1% 2% $Id$ 3% 4\label{sec:geom} 5 6The \verb+GEOMETRY+ directive is a compound directive that allows the 7user to define the geometry to be used for a given calculation. The 8directive allows the user to specify the geometry with a relatively 9small amount of input, but there are a large number of optional 10keywords and additional subordinate directives that the user can 11specify, if needed. The directive therefore appears to be rather long 12and complicated when presented in its general form, as follows: 13\begin{verbatim} 14 GEOMETRY [<string name default geometry>] \ 15 [units <string units default angstroms>] \ 16 [(angstrom_to_au || ang2au) \ 17 <real angstrom_to_au default 1.8897265>] \ 18 [print [xyz] || noprint] \ 19 [center || nocenter] \ 20 [bqbq] \ 21 [autosym [real tol default 1d-2]] \ 22 [autoz || noautoz] \ 23 [adjust] \ 24 [(nuc || nucl || nucleus) <string nucmodel>] 25 26 27 [SYMMETRY [group] <string group_name> [print] \ 28 [tol <real tol default 1d-2>]] 29 30 31 32 <string tag> <real x y z> [vx vy vz] [charge <real charge>] \ 33 [mass <real mass>] \ 34 [(nuc || nucl || nucleus) <string nucmodel>] 35 ... ] 36 37 [ZMATRIX || ZMT || ZMAT 38 <string tagn> <list_of_zmatrix_variables> 39 ... 40 41 [VARIABLES 42 <string symbol> <real value> 43 ... ] 44 45 [CONSTANTS 46 <string symbol> <real value> 47 ... ] 48 49 (END || ZEND)] 50 51 [ZCOORD 52 CVR_SCALING <real value> 53 BOND <integer i> <integer j> \ 54 [<real value>] [<string name>] [constant] 55 ANGLE <integer i> <integer j> \ 56 [<real value>] [<string name>] [constant] 57 TORSION <integer i> <integer j> <integer k> <integer l> \ 58 [<real value>] [<string name>] [constant] 59 END] 60 61 [SYSTEM surface <molecule polymer surface crystal default molecule> 62 lat_a <real lat_a> lat_b <real lat_b> lat_c <real lat_c> 63 alpha <real alpha> beta <real beta> gamma <real gamma> 64 END] 65 66 END 67 68 69\end{verbatim} 70 71The three main parts of the \verb+GEOMETRY+ directive 72are: 73 74\begin{itemize} 75\item keywords on the first line of the directive (to specify such optional 76input as the geometry name, input units, and print level for the output) 77\item symmetry information 78\item Cartesian coordinates or Z-matrix input to specify the locations 79of the atoms and centers 80\item lattice parameters (needed only for periodic systems) 81\end{itemize} 82 83The following sections present the input for this compound directive in 84detail, describing the options available and the usages of the various 85keywords in each of the three main parts. 86 87 88\section{Keywords on the {\tt GEOMETRY} directive} 89\label{sec:geomkeys} 90 91This section presents the options that can be specified using the keywords 92and optional input on the main line of the {\tt GEOMETRY} directive. 93As described above, the first line of the directive has the general form, 94\begin{verbatim} 95 GEOMETRY [<string name default geometry>] \ 96 [units <string units default angstroms>] \ 97 [bqbq] \ 98 [print [xyz] || noprint] \ 99 [center || nocenter] \ 100 [autosym [real tol default 1d-2]] \ 101 [autoz || noautoz] \ 102 [adjust] \ 103 [(nuc || nucl || nucleus) <string nucmodel>] 104\end{verbatim} 105 106All of the keywords and input on this line are optional. The following 107list describes all options and their defaults. 108 109\begin{itemize} 110\item \verb+<name>+ -- user-supplied name for the geometry; the 111 default name is \verb+geometry+, and all NWChem modules look for a 112 geometry with this name. However, multiple geometries may 113 be specified by using a different name for each. Subsequently, 114 the user can direct a module to a named geometry by 115 using the \verb+SET+ directive (see 116 the example in Section \ref{sec:set}) to associate the default 117 name of \verb+geometry+ with the alternate name. 118 119% \subsection*{{\tt UNITS}} 120\item \verb+units+ -- keyword specifying that a value will be entered 121 by the user for the string variable \verb+<units>+. The default 122 units for the geometry input are \angstroms\ (Note: atomic units or 123 Bohr are used within the code, regardless of the option specified 124 for the input units. The default conversion factor used in the code 125 to convert from {\angstroms} to Bohr is $1.8897265$ which may be 126 overidden with the \verb+angstrom_to_au+ keyword described below.). The code 127 recognizes the following possible values for the string variable 128 \verb+<units>+: 129\begin{itemize} 130\item \verb+angstroms+ or \verb+an+ --- Angstroms (\AA), the default 131 (converts to A.U. using the \AA to A.U. conversion factor) 132\item \verb+au+ or \verb+atomic+ or \verb+bohr+ --- Atomic units (A.U.) 133\item \verb+nm+ or \verb+nanometers+ --- nanometers (converts to 134 A.U. using a conversion factor computed as $10.0$ times the 135 \AA\ to A.U. conversion factor) 136\item \verb+pm+ or \verb+picometers+ --- picometers (converts to 137 A.U. using a conversion factor computed as $0.01$ times the 138 \AA\ to A.U. conversion factor) 139\end{itemize} 140 141\item \verb+angstrom_to_au+ -- may also be specified as 142 \verb+ang2au+. This enables the user to modify the conversion 143 factors used to convert between \AA\ and A.U.. The default value is 144 $1.8897265$. 145 146\item \verb+bqbq+ -- keyword to specify the treatment of interactions 147 between dummy centers. The default in NWChem is to ignore such 148 interactions when computing energies or energy derivatives. These 149 interactions will be included if the keyword \verb+bqbq+ is 150 specified. 151 152\item \verb+print+ and \verb+noprint+ -- complementary keyword pair to 153 enable or disable printing of the geometry. The default is to print 154 the output associated with the geometry. In addition, the keyword 155 \verb+print+ may be qualified by the additional keyword \verb+xyz+, 156 which specifies that the coordinates should be printed in the XYZ 157 format of molecular graphics program XMol. 158 159\item \verb+center+ and \verb+nocenter+ -- complementary keyword pair 160 to enable or disable translation of the center of nuclear charge to 161 the origin. With the origin at this position, all three components 162 of the nuclear dipole are zero. The default is to move the center 163 of nuclear charge to the origin. 164 165\item \verb+autosym+ -- keyword to specify that the symmetry of the 166 geometric system should be automatically determined. This option is on 167 by default. Only groups up to and including $O_{h}$ are recognized. 168 Occasionally NWChem will be unable to determine the full symmetry 169 of a molecular system, but will find a proper subgroup of the full 170 symmetry. The default tolerance is set to work for most cases, but may 171 need to be decreased to find the full symmetry of a geometry. Note that 172 autosym will be turned off if the \verb+SYMMETRY+ group input is given 173 (See section \ref{sec:symgrp}). 174 175\item \verb+noautoz+ -- by default NWChem (release 3.3 and later) 176 will generate redundant internal coordinates from user input 177 Cartesian coordinates. The internal coordinates will be used in 178 geometry optimizations. The \verb+noautoz+ keyword disables use of 179 internal coordinates. The \verb+autoz+ keyword is provided only for 180 backward compatibility. See Section \ref{sec:zcoord} for a more 181 detailed description of redundant internal coordinates, including 182 how to force the definition of specific internal variables in 183 combination with automatically generated variables. 184 185\item \verb+adjust+ -- This indicates that an existing geometry is 186 to be adjusted. Only new input for the redundant internal 187 coordinates may be provided (Section \ref{sec:zcoord}). It is 188 not possible to define new centers or to modify the point 189 group using this keyword. See Section \ref{sec:zcoord} for 190 an example of its usage. 191 192\item \verb+nucleus+ -- keyword to specify the default model for the nuclear 193 charge distribution. The following values are recognized: 194\begin{itemize} 195\item \verb+point+ or \verb+pt+ --- point nuclear charge distribution. This 196 is the default. 197\item \verb+finite+ or \verb+fi+ --- finite nuclear charge distribution 198 with a Gaussian shape. The RMS radius of the Gaussian is determined from 199 the nuclear mass number $A$ by the expression 200 $r_{\rm RMS} = 0.836*A^{1/3}+0.57$ fm. 201\end{itemize} 202NOTE: If you specify a finite nuclear size, you should ensure that the basis 203set you use is contracted for a finite nuclear size. See the Section 204\ref{sec:basis} for more information. 205 206\end{itemize} 207 208The following examples illustrate some of the various options that the 209user can specify on the first input line of the \verb+GEOMETRY+ 210directive, using the keywords and input options described above. 