XX-RR 3YY-RR 3ZZ-RR ----------------------------------------------------- 1 Atom .298838 -.115349 -.183489 2 Atom -.018598 .010318 .008280 3 Atom -.018598 .010318 .008280 4 Atom 2.540947 -1.252690 -1.288257 ----------------------------------------------------- Center ---- Spin Dipole Couplings ---- XY XZ YZ ----------------------------------------------------- 1 Atom -.074772 .000000 .000000 2 Atom .004800 .007098 .035617 3 Atom .004800 -.007098 -.035617 4 Atom -.099769 .000000 .000000 ------------------------------------------------------------------------------ Anisotropic Spin Dipole Couplings in Principal Axis System ------------------------------------------------------------------------------ Atom a.u. MegaHertz Gauss 10(-4) cm-1 Axes Baa -.1835 -7.077 -2.525 -2.361 .0000 .0000 1.0000 1 N(14) Bbb -.1284 -4.953 -1.767 -1.652 .1724 .9850 .0000 Bcc .3119 12.030 4.293 4.013 .9850 -.1724 .0000 1/R**3 -.5394 -20.803 -7.423 -6.939 Baa -.0268 -14.276 -5.094 -4.762 -.2361 -.6571 .7158 2 H Bbb -.0193 -10.278 -3.667 -3.428 .9631 -.2560 .0828 Bcc .0460 24.554 8.762 8.190 .1288 .7090 .6933 1/R**3 .0633 33.780 12.053 11.268 Baa -.0268 -14.276 -5.094 -4.762 .2361 .6571 .7158 3 H Bbb -.0193 -10.278 -3.667 -3.428 .9631 -.2560 -.0828 Bcc .0460 24.554 8.762 8.190 .1288 .7090 -.6933 1/R**3 .0633 33.780 12.053 11.268 Baa -1.2883 93.221 33.264 31.095 .0000 .0000 1.0000 4 O(17) Bbb -1.2553 90.837 32.413 30.300 .0263 .9997 .0000 Bcc 2.5436 -184.059 -65.677 -61.395 .9997 -.0263 .0000 1/R**3 -1.2318 89.138 31.807 29.733 ------------------------------------------------------------------------------ ------------------------------------------------------------------------------- Vincenzo Barone | Professor of Theoretical Chemistry | Dipartimento di Chimica | tel. +39-81-5476503 Universita' Federico II | fax +39-81-5527771 via Mezzocannone 4 | e-mail ENZO@CHEMNA.DICHI.UNINA.IT I-80134 Napoli | Italy | ________________________________________________________________________________ From qibvigap@lg.ehu.es Wed Mar 19 13:30:24 1997 Received: from lgsx01.lg.ehu.es for qibvigap@lg.ehu.es by www.ccl.net (8.8.3/950822.1) id NAA11845; Wed, 19 Mar 1997 13:05:45 -0500 (EST) Received: from lgdx02.lg.ehu.es by lgsx01.lg.ehu.es (4.1/4.7 ) id AA12788; Wed, 19 Mar 97 19:03:56 GMT Received: by lgdx02.lg.ehu.es (5.65/4.7) id AA00949; Wed, 19 Mar 1997 19:12:55 GMT Date: Wed, 19 Mar 1997 19:12:55 +0000 (WET) From: Pablo Vitoria Garcia X-Sender: qibvigap@lgdx02 To: ccl Subject: Slater-type orbitals in GAMESS or Gaussian94 Message-Id: Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Hi, I want to do some calculations in GAMESS with a STO basis. Is it possible to input directly the exponents of the STOs? Thanks a lot Pablo -------------------------------------------------------------------------------- Pablo Vitoria Garcia Departamento de Quimica Inorganica, Facultad de Ciencias Universidad del Pais Vasco (UPV/EHU) Apartado 644, E-48080 Bilbao SPAIN e-mail: qibvigap@lgdx02.lg.ehu.es Phone: +34 4 4647700 Ext. 2450 -------------------------------------------------------------------------------- From serge@org.chem.msu.su Wed Mar 19 15:30:27 1997 Received: from org.chem.msu.su for serge@org.chem.msu.su by www.ccl.net (8.8.3/950822.1) id OAA12414; Wed, 19 Mar 1997 14:36:13 -0500 (EST) Received: from org-qsar7.chem.msu.su (org-qsar7.chem.msu.su [158.250.48.104]) by org.chem.msu.su (8.8.5/8.8.5) with ESMTP id WAA13514 for ; Wed, 19 Mar 1997 22:36:07 +0300 (MSK) Message-Id: <199703191936.WAA13514@org.chem.msu.su> From: "Serge A. Pisarev" To: Subject: Visualization of GAMESS results... Date: Wed, 19 Mar 1997 22:36:17 +0300 X-MSMail-Priority: Normal X-Priority: 3 X-Mailer: Microsoft Internet Mail 4.70.1155 MIME-Version: 1.0 Content-Type: text/plain; charset=KOI8-R Content-Transfer-Encoding: 7bit Dear CCLers! Who could help to find the means or software (free preferable) to visualize the results of GAMESS calculations (structures, orbitals, etc.) from PUNCH file. All hints are welcome. I would summarize the results of the search.. Thanks in advance. Serge. ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Serge A. Pisarev, PhD student | email : serge@org.chem.msu.su Department of Chemistry | Moscow State University | Vorobievy Mts., Zip 116899, | Moscow, Russia | vvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvvv From youngd2@mallard.duc.auburn.edu Wed Mar 19 17:30:27 1997 Received: from mallard.duc.auburn.edu for youngd2@mallard.duc.auburn.edu by www.ccl.net (8.8.3/950822.1) id QAA13065; Wed, 19 Mar 1997 16:48:30 -0500 (EST) Received: from wood.mail.auburn.edu by mallard.duc.auburn.edu (SMI-8.6/SMI-SVR4) id PAA05762; Wed, 19 Mar 1997 15:48:06 -0600 Received: by wood.mail.auburn.edu (SMI-8.6/SMI-SVR4) id PAA28427; Wed, 19 Mar 1997 15:48:05 -0600 Date: Wed, 19 Mar 1997 15:48:05 -0600 From: youngd2@mail.auburn.edu Message-Id: <199703192148.PAA28427@wood.mail.auburn.edu> To: CHEMISTRY@www.ccl.net Subject: Chem Topic: SCF Convergence and Chaos Theory Hello all, I have written the following short essay for my users and am posting it here for your enjoyment and comments. Please let me know if I missed any important