$RELWFN group (optional) This group is relevant if RELWFN in $CONTRL choses any of the relativistic transformations for elimination of the small components of relativistic wavefunctions, to produce corrected single component wavefunctions. These scalar relativistic corrections may be included during any self- consistent method, and any correlation treatment may be used. Wavefunctions incorporating scalar relativity may also be used by the spin-orbit coupling perturbation program (see RUNTYP=TRANSITN, and NESOC just below). The RELWFN keywords are intended for use in all- electron calculations only. Scalar relativistic effects may also be treated by the use of ECP-type or MCP-type core potentials, in which case see the PP keyword in $CONTRL. One family of ESC methods began with the relativistic elimination of small components (RESC), continued through second and third order Douglas/Kroll (DK), reaching an infinite order two component scheme (IOTC) equivalent to converging the DK series. The pinnacle of this line is the local unitary transformation approximation to full IOTC (LUT-IOTC). RELWFN=LUT-IOTC is the most numerically accurate and fastest running method available, so the use of LUT-IOTC is recommended. Within this ESC progression, only one electron kinetic energy, nuclear attraction, and overlap integrals (and associated one electron gradient terms) are modified. Note that scalar 2e- relativistic corrections exist in nature, as well as the Dirac-Coulomb equation, but are not treated by RESC, DK, IOTC, or LUT-IOTC. One electron effects are larger by far, being about 1,147 Hartree for a gold atom, compared to 27 Hartrees for Au's two electron correction. The Normalized Elimination of Small Components (NESC) treats corrections to two electron integrals by means of a relativistically averaged basis set. This is in addition to the one electron modifications mentioned above. All of the relativistic methods in GAMESS neglect two-electron corrections coming from pVp integrals. Analytic gradients are available for any RELWFN choice, provided the basic quantum chemistry method itself has gradient programming. NESC, RESC, and LUT-IOTC have fully analytical gradients. For DK and IOTC, the relativistic gradient contributions are evaluated numerically by a double difference formula, so that one might think of their gradients as "semi-analytic". Relativistic force constant matrices are evaluated by semi-numerical differencing of relativistic gradients. The accuracy of the LUT-IOTC gradients is similar to non-relativistic runs, and should be suitable for frequency evaluation. For NESC, RESC, any order DK, or IOTC (but not LUT- IOTC), the 1e- part of the Breit-Pauli operator's integrals are corrected only to first order (DK1): this is keyword NESOC=1 below. It has been observed by many people that even the first order correction is small, and thus should be sufficient. Scalar relativity produces great changes in radial sizes of atomic orbitals, so care must be paid to the basis set. Certainly at the bottom of the periodic table, one must use basis sets which have been contracted using some kind of relativistic treatment (literature basis sets often use 2nd order DK when contracting, and these are fine to use with RELWFN=LUT-IOTC. The best choices available, at present, are the Sapporo core/valence type relativistic bases (see SPKrnDZ, n=D,T,Q in $BASIS), available H-Rn. Alternatives include the University of Tokyo's DK3 basis sets for H-Lr obtained at U. of Tokyo which exist in the form of general contractions. The web site http://www.riken.jp/qcl/ publications/dk3bs/periodic_table.html gives the supplemental data from T.Tsuchiya, M.Abe, T.Nakajima, K.Hirao J.Chem.Phys. 115,4463-4472(2001) which may be processed into $DATA input with the helper program dk3.f found in source code distributions of GAMESS. Using uncontracted WTBS basis sets may be reasonable for very small molecules. Finally, one might check the PNNL web site looking for other relativistic basis sets. For NESC, you must provide three basis sets, for the large and small components and an averaged one, which are given in $DATAL, $DATAS, $DATA, respectively. The only possible choice for these basis sets is due to Dyall, and these are available from http://www.emsl.pnl.gov:2080/forms/basisform.html Their names are similar to cc-pVnZ(pt/sf/lc), pt=point or fi=finite nucleus, sf for spin-free and the final field is lc=large component ($DATAL), sc=small component ($DATAS), and wf is a typo for Foldy-Wouthuysen 2e- basis ($DATA). In GAMESS you can only use point nucleus approximation, so do not select any of the 'finite nucleus size' type. The need to input three basis sets means that you cannot use $BASIS input, and you must use COORD=UNIQUE style input in the various $DATA's. The three $DATA input groups must contain identical information except for the primitive expansion coefficients, as the three basis sets must have the same exponents. In case the options below to treat only some atoms relativistically is chosen, all non- relativistic atoms must have identical basis input in all three groups. During geometry optimizations, in rare cases, the number of nearly linearly independent functions in the Resolution of the Identity (RI) used to evaluate the most difficult integrals may change at some new geometry. If so, the job will quit with an error message, and the user must restart it again manually. * * * the next parameter applies only to RELWFN=DK: NORDER gives the order of the DK transformation to be applied to the one-electron potential: = 1 corresponds to the free particle = 2 is the most commonly implemented DK method. It has all relativistic corrections to second order. (default) = 3 represents 3rd order DK transformation. It does not include all 3rd order relativity corrections, in the sense of collecting all terms in the same order of c (speed of light), due to using only a 2nd order form of the Coulomb potential (1/rij). However, DK3 gives the closest approximation to the Dirac-Coulomb equation of all methods here. * * * the next parameter applies to spin-orbit coupling: NESOC requests the Douglas-Kroll 1st order relativistic corrections for the 1e- SOC integrals. It has been observed that the 1st order correction is often sufficient. NESOC