211 212The following directives all specify the same geometry for $H_2$ (a 213bond length of 0.732556\ \AA): 214\begin{verbatim} 215 geometry geometry units nm 216 h 0 0 0 h 0 0 0 217 h 0 0 0.732556 h 0 0 0.0732556 218 end end 219 220 geometry units pm geometry units atomic 221 h 0 0 0 h 0 0 0 222 h 0 0 73.2556 h 0 0 1.3843305 223 end end 224\end{verbatim} 225 226\section{{\tt SYMMETRY} --- Symmetry Group Input} 227\label{sec:symgrp} 228 229The \verb+SYMMETRY+ directive is used (optionally) within the compound 230\verb+GEOMETRY+ directive to specify the point group for the molecular 231geometry. 232The general form of the directive, as described above within the general 233form of the \verb+GEOMETRY+ directive, is as follows: 234\begin{verbatim} 235 [SYMMETRY [group] <string group_name> [print] \ 236 [tol <real tol default 1d-2>]] 237\end{verbatim} 238The keyword \verb+group+ is optional, and can be omitted without 239affecting how the input for this directive is processed\footnote{For 240 periodic systems, there are additional keywords within this 241 directive (not yet documented), so having a keyword for the group 242 name is useful.}. However, if the \verb+SYMMETRY+ directive is 243used, a group name must be specified by supplying an entry for the 244string variable \verb+<group_name>+. The group name should be 245specified as the standard Sch\"{o}flies symbol. Examples of expected 246input for the variable \verb+group_name+ include such entries as: 247 248\begin{itemize} 249\item \verb+c2v+ -- for molecular symmetry $C_{2{\it v}}$ 250\item \verb+d2h+ -- for molecular symmetry $D_{2h}$ 251\item \verb+Td+ -- for molecular symmetry $T_d$ 252\item \verb+d6h+ -- for molecular symmetry $D_{6h}$ 253\end{itemize} 254 255The \verb+SYMMETRY+ directive is optional. The default is no symmetry 256(i.e., $C_1$ point group). Automatic detection of point 257group symmetry is available through the use of \verb+autosym+ in the 258\verb+GEOMETRY+ directive main line (discussed in Section \ref{sec:geomkeys}). 259Note: if the \verb+SYMMETRY+ directive is present the \verb+autosym+ 260keyword is ignored. 261 262If only symmetry-unique atoms are specified, the others will be 263generated through the action of the point group operators, but the 264user if free to specify all atoms. The user must know the symmetry of 265the molecule being modeled, and be able to specify the coordinates of 266the atoms in a suitable orientation relative to the rotation axes and 267planes of symmetry. Appendix \ref{symexamples} lists a number of 268examples of the 269\verb+GEOMETRY+ directive input for specific molecules having symmetry 270patterns recognized by NWChem. The exact point group symmetry will be 271forced upon the molecule, and atoms within $10^{-3}$ A.U. of a 272symmetry element (e.g., a mirror plane or rotation axis) will be 273forced onto that element. Thus, it is not necessary to specify to a 274high precision those coordinates that are determined solely by 275symmetry. 276 277The keyword \verb+print+ gives information concerning the point group 278generation, including the group generators, a character table, the 279mapping of centers, and the group operations. 280 281The keyword \verb+tol+ relates to the accuracy with which the symmetry-unique 282atoms should be specified. When the atoms are generated, those that are 283within the tolerance, \verb+tol+, are considered the same. 284 285\section{Cartesian coordinate input} 286\label{sec:cart} 287 288The default in NWChem is to specify the geometry information entirely 289in Cartesian coordinates, and examples of this format have 290appeared above (e.g, Section \ref{sec:realsample}). Each center 291(usually an atom) is identified on a line of the following form: 292\begin{verbatim} 293 294 <string tag> <real x y z> [vx vy vz] \ 295 [charge <real charge>] [mass <real mass>] \ 296 [(nuc || nucl || nucleus) <string nucmodel>] 297 298\end{verbatim} 299 300The string \verb+<tag>+ is the name of the atom or center, and its case 301(upper or lower) is important. The tag is limited to 16 characters 302and is interpreted as follows: 303\begin{itemize} 304\item If the entry for \verb+<tag>+ begins with either the symbol or 305 name of an element (regardless of case), then the center is treated 306 as an atom of that type. The default charge is the atomic number 307 (adjusted for the presence of ECPs by the ECP \verb+NELEC+ directive 308 ; see Section \ref{sec:ecp}). Additional characters can be added to 309 the string, to distinguish between atoms of the same element (For 310 example, the tags \verb+oxygen+, \verb+O+, \verb+o34+, 311 \verb+olonepair+, and \verb+Oxygen-ether+, will all be interpreted 312 as oxygen atoms.). 