points. My compilation of chemical topics can be accessed via the web at URL http://www.auburn.edu/~youngd2/topics/contents.html Dave Young youngd2@mail.auburn.edu --------------------------------------------------------------------------- SCF Convergence and Chaos Theory David Young Division of University Computing 144 Parker Hall Auburn University Auburn, AL 36849 WHAT ARE NONLINEAR SYSTEMS The term "nonlinear" is probably one of the most over used terms in mathematics. In the case of chaos theory, a nonlinear equation is one of the form x = f(x) Computational chemists should recognize this as exactly what a self consistent field (SCF) calculation is. In the SCF method, an initial set of orbitals is used to generate a new set of orbitals and the procedure is repeated until some convergence criteria is met. The branch of mathematics called "chaos theory" which has been created and explored over the last decade is the study of equations and systems of equations of this type. To some extent the mathematicians are tacking new names onto behavior that computational chemists have been seeing for years, but they are also learning more about why these systems behave the way they do. It is hoped that, in time, the work being done by mathematicians will provide the insight necessary to create better SCF convergence methods. The purpose of this document is two fold. First it attempts to make the connections between the field of chaos theory and SCF calculations. Second it gives suggestions on how to fix calculations with convergence problems. WHAT NONLINEAR SYSTEMS DO If one chooses a nonlinear equation, picks a starting value for the nonlinear variable then iterates there are several possible outcomes. 1. After a number of iterations, the value returned by the equation may be the value that was put in on that iteration. This is what chemists desire - a converged solution. 2. The values could be almost repeating but not quite. These are called Lorenz attractor systems in chaos theory. 3. The values produced from one iteration to the next may oscillate between 2 values, 4 values or any other power of 2. (I am not aware of any examples other than powers of 2.) 4. The values produced may be random within some fixed range. Random number generators use this property intentionally, but it is rather annoying when an SCF calculation does so. 5. The values produced may be random and not bounded within any upper or lower limits. Which type of non-linear behavior is seen depends upon several things; the equation being used, the constants in the equation and the initial value of the variables. It stands to reason that the total energy may follow any of these patterns during SCF iterations. We have encountered oscillating and random behavior in the convergence of open shell transition metal compounds but have never tried to determine if the random values were bounded or not. HOW TO CONTROL NONLINEAR BEHAVIOR Changing the constants in a non-linear equation would be roughly equivalent to switching the basis set used for an SCF calculation. Since a particular basis set is often chosen for a desired accuracy and speed, this is not generally the most practical solution to a convergence problem. Plots of behavior vs constant values are the bifurcation diagrams which are found in many explanations of chaos theory. Another way of changing the constants in an SCF calculation is to change the geometry a bit. Often pulling a bond length a bit shorter than expected is effective (say making the length 90% of the expected value). lengthening bond lengths a bit and avoiding eclipsed or gauche conformations are second and third best. Once you have a converged wave function move the geometry back where you want it and use the converged function as the initial guess. Changing the initial value of variables is equivalent to using a different initial guess in an SCF calculation. The best initial guess is usually a converged SCF calculation for a different state of the same molecule or a slightly different geometry of the same molecule. This can be a very effective way to circumvent convergence problems. In the worst case it may be necessary to construct an initial guess by hand in order to ensure that the nodal properties of all of the orbitals are correct for the desired electronic state of the molecule. The construction of the virtual orbitals as well as the occupied orbitals can have a significant effect on convergence. Chaos theorists will try many starting points and color code a plot by which solution is obtained for each starting point, this is called fractal geometry (i.e. the famous Mandelbrot diagram). There are quite a number of ways to effectively change the equation in an SCF calculation. These include switching computation methods, using level shifting and using forced convergence methods. Switching between Hartree-Fock (HF), semiempirical, generalized valence bond (GVB), multi-configuration self consistent field (MCSCF), complete active space self consistent field (CASSCF) and Moller-Plesset calculations (MPn) will change the convergence properties. Configuration interaction (CI) and coupled