is relevant only if OPERAT=HSO1, HSO2P, or HSO2, for RUNTYP=TRANSITN. = 0 no corrections (default for no relativity) This is the only choice possible for LUT-IOTC. = 1 apply DK1 correction to one-electron spin-orbit integrals. This is the default if any of RESC, NESC, DK, or IOTC scalar relativity was chosen). * * * the next few parameters are used by * * * LUT-IOTC, IOTC, DK, and RESC: MODEQR are options for quasi-relativistic calculations. The default is 1. Most runs will select 1, or else 9 if additional accuracy is needed in generating the RI basis due to a large span in Gaussian exponents. These are additive (bitwise) options, meaning you would enter 11 to request options 1+2+8: = 0 use the input contracted atomic basis set for the Resolution of the Identity (RI) used to simplify the pVp relativistic integrals, in order to evaluate them in closed form. The accuracy of the RI will be severely compromised, so this option is not recommended. = 1 use the Gaussian primitives constituting the input contracted atomic basis set to define the RI. This produces a considerable increase in accuracy of the integrals compared to "0". = 2 The uncontracted GTO basis set will be used in spherical harmonic form, which helps eliminate linear dependence cleanly from the RI steps. However, this option is not available for nuclear gradients, so it is not used by default. You might choose to this for extra accuracy, when doing final single point energy runs. ISPHER=1 to choose spherical harmonics for the contracted basis used elsewhere in the run may always be used, and should be selected if "2" is chosen. = 4 avoid redundant exponents when splitting L shells into s and p, when generating the internally uncontracted basis set. This is necessary if you are using s or p primitives with the same exponents as in some L shell. This is unlikely to occur, but if so, the L shell must be entered before the s or p. Option 4 requires option 1. = 8 use 128 bit precision in the RIs. Select this option if your exponent range is larger than 64 bits can handle - it is a little difficult to relate Gaussian exponents to overlap matrix precision, but if the range of exponents reaches ten, one should think about using 128 bit math. This is a concern mainly for 6th row elements, where it may easily be probed by comparing the the energy and gradient for MODEQR=1 to 9. Notes: 1. 128 bit math can be very slow, depending on your CPU and/or compiler's support for it. Only relativistic 1e- integrals use 128 bits. 2. LUT-IOTC's local nature makes "8" much more economical than for the other ESC schemes. 3. If your FORTRAN library does not support the REAL*16 data type (128 bits), the code compiles itself in 64 bit mode, and will halt if you ask for 128 bits. QMTTOL same as in $CONTRL, but used for the preparation of the RI space (see MODEQR suboption "1"). LUT-IOTC's RI applies to atomic domains, separately, whereas RESC, DK, and IOTC use this parameter for the entire molecule's uncontracted basis set, where linear dependence is an even greater concern. Usually values considerably smaller than the QMTTOL of $CONTRL, which applies to the contracted working basis may be used, improving accuracy. The default is 1d-10. QRTOL accuracy parameter for relativistic gradients. RESC or LUT-IOTC: tolerance for equating nearly degenerate eigenvalues of the kinetic energy and overlaps, when evaluating the gradient. Values that are too large (>1e-6) cause numerical errors in the gradient, approximately on the same order as QRTOL. Values that are too small can cause large gradient errors due to divsion by small numbers not screened away by QRTOL. (LUT-IOTC default = smaller of 1d-10 or QMTTOL) (RESC default = smaller of 1d-08 or QMTTOL) DK or IOTC: Coordinate offset in bohr used for the numerical differentiation of the relativistic contributions to the gradient (analogous to VIBSIZ in $HESS). Only totally symmetric coordinate directions are explored (analogous to NUMGRD in $CONTRL). All other gradient terms are still computed analytically, but the effect of this single numerical step is to make DK or IOTC gradients be somewhat less accurate than most analytic gradients. See also NVIB. Default for DK or IOTC: 0.01 Bohr NVIB The number of offsets per coordinate (similar to NVIB in $FORCE). NVIB can be 1 or 2 (or -1 or -2). This parameter applies only to DK or IOTC gradients, as RESC and LUT-IOTC are fully analytic. Positive values correspond to the projected mode, in which translations, rotations, and any modes which are not totally symmetric are projected out. Negative values correspond to using Cartesian coordinates. In most cases projected modes are superior; however they can cause slight distortions away from the true symmetry -IF- you specify lower symmetry than the molecule actually possesses. (default=2) * * * the next parameter applies only to LUT-IOTC: TAU The distance cutoff to consider "local" for the local unitary transformation approximation. The value should include any bonded atom pairs, but is chosen to eliminate most next nearest neighbor atom pairs. Increasing TAU causes LUT-IOTC to converge to the full IOTC result (apart from some technical differences in the RI treatment of integrals). The default is 3.5 Angstroms. * * * the next few parameters apply mainly to NESC: NRATOM the number of different elements to be treated nonrelativistically. For example, in Pb(CH3)2, to treat only lead relativistically, enter NRATOM=2. The elements to be treated nonrelativistically are defined by CHARGE. (default=0) For NESC, this parameter affects the choice of the basis sets, you should use identical large, small, and averaged basis set for such atoms. For DK or RESC, MODEQR=1 won't uncontract to the primitives of such atoms. CHARGE is an array containing nuclear charges of the atoms to be treated nonrelativistically. For example, CHARGE(1)=6.0,1.0, to drop all C/H atoms in Pb(CH3)2. *** for those who wish to live in other universes *** CLIGHT gives the speed of light (atomic units), introduced as a parameter in order to reproduce exactly results published with a slightly different choice. Default: 137.0359895 ========================================================== ==========================================================

generated on 7/7/2017