313\item If the entry for \verb+<tag>+ begins with the characters 314 \verb+bq+ or \verb+x+ (regardless of case), then the center is 315 treated as a dummy center with a default zero charge (Note: a tag 316 beginning with the characters \verb+xe+ will be interpreted as a 317 xenon atom rather than as a dummy center.). Dummy centers may 318 optionally have basis functions or non-zero charge. See Section 319 \ref{sec:sample2} for a sample input using dummy centers with 320 charges. 321\end{itemize} 322 323It is {\em important} to be aware of the following points regarding 324the definitions and usage of the values specified for the variable 325\verb+<tag>+ to describe the centers in a system: 326\begin{itemize} 327\item If the tag begins with characters that cannot be matched against 328 an atom, and those characters are not \verb+BQ+ or \verb+X+, then a 329 fatal error is generated. 330\item The tag of a center is used in the \verb+BASIS+ (Section 331 \ref{sec:basis}) and \verb+ECP+ (Section \ref{sec:ecp}) directives 332 to associate functions with centers. 333\item All centers with the same tag will have the same basis 334 functions. 335\item When using automatic symmetry detection, 336 only centers with the same tag will be candidates for testing for 337 symmetry equivalence. 338\item The user-specified charges (of all centers, atomic and dummy) 339 and any net total charge of the system (Section \ref{sec:charge}) 340 are used to determine the number of electrons in the system. 341\end{itemize} 342 343The Cartesian coordinates of the atom in the molecule are specified as 344real numbers supplied for the variables \verb+x+, \verb+y+, and 345\verb+z+ following the characters entered for the tag. The values 346supplied for the coordinates must be in the units specified by the 347value of the variable \verb+<units>+ on the first line of the 348\verb+GEOMETRY+ directive input. 349 350After the Cartesian coordinate input, optional velocities may be 351entered as real numbers for the variables \verb+vx+, \verb+vy+, and 352\verb+vz+. The velocities should be given in atomic units and are 353used in QMD and PSPW calculations. 354 355The Cartesian coordinate input line also contains the optional keywords 356\verb+charge+, \verb+mass+ and \verb+nucleus+, which allow the user to 357specify the charge of the atom (or center) and its mass (in atomic mass 358units), and the nuclear model. The default charge for an atom is 359its atomic number, adjusted for the presence of ECPs (see Section 360\ref{sec:ecp}). In order to specify a different value for the charge on a 361particular atom, the user must enter the keyword \verb+charge+, followed by 362the desired value for the variable \verb+<charge>+. 363 364The default mass for an atom is taken to be the mass of its most abundant 365naturally occurring isotope or of the isotope with the longest half-life. 366To model some other isotope of the element, its mass must be defined 367explicitly by specifying the keyword \verb+mass+, followed by the value (in 368atomic mass units) for the variable \verb+<mass>+. 369 370The default nuclear model is a point nucleus. The keyword \verb+nucleus+ (or 371\verb+nucl+ or \verb+nuc+) followed by the model name \verb+<nucmodel>+ 372overrides this default. Allowed values of \verb+<nucmodel>+ are \verb+point+ or 373\verb+pt+ and \verb+finite+ or \verb+fi+. The \verb+finite+ option is 374a nuclear model with a Gaussian shape. The RMS radius of the Gaussian is 375determined by the atomic mass number via the formula $r_{\rm RMS} = 0.836* 376A^{1/3} + 0.57$ fm. The mass number $A$ is derived from the variable 377\verb+<mass>+. 378 379The geometry of the system can be specified entirely in Cartesian 380coordinates by supplying a \verb+<tag>+ line of the type described 381above for each atom or center. The user has the option, however, of 382supplying the geometry of some or all of the atoms or centers using a 383Z-matrix description. In such a case, the user supplies the input tag 384line described above for any centers to be described by Cartesian 385coordinates, and then specifies the remainder of the system using the 386optional \verb+ZMATRIX+ directive described below in Section 387\ref{sec:Z-matrix}. 