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23 | <TR><TH><A Href="expgui.html">EXPGUI top</A> |
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24 | </TH><TH><A Href="expgui7.html">Next page</A> |
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25 | </TH><TH><A Href="expgui6.html">Previous page</A> |
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27 | |
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28 | <center><h1> |
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29 | <HR noshade width="75%" size="2" align="center"> |
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30 | EXPGUI, part 7 |
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31 | <HR noshade width="75%" size="2" align="center"> |
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32 | </h1></center> |
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33 | |
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34 | <h3>A.7 Rigid Body Introduction</h3> |
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35 | <DL><DL> |
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36 | GSAS Rigid bodies are another way to constrain relative atomic |
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37 | positions. In a rigid body fit, |
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38 | a group of atoms are constrained so that they rotate and/or translate as a unit. |
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39 | GSAS allows quite complex rigid bodies, with up to 9 scaling parameters and |
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40 | when multiple rigid bodies are used with grouped parameters even more complex |
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41 | constraints can be developed. The EXPGUI rigid body interface allows access to |
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42 | most of the GSAS features and offers some setup features not in GSAS, but |
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43 | expert users may need to use EXPEDT for some very complex constraint models. |
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44 | <P> |
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45 | Use of a rigid body reduces |
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46 | the number of parameters refined, prevents deviations from chemical |
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47 | reasonableness and generally helps obtain a more stable refinement. This can be especially important in the |
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48 | early stages of refinement. Rigid |
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49 | bodies are commonly used to constrain rigid moieties such phenyl or cyclopentadienyl rings but, they can be generated for much |
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50 | more complicated structures. Rigid bodies in GSAS are always |
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51 | represented by a set of Cartesian coordinates describing the relative positions |
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52 | of the atoms to be constrained. More complex frameworks can be constructed |
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53 | using multiple sets of Cartesian coordinates with variable multipliers, for |
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54 | more complex constraints. Even more sophisticated refinements are possible when |
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55 | multiple rigid bodies are constrained to share an origin or positioning (Euler) |
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56 | angles. |
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57 | <P> |
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58 | Once created, the |
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59 | rigid body framework is applied as a constraint by mapping it onto atoms in a |
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60 | phase. The same rigid body framework can be mapped multiple times into one or |
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61 | more phases. |
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62 | Once mapped, the set |
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63 | of atoms will refine as a single body with 3 parameters describing the |
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64 | translation of the rigid body origin (generally the centroid of mass of the |
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65 | atomic grouping but, this is optional) and 3 parameters describing the rotation |
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66 | of the body about the origin (Euler Angles). TLS terms (translation, libration, |
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67 | screw) can be used to model cooperative thermal motion about the rigid |
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68 | body. The EXPGUI rigid body routines |
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69 | will allow the user to readily generate the rigid body framework (called matrices |
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70 | in EXPGUI terminology) and map the rigid body to sets of atoms already present |
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71 | in the GSAS EXP file. |
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72 | |
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73 | The EXPGUI Rigid Body Panel allows for the |
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74 | creation or viewing of rigid bodies. |
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75 | A rough outline of the procedure to generate and refine with a rigid body |
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76 | is as follows: |
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77 | |
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78 | <OL> |
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79 | <LI>Define the framework of the rigid |
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80 | body with a set of Cartesian coordinates representing the relative atomic |
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81 | positions. This can be done by |
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82 | manual input, loading the coordinates from an ASCII file, |
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83 | converting Z-matrix coordinates to Cartesian or generating Cartesian coordinates |
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84 | from fractional coordinates in an existing molecular fragment in the GSAS EXP |
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85 | file. |
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86 | <LI> |
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87 | The rigid body |
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88 | framework must be mapped upon the crystal structure. |
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89 | This requires that the atoms in the |
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90 | phase be sequential and must match the order of atoms in the rigid body |
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91 | framework. |
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92 | To change the sequential |
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93 | order in the rigid body, the Edit Matrix routine may be used to reorder the |
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94 | rigid body coordinates. |
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95 | In the |
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96 | mapping procedure, this number of the first atom in the phase to match the |
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97 | rigid body is designated (since the mapping then follows) and both the Euler angles |
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98 | and rigid body origin are specified; EXPGUI can help determine values |
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99 | for these. |
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100 | This can be repeated to map the rigid |
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101 | body framework to other parts of the structure. |
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102 | <LI> |
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103 | Once the rigid body framework |
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104 | is mapped to the crystal structure, the refinement flags for the Euler angles |