cluster (CC) calculations usually start with an SCF calculation, thus will not circumvent problems with an SCF. In general higher levels of theory tend to be harder to converge. Ease of convergence as well as calculation speed are why lower level calculations are usually used to generate the initial guess for higher level calculations. Oscillating convergence in an SCF calculation is usually an oscillation between wave functions that are close to different states or a mixing of states. Thus oscillating convergence can often be helped by level shifting, which artificially raises the energies of the virtual orbitals. Level shifting may or may not help in cases of random convergence. Most programs will stop trying to converge a problem after a certain number of iterations. In a few rare cases the wave function will converge if given more than the default number of iterations. Most SCF programs do not actually compute orbitals from the previous iteration orbitals in the way that is described in introductory descriptions of the SCF method. Most programs use a convergence excelleration method which is designed to reduce the number of iterations necessary to converge to a solution. The method of choice is usually Pulay's DIIS method (Direct Inversion of the Iterative Subspace). Some programs also give the user the capability to modify the DIIS method, such as putting in a dampening factor. These modifications can be useful for fixing convergence problems but they usually require a significant amount of experience to know how best to modify the procedure. Turning off the DIIS extrapolation can help a calculation converge, but usually requires more iterations. Some programs contain alternative convergence methods that are designed to force even the most difficult problems to converge. These methods are often called direct covergence or quadratic convergence methods. While these methods almost always work, they often require a very large number of iterations and thus a very large amount of CPU time. WHAT TO TRY FIRST If you have an SCF calculation that failed to converge, which of these tricks should you try first? Here are my suggestions with number one being the first thing I try and etc. 1. Try a different initial guess (using the "guess" keyword in Gaussian). 2. Try level shifting ( "SCF=Vshift" in Gaussian). 3. Try changing the geometry. First slightly shortening a bond length then slightly lengthening a bond length then shifting the conformation a bit. 4. Consider trying a different basis set. 5. Consider doing the calculation at a different level of theory. This isn't always practical, but beyond this point the increased number of iterations may make the computation time as much as using a higher level of theory anyway. 6. Turn off the DIIS extrapolation ( "SCF=NoDIIS" in Gaussian ). You should probably give the calculation more iterations along with this. 7. Give the calculation more SCF iterations ( "SCF(MaxCyc=N)" where N is the number of iterations in Gaussian ). This seldom helps but the next option often uses so many iterations that its worth a try. 8. Use a forced convergence method. (In Gaussian "SCF=QC" is usually the best but on rare occasions "SCF=DM" will be faster). Don't forget to give the calculation an extra thousand iterations or so. The wave function obtained by these methods should be tested to make sure it is a minimum and not just a stable point ( see the "stable" keyword in Gaussian ). 9. See if the software documentation suggests any other ways to change the DIIS method. You may well have to run hundreds of calculations to get enough experience with this to know what works when and how much to change it by. FURTHER INFORMATION The manuals accompanying many software packages contain discussions of how to handle convergence difficulties. There is a very small discussion of handling convergence problems in T. Clark "A Handbook of Computational Chemistry" Wiley-Interscience (1985) A good introduction to chaos theory is J. Gleick "Chaos: Making a New Science" Viking (1987) A more mathematical treatment of chaos theory is S. H. Strogatz "Nonlinear Dynamics and Chaos With Applications to Physics, Biology, Chemistry and Engineering" Addison Wesley (1994) --------------------------------------------------------------------------- From genghis@darkwing.uoregon.edu Wed Mar 19 20:30:28 1997 Received: from darkwing.uoregon.edu for genghis@darkwing.uoregon.edu by www.ccl.net (8.8.3/950822.1) id UAA14027; Wed, 19 Mar 1997 20:30:03 -0500 (EST) Received: from localhost (genghis@localhost) by darkwing.uoregon.edu (8.8.5/8.8.5) with SMTP id RAA00679 for ; Wed, 19 Mar 1997 17:29:54 -0800 (PST) Date: Wed, 19 Mar 1997 17:29:54 -0800 (PST) From: Dale Andrew Braden To: cclpost Subject: ESR simulation software Message-ID: MIME-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII Dear CCL, Does anybody know of any software (for PC, Mac, or SGI) that would allow me to simulate ESR spectra of systems in which both the g and A tensors are anisotropic? Cheers to all, Dale Braden Department of Chemistry University of Oregon Eugene, OR 97403-1253 genghis@darkwing.uoregon.edu