388 389\section{{\tt ZMATRIX} --- Z-matrix input} 390\label{sec:Z-matrix} 391 392The \verb+ZMATRIX+ directive is an optional directive that can be used 393within the compound \verb+GEOMETRY+ directive to specify the structure 394of the system with a Z-matrix, which can include both internal and 395Cartesian coordinates. The \verb+ZMATRIX+ directive is itself a 396compound directive that can include the \verb+VARIABLES+ and 397\verb+CONSTANTS+ directives, depending on the options selected. The 398general form of the compound \verb+ZMATRIX+ directive is as follows: 399\begin{verbatim} 400 [ZMATRIX || ZMT || ZMAT 401 <string tagn> <list_of_zmatrix_variables> 402 ... 403 404 [VARIABLES 405 <string symbol> <real value> 406 ... ] 407 408 [CONSTANTS 409 <string symbol> <real value> 410 ... ] 411 412 (END || ZEND)] 413\end{verbatim} 414 415The input module recognizes three possible spellings of this directive 416name. It can be invoked with \verb+ZMATRIX+, \verb+ZMT+, or 417\verb+ZMAT+. The user can specify the molecular structure using 418either Cartesian coordinates or 419internal coordinates (bond lengths, bond angles and dihedral angles. 420The Z-matrix input for a center defines connectivity, bond length, and 421bond or torsion angles. Cartesian coordinate input for a center 422consists of three real numbers defining the x,y,z coordinates of the 423atom. 424 425Within the Z-matrix input, bond lengths and Cartesian coordinates must 426be input in the user-specified units, as defined by the value specified 427for the variable \verb+<units>+ on the first line of the \verb+GEOMETRY+ 428directive. All angles are specified in 429degrees. 430 431The individual centers (denoted as \verb+i+, \verb+j+, and \verb+k+ 432below) used to specify Z-matrix connectivity may be designated either 433as integers (identifying each center by number) or as tags ({\em If 434 tags are used, the tag must be unique for each center.}) The use of 435``dummy'' atoms is possible, by using \verb+X+ or \verb+BQ+ at the 436start of the tag. 437 438Bond lengths, bond angles and dihedral angles (denoted below as {\tt 439 R}, {\tt alpha}, and {\tt beta}, respectively) may be specified 440either as numerical values or as symbolic strings that must be 441subsequently defined using the \verb+VARIABLES+ or \verb+CONSTANTS+ 442directives. The numerical values of the symbolic strings labeled 443\verb+VARIABLES+ may be subject to changes during a geometry 444optimization say, while the numerical values of the symbolic strings 445labeled \verb+CONSTANTS+ will stay frozen to the value given in the 446input. The same symbolic string can be used more than once, and 447any mixture of numeric data and symbols is acceptable. Bond angles 448($\alpha$) must be in the range $0 < \alpha < 180$. 449 450The Z-matrix input is specified sequentially as follows: 451\begin{verbatim} 452 tag1 453 tag2 i R 454 tag3 i R j alpha 455 tag4 i R j alpha k beta [orient] 456 ... 457\end{verbatim} 458 459The structure of this input is described in more detail below. In the 460following discussion, the tag or number of the center being currently 461defined is labeled as \verb+C+ (``C'' for current). The values 462entered for these tags for centers defined in the Z-matrix input are 463interpreted in the same way as the \verb+<tag>+ entries for Cartesian 464coordinates described above (see Section \ref{sec:cart}). Figures 465\ref{fig:zmat1}, \ref{fig:zmat2} and \ref{fig:zmat3} display the 466relationships between the input data and the definitions of centers 467and angles. 468 469\begin{figure}[htbp] 470\centering 471\begin{latexonly} 472\ifx\pdfoutput\undefined 473\includegraphics[angle=270,width=6in]{zmat1.eps} 474\else 475\includegraphics[angle=0,width=6in]{zmat1.pdf} 476\fi 477\end{latexonly} 478\begin{htmlonly} 479\psfig{figure=zmat1.eps,angle=270,width=6in} 480\end{htmlonly} 481\caption{\label{fig:zmat1} Relationships between the centers, bond angle 482and dihedral angle in Z-matrix input.} 483\end{figure} 484 485\begin{figure}[htbp] 486\centering 487\begin{latexonly} 488\ifx\pdfoutput\undefined 489\includegraphics[angle=270,width=6in]{zmat2.eps} 490\else 491\includegraphics[angle=270,width=6in]{zmat2.pdf} 492\fi 493\end{latexonly} 494\begin{htmlonly} 495\psfig{figure=zmat2.eps,angle=270,width=6in} 496\end{htmlonly} 497 498\caption{\label{fig:zmat2} Relationships between the centers and two 499 bond angles in Z-matrix input with optional parameter specified as $+1$.} 500\end{figure} 501 502\begin{figure}[htbp] 503\centering 504\begin{latexonly} 505\ifx\pdfoutput\undefined 506\includegraphics[angle=270,width=6in]{zmat3.eps} 507\else 508\includegraphics[angle=270,width=6in]{zmat3.pdf} 509\fi 510\end{latexonly} 511\begin{htmlonly} 512\psfig{figure=zmat3.eps,angle=270,width=6in} 513\end{htmlonly} 514\caption{\label{fig:zmat3} Relationships between the centers and two 515 bond angles in Z-matrix input with optional parameter specified as $-1$.