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105 | and Origin can be set. This will turn on the 'X' refinement flags for the |
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106 | included atoms in the Phase Panel. It is important that these match the state |
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107 | of the rigid body refinement flags or GENLES will crash. |
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108 | </OL> |
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109 | </DL></DL> |
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110 | <H3>A.7.a Main Rigid Body Panel</H3> |
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111 | <DL><DL> |
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112 | The main panel for rigid bodies presents a interface where bodies can |
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113 | be initially defined. When bodies have been defined, a tab appears |
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114 | for each defined body, where these bodies can be used or |
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115 | edited. This main panel is shown below and subsequent sections |
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116 | describe how bodies are initially defined. |
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117 | <BR><img src="rb001.jpg" alt="RB start panel"> |
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118 | <BR> |
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119 | Rigid bodies are created |
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120 | from one or more sets of Cartesian coordinates multiplied by a scale factor and |
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121 | then summed to create Cartesian coordinates in Angstroms. This can be expressed |
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122 | as a linear algebra expression, |
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123 | <P><DL><DL> |
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124 | XYZ = M1*XYZ1 + M2*XYZ2 + ... |
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125 | </DL></DL> |
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126 | <P> |
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127 | Where XYZ, XYZ1, ...are 3 by N matrices (3 columns by N atoms) and M1, |
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128 | M2,... |
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129 | are scalars. Therefore in EXPGUI terminology, each set of Cartesian |
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130 | coordinates is called a "Matrix." The |
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131 | sum of these scaled matrices describes the rigid body framework that is to be |
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132 | mapped upon the atoms of the crystal structure. Most commonly, however, only |
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133 | one matrix is used and M1=1. In this case the matrix is simply a set of Cartesian |
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134 | coordinates in Angstroms, which can be input by multiple methods. |
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135 | As a reminder, note that the rigid body |
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136 | framework will be mapped to consecutive atoms in the EXP file must be so the Cartesian |
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137 | coordinates of the rigid body MUST be listed in a corresponding order. |
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138 | <P> |
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139 | If the ordering of the Cartesian |
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140 | coordinates of the rigid body, as input, is incorrect, they may be rearranged |
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141 | with the Edit Matrix panel invoked |
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142 | from the Rigid Body Type panel. |
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143 | <P> |
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144 | Advanced refinements |
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145 | may take advantage of the GSAS feature of multiple matrices, each with its own |
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146 | matrix multiplier. This can result is some very advanced refinements such as |
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147 | independently refining the C-C and C-H bond distances in a hydrocarbon |
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148 | ring. |
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149 | <P> |
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150 | The "Create Rigid Body" tab offers several ways to create a rigid |
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151 | body: |
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152 | <UL><LI>Manual rigid body definition |
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153 | <LI>Cartesian coordinates from ASCII text file |
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154 | <LI>Cartesian coordinates from a Z-matrix |
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155 | <LI>Compute Cartesian coordinates from EXP file (fractional coordinates) |
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156 | </UL> |
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157 | |
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158 | <H4>A.7.a1 Manual rigid body definition</H4> |
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159 | <DL> |
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160 | The manual definition window allows input of coordinates and |
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161 | multipier(s) by typing values into boxes. Number of matrices |
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162 | determines the number of multipliers and sets of coordinates that |
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163 | are added. Number of Cartesian sites is the number of atoms in the |
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164 | rigid body. The "Save Rigid Body" button creates a new rigid body |
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165 | with the specified input. The "Export Cartesian Coordinates..." |
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166 | writes an ASCII file with the current input. |
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167 | <BR><img src="rb002.jpg" alt="Manual RB creation window"> |
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168 | </DL> |
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169 | <H4>A.7.a2 Cartesian coordinates from ASCII text file</H4> |
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170 | <DL> |
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171 | Cartesian coordinates |
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172 | can be read from any ASCII file containing Cartesian coordinates in a standard |
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173 | tabular format. |
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174 | This routine allows |
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175 | the user to determine which columns (separated by a delimiter) represents the X, |
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176 | Y and Z coordinates. |
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177 | The user also |
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178 | has the option to ignore any row or column that contains irrelevant |
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179 | information. |
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180 | Once the Cartesian |
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181 | coordinates are isolated, and the "Continue" button is pressed, |
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182 | the user continues to the "Create Rigid Body" window (see above). |
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183 | <BR><img src="rb003.jpg" alt="ASCII RB input window"> |
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184 | </DL> |
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185 | |
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186 | <H4>A.7.a3 Cartesian coordinates from a Z-matrix</H4> |
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187 | <DL> |
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188 | Cartesian coordinates |
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189 | can also be calculated from a Z-matrix in an appropriate ASCII format. |