} 516\end{figure} 517 518The Z-matrix input shown above is interpreted as follows: 519\begin{enumerate} 520 521 \item \verb+tag1+ 522 523 Only a tag is required for the first center. 524 525 \item \verb+tag2 i R+ 526 527 The second center requires specification of its tag and the 528 bond length ($R_{Ci}$) distance to a previous atom, which is identified by 529 \verb+i+. 530 531 \item \verb+tag3 i R j alpha+ 532 533 The third center requires specification of its tag, its bond length distance 534 ($R_{Ci}$) to one of the two previous centers (identified by the 535 value of \verb+i+), and the bond angle $\alpha = \widehat{Cij}$. 536 537 \item \verb+tag i R j alpha k beta [<integer orient default 0>]+ 538 539 The fourth, and all subsequent centers, require the tag, a bond 540 length ($R_{Ci}$) relative to center \verb+i+, the bond angle with 541 centers \verb+i+ and \verb+j+ ($\alpha = \widehat{Cij}$), and {\em either} 542 \begin{enumerate} 543 \item the dihedral angle ($\beta$) between the current center and centers 544 \verb+i+, \verb+j+, and \verb+k+ (Figure \ref{fig:zmat1}), or 545 \item a second bond angle $\beta = \widehat{Cik}$ and an orientation to 546 the plane containing the other three centers (Figure 547 \ref{fig:zmat2} and \ref{fig:zmat3}). 548 \end{enumerate} 549 550 By default, $\beta$ is interpreted as a dihedral angle (see Figure 551 \ref{fig:zmat1}), but if the optional final parameter (\verb+<orient>+) is 552 specified with the value $\pm 1$, then $\beta$ is interpreted as 553 the angle $\widehat{Cik}$. The sign of \verb+<orient>+ specifies the 554 direction of the bond angle relative to the plane containing the 555 three reference atoms. If \verb+<orient>+ is $+1$, then the new center 556 (\verb+C+) is above the plane (Figure \ref{fig:zmat2}); and if 557 \verb+<orient>+ is $-1$, then \verb+C+ is below the plane (Figure 558 \ref{fig:zmat3}). 559\end{enumerate} 560 561Following the Z-matrix center definitions described above, the user can 562 specify initial values for any symbolic variables used to define the 563Z-matrix tags. This is done using the optional \verb+VARIABLES+ directive, 564which has the general form: 565 566% <string symbol> <real value> <real value> 567\begin{verbatim} 568 VARIABLES 569 <string symbol> <real value> 570 ... 571\end{verbatim} 572Each line contains the name of a variable followed by its value. 573Optionally, an equals sign (\verb+=+) can be included between the 574symbol and its value, for clarity in reading the input file. 575 576%If a second value follows the first value, a second structure gets 577%created, built from all the second valued internal coordinates and 578%the lone valued internal coordinates for those which are attributed 579%only a single vale. the program will define 580%a Linear Synchronous Transit (LST) path between the first structure 581%and the second structure ( the initial and final structures respectively). 582%A number of structures (11 in total) get created in equal increments 583%of the internal coordinates. The set of coordinates get written 584%to the file ./xxxx.lst.coord. In an 'LST' task , specified by 585%'task <theory> lst', the program calculates the energy of the 586%system for all these structures in sequence. 587 588Following the \verb+VARIABLES+ directive, the \verb+CONSTANTS+ 589directive may be used to define any Z-matrix symbolic variables that remain 590unchanged during geometry optimizations. 591To freeze the Cartesian coordinates of an atom, refer 592to Section \ref{sec:activeatoms}. The general form of this directive 593is as follows: 594\begin{verbatim} 595 CONSTANTS 596 <string symbol> <real value> 597 ... 598\end{verbatim} 599Each line contains the name of a variable followed by its value. As 600with the \verb+VARIABLES+ directive, an equals sign (\verb+=+) can be 601included between the symbol and its value. 602 603The end of the Z-matrix input using the compound \verb+ZMATRIX+ 604directive is signaled by a line containing either \verb+END+ or 605\verb+ZEND+, following all input for the directive itself and its 606associated optional directives. 607 608A simple example is presented for water. All Z-matrix parameters are 609specified numerically, and symbolic tags are used to specify 610connectivity information. This requires that all tags be unique, and 611therefore different tags are used for the two hydrogen atoms, which may 612or may not be identical. 613\begin{verbatim} 614 geometry 615 zmatrix 616 O 617 H1 O 0.95 618 H2 O 0.95 H1 108.0 619 end 620 end 621\end{verbatim} 622 623The following example illustrates the Z-matrix input for the molecule 624$CH_3CF_3$. This input uses the numbers of centers to specify 625the connectivity information (\verb+i+, \verb+j+, and \verb+k+), and 626uses symbolic variables for the Z-matrix parameters {\tt R}, {\tt 627 alpha}, and {\tt beta}, which are defined in the inputs for the 628\verb+VARIABLES+ and 629\verb+CONSTANTS+ directives. 630 631\begin{verbatim} 632geometry 633 zmatrix 634 C 635 C 1 CC 636 H 1 CH1 2 HCH1 637 H 1 CH2 2 HCH2 3 TOR1 638 H 1 CH3 2 HCH3 3 -TOR2 639 F 2 CF1 1 CCF1 3 TOR3 640 F 2 CF2 1 CCF2 6 FCH1 641 F 2 CF3 1 CCF3 6 -FCH1 642 variables 643 CC 1.4888 644 CH1 1.0790 645 CH2 1.0789 646 CH3 1.0789 647 CF1 1.3667 648 CF2 1.3669 649 CF3 1.3669 650 constants 651 HCH1 104.28 652 HCH2 104.74 653 HCH3 104.7 654 CCF1 112.0713 655 CCF2 112.0341 656 CCF3 112.0340 657 TOR1 109.3996 658 TOR2 109.3997 659 TOR3 180.0000 660 FCH1 106.7846 661 end 662end 663\end{verbatim} 664 665The input for any centers specified with Cartesian coordinates must 666be specified using the format of the \verb+<tag>+ lines described 667in Section \ref{sec:cart} above. However, in 668order to correctly specify these Cartesian coordinates 669within the Z-matrix, the user must 670understand the orientation of centers specified using 671internal coordinates. These are arranged as follows: 672\begin{itemize} 673\item The first center is placed at the origin. 674\item The second center is placed along the positive z-axis. 675\item The third center is placed in the z-x plane. 676\end{itemize} 677 678\section{{\tt ZCOORD} --- Forcing internal coordinates} 679\label{sec:zcoord} 680 681By default redundant internal coordinates are generated for use in 682geometry optimizations. Connectivity is inferred by comparing 683inter-atomic distances with the sum of the van der Waals radii of the 684two atoms involved in a possible bond, times a scaling factor. The 685scaling factor is an input parameter of \verb+ZCOORD+ which maybe 686changed from its default value of 1.3. Under some circumstances 687(unusual bonding, bond dissociation, \ldots) it will be necessary to 688augment the automatically generated list of internal coordinates to 689force some specific internal coordinates to be included in among the 690internal coordinates. This is accomplished by including the optional 691directive {\tt ZCOORD} within the geometry directive. The general 692form of the \verb+ZCOORD+ directive is as follows: 693\begin{verbatim} 694 ZCOORD 695 CVR_SCALING <real value> 696 BOND <integer i> <integer j> \ 697 [<real value>] [<string name>] [constant] 698 ANGLE <integer i> <integer j> <integer k> \ 699 [<real value>] [<string name>] [constant] 700 TORSION <integer i> <integer j> <integer k> <integer l> \ 701 [<real value>] [<string name>] [constant] 702 END 703\end{verbatim} 704 705The centers \verb+i+, \verb+j+, \verb+k+ and \verb+l+ {\em must} be 706specified using the numbers of the centers, as supplied in the input 707for the Cartesian coordinates. The \verb+ZCOORD+ input parameters are 708defined as follows: 709 710\begin{itemize} 711\item {\tt cvr\_scaling} --- scaling factor applied to van der Waals radii. 712\item {\tt bond} --- a bond between the two centers. 713\item {\tt angle} --- a bond angle $\widehat{ijk}$. 714\item {\tt torsion} --- a torsion (or dihedral) angle. The 715 angle between the planes \verb+i-j-k+ and \verb+j-k-l+. 716\end{itemize} 717 718A value may be specified for a user-defined internal coordinate, in 719which case it is forced upon the input Cartesian coordinates while 720attempting to make only small changes in the other internal 721coordinates. If no value is provided the value implicit in the input 722coordinates is kept. If the keyword \verb+constant+ is specified, then 723that internal variable is not modified during a geometry optimization 724with DRIVER (Section \ref{sec:driver}). Each internal coordinate may 725also be named either for easy identification in the output, or 726for the application of constraints (Section \ref{sec:constraints}). 727 728If the keyword \verb+adjust+ is specified on the main \verb+GEOMETRY+ 729directive, only \verb+ZCOORD+ data may be specified and it can 730be used to change the user-defined internal coordinates, including 731adding/removing constraints and changing their values. 