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190 | The conversion routine will allow dummy |
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191 | atoms to be identified and ignored in the conversion process. |
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192 | Upon pressing the "Continue" button, the Z-matrix |
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193 | is converted to Cartesian coordinates and the user progresses to the |
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194 | "Create Rigid Body" window (see above). |
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195 | <BR><img src="rb004.jpg" alt="Z-matrix RB input window"> |
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196 | </DL> |
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197 | <H4>A.7.a4 Compute Cartesian coordinates from EXP file (fractional coordinates)</H4> |
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198 | <DL> |
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199 | Cartesian coordinates |
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200 | can also be determined from atoms in the EXP file. |
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201 | In order to generate Cartesian |
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202 | coordinates, the number of sites in the rigid body framework must be specified |
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203 | as well as the starting atom (remember rigid bodies are mapped consecutively). |
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204 | Once the number of atoms in the body is |
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205 | set, the "Choose Start Atom" button is pressed. This creates buttons for |
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206 | all possible choices for the first atom to define the body. Once the starting |
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207 | atom is selected by pressing one of these button(s), the atoms to be used to |
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208 | define the rigid body framework have been determined. The user must than select |
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209 | which atoms will be used to define the origin (the origin will be at the |
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210 | centroid of the atoms chosen) and must define the axes that will be used to |
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211 | generate the x-axis and the xy plane. |
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212 | The Cartesian coordinates can then be generated. |
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213 | Either the defined body can be determined and mapped (with the "Save and Map |
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214 | Rigid Body" button), or the Cartesian coordinates can exported to an |
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215 | ASCII text file (with the "Export Cartesian Coordinates" |
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216 | button). |
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217 | <BR><img src="rb005.jpg" alt="Fraction Coords RB input window"> |
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218 | </DL> |
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219 | |
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220 | </DL></DL> |
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221 | <H3>A.7.b Rigid Body Panel</H3> |
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222 | <DL><DL> |
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223 | As each rigid body is |
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224 | defined, a "Rigid Body Type N" panel will be created.<span |
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225 | style="mso-spacerun:yes"> |
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226 | This panel will show how the rigid body |
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227 | is mapped, and will allow the user to map / unmap the |
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228 | rigid body on to the crystal structure, view the rigid body (this |
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229 | assumes the |
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230 | <A HREF="http://www.lwfinger.net/drawxtl/">DRAWxtl</A> program is installed on their computer), edit the |
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231 | rigid body, set refinement flags, or delete the rigid body. |
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232 | <BR><img src="rb006.jpg" alt="RB edit panel"> |
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233 | |
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234 | <H4>A.7.b1 Plot Rigid Body</H4> |
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235 | <DL> |
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236 | <A HREF="http://www.lwfinger.net/drawxtl/">DRAWxtl</A> |
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237 | is a very useful viewing program that |
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238 | EXPGUI can invoke, if installed. It |
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239 | allows for the viewing of the rigid body to ensure it is correct before mapping |
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240 | and matches the ordering of the atoms in the EXP file. The plot below |
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241 | was obtained from the "Plot Rigid Body" button. |
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242 | <BR><img src="rb007.png" alt="DRAWxtl screen"> |
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243 | </DL> |
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244 | |
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245 | <H4>A.7.b2 Map Rigid Body</H4> |
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246 | <DL> |
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247 | The rigid body must be mapped to the |
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248 | crystal structure to define the constraint. This is done by pressing |
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249 | the "Map Rigid Body" button, which raises the window below. |
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250 | <BR><img src="rb008.png" alt="Map RB"><BR> |
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251 | In order to map the rigid body the user |
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252 | will need to specify the phase and the sequence number of the first atom in the |
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253 | .EXP file to be included. |
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254 | This will |
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255 | be the atom assigned to the first set of coordinates in the rigid |
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256 | body. |
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257 | Each succeeding atom will be assigned |
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258 | the consecutive set of coordinates. |
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259 | The origin and Euler angles for the rigid body placement must be |
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260 | determined; this can be done by fitting to the atoms in the |
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261 | .EXP file using the "Fit rigid body to phase" button. A |
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262 | table of RMS (~ A distances) between the mapped rigid body placement |
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263 | and the initial atom placements -- this describes the quality of the fit. |
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264 | If the fit is poor, it is |
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265 | likely that the ordering of Cartesian coordinates is incorrect, resulting in high |
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266 | RMS values. If this occurs, the ordering of the Cartesian coordinates must be |
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267 | modified with the Edit Matrix routine. |
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268 | <BR><img src="rb010.png" alt=""><BR> |
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269 | <img src="rb009.png" alt="" ALIGN="RIGHT"> |
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270 | The fit can be visually examined with |
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271 | the "Plot rigid body & phase" button with results as |