732 733\section{Applying constraints in geometry optimizations} 734\label{sec:activeatoms} 735\label{sec:constraints} 736 737Internal coordinates specified as constant in a \verb+ZCOORD+ directive 738or in the constants section of a \verb+ZMATRIX+ directive, will be 739frozen at their initial values if a geometry optimization is 740performed with DRIVER (Section \ref{sec:driver}). 741 742If internal coordinates have the same name (give or take 743an optional sign for torsions) then they are forced to have 744the same value. This may be used to force bonds or angles to 745be equal even if they are not related by symmetry. 746 747When atoms have been specified by their Cartesian coordinates, {\em 748and} internal coordinates are not being used, it is possible to freeze 749the cartesian position of selected atoms. This is useful for such 750purposes as optimizing a molecule absorbed on the surface of a cluster 751with fixed geometry. Only the gradients associated with the active 752atoms are computed. This can result in a big computational saving, 753since gradients associated with frozen atoms are forced to zero (Note, 754however, that this destroys the translational and rotational 755invariance of the gradient. This is not yet fully accommodated by the 756STEPPER geometry optimization software, and can sometimes result in 757slower convergence of the optimization. The DRIVER optimization 758package does not suffer from this problem). 759 760The \verb+SET+ directive (Section \ref{sec:set}) is used to freeze 761atoms, by specifying a directive of the form: 762\begin{verbatim} 763 set geometry:actlist <integer list_of_center_numbers> 764\end{verbatim} 765This defines only the centers in the list as active. All other 766centers will have zero force assigned to them, and will remain frozen 767at their starting coordinates during a geometry optimization. 768 769For example, the following directive specifies that atoms numbered 1, 7705, 6, 7, 8, and 15 are active and all other atoms are frozen: 771\begin{verbatim} 772 set geometry:actlist 1 5:8 15 773\end{verbatim} 774or equivalently, 775\begin{verbatim} 776 set geometry:actlist 1 5 6 7 8 15 777\end{verbatim} 778 779If this option is not specified by entering a \verb+SET+ directive, 780the default behavior in the code is to treat all atoms as active. To 781revert to this default behavior after the option to define frozen 782atoms has been invoked, the \verb+UNSET+ directive must be used (since 783the database is persistent, see Section \ref{sec:persist}). The form 784of the \verb+UNSET+ directive is as follows: 785\begin{verbatim} 786 unset geometry:actlist 787\end{verbatim} 788 789\section{{\tt SYSTEM} --- Lattice parameters for periodic systems} 790\label{sec:latticeparam} 791 792This keyword is needed only for for 1-, 2-, and 3-dimensional 793periodic systems. 794 795The {\tt system} keyword can assume the following values 796 797\begin{itemize} 798\item {\tt polymer} --- system with 1-d translational symmetry. 799\item {\tt surface} --- system with 2-d translational symmetry. 800\item {\tt crystal} --- system with 3-d translational symmetry. 801\item {\tt molecule} --- no translational symmetry (this is the default) 802\end{itemize} 803 804When the system possess translational symmetry, {\bf fractional} coordinates 805are used in the directions where translational symmetry exists. 806This means that for crystals $x$, $y$ and $z$ are fractional, for 807surfaces $x$ and $y$ are fractional, whereas for polymers only $z$ is 808fractional. 809For example, in the following H$_2$O layer input (a 2-d periodic 810system), $x$ and $y$ coordinates are fractional, whereas $z$ 811is expressed in \AA . 812\begin{verbatim} 813geometry units angstrom 814 O 0.353553 0.353553 2.100000000 815 H 0.263094 0.353553 2.663590000 816 H 0.444007 0.353553 2.663590000 817\end{verbatim} 818 819Since no space group symmetry is available yet other than $P1$, input 820of cell parameters is relative to the primitive cell. For example, 821this is the input required for the cubic face-centered type structure 822of bulk MgO. 823 824\begin{verbatim} 825 826 system crystal 827 lat_a 2.97692 lat_b 2.97692 lat_c 2.97692 828 alpha 60.00 beta 60.00 gamma 60.00 829 end 830\end{verbatim} 831 832 833 834 835 836%%% Local Variables: 837%%% mode: latex 838%%% TeX-master: "user" 839%%% End: 840