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272 | show to the right. |
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273 | The rigid body is shown in |
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274 | red and the .EXP file coordinates are shown in green. Note that it is often |
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275 | easier to understand what is being plotted, when bonds are drawn. The input in |
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276 | the "Bonds" box specifies ranges of distances where 0.9-1.1, 1.3-1.6 draws bonds |
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277 | between atoms spaced 0.9 to 1.1 A (typical C-H bonds) and 1.3 to 1.6 A (typical |
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278 | organic molecule bonds). You may wish to specify different |
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279 | ranges where other types of bonding are present. One can also change |
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280 | the display from the DRAWxtl menus. |
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281 | <BR Clear="all"> |
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282 | </DL> |
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283 | <H4>A.7.b3 Edit Rigid Body</H4> |
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284 | <DL> |
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285 | |
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286 | Pressing the "Edit Matrix" button on the "Rigid Body Type N" panel |
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287 | provides an interface that will allow the Cartesian coordinates to be modified by |
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288 | sorting, swapping, adding or deleting matrix elements. |
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289 | It will also allow for setting the refinement flag for Matrix |
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290 | Multipliers. |
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291 | <BR><img src="rb011.jpg" alt=""><BR> |
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292 | <img src="rb012.png" alt="" ALIGN="RIGHT"> |
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293 | Note that repeating the previous |
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294 | mapping, after reordering |
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295 | of the Cartesian coordinates, the following fit of a cyclopentadienyl |
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296 | ligand is accomplished and the RMS differences in the |
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297 | fitting procedure are small. |
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298 | Below |
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299 | shows the correct fit. |
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300 | <BR><img src="rb013.png" alt=""><BR> |
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301 | <BR><img src="rb014.png" alt=""><BR> |
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302 | </DL> |
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303 | |
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304 | </DL></DL> |
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305 | <H3>A.7.c Setting Rigid Body Refinement Flags</H3> |
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306 | <DL><DL> |
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307 | The "Refinement Flags" button opens a window that allows the |
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308 | user to set flags to refine various parameters. |
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309 | Parameters can be set up to refine as |
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310 | free variables or constrained variables. |
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311 | The TLS (translation, librations, screw) terms describe the rigid body |
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312 | thermal motions and are normally off. |
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313 | They should only be turned on if the user has a strong understanding of |
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314 | the relationships between the TLS terms. |
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315 | Note: if an Origin or Euler angle |
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316 | flag is enabled, the appropriate atom X refinement flag on the phase panel will |
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317 | be set. |
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318 | GENLES will have errors if |
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319 | rigid body parameters are refined, but not the positions of the corresponding |
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320 | atoms. |
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321 | |
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322 | Note that in EXPEDT, |
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323 | rigid body parameters can be grouped by assigning them the same variable |
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324 | number. The same feature is possible via a graphical interface by "tagging" (pressing |
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325 | the appropriate button for) items to vary and then using the following buttons: |
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326 | <UL><LI> |
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327 | "Set Free Variables" - will assign each tagged parameter as |
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328 | an unconstrained variable by providing a unique variable number. |
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329 | |
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330 | <LI>Do Not Refine Variables - will turn off the refinement flag |
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331 | for all tagged parameters. |
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332 | |
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333 | <LI>Set Constrained variables - will constrain all tagged parameters |
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334 | and assign a single variable for refinement. |
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335 | <LI>Clear All Variables - will clear all refinement flags. |
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336 | |
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337 | <LI>Assign Variables and Save - will assign variable numbers to each |
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338 | unique parameter to be refined and close the Refinement Flag window. |
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339 | <BR><img src="rb015.png" alt=""><BR> |
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340 | <BR><img src="rb016.png" alt=""><BR> |
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341 | |
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342 | The above Phase Panel shows the 'X' |
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343 | refinement flags active allowing the rigid body refinement to |
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344 | commence. |
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345 | These flags were set automatically when |
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346 | the rigid body position parameter were set to be refined. If these flags are |
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347 | turned off, it is likely that GENLES will crash. |
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348 | |
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349 | </DL></DL> |
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350 | <hr> |
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351 | <TABLE BORDER BGCOLOR="#FFFF40" ALIGN=RIGHT> |
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352 | <TR><TH><A Href="expgui.html">EXPGUI top</A> |
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353 | </TH><TH><A Href="expgui7.html">Next page</A> |
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354 | </TH><TH><A Href="expgui6.html">Previous page</A> |
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355 | </TH></TR></TABLE> |
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356 | |
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357 | </blockquote> |
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359 | </html> |
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