## Mixed Cartesian and Internal Coordinate Definition

With the exception of the first atom, real or dummy, atom positions may be defined using either Cartesian or internal coordinates.  The coordinates of an atom are defined using internal coordinates if a connectivity is supplied.  If the connectivity is missing, the atom is defined in terms of Cartesian coordinates. Atom 1, because it does not have a connectivity, is always defined in Cartesian coordinates.  Although these are usually (0.0, 0.0, 0.0) there is no a priori reason for this, and atom 1 can be put at any user-defined position.

An atom's position can be defined using internal coordinates involving atoms whose positions have not yet been defined if those atoms are defined using Cartesian coordinates.  This is different from the normal restriction of internal coordinates, where an atom's position can only be defined using atoms that have already been defined.  Put another way, if the position of atom 100 is defined using atoms 110, 120, and 60, then the positions of atoms 110 and 120 must be defined using Cartesian coordinates.  Atom 60 can be in Cartesian or internal, since its position has already been defined.

In the following example, the geometry of a tripeptide is defined using Cartesian coordinates for atom 1 and all the atoms in the second residue.  The rest of the atoms in residue 1 and all the atoms in residue 3 are defined using internal coordinates.

Note that  the first three atoms of the third residue are defined using atoms whose positions are given in Cartesian coordinates.  This is a valid definition - Cartesian and internal coordinates can be mixed together in any way desired.

Example of a mixed coordinate definition:

``` Gradients 1scf
Example of mixed coordinates. A tripeptide with residues 1 and 3 in internal coordinates
residue 2 is in Cartesian coordinates
N         0.00000000 +0    0.0000000 +0    0.0000000 +0
C         1.45099200 +1    0.0000000 +0    0.0000000 +0     1     0     0
C         1.51835900 +1  114.2160460 +1    0.0000000 +0     2     1     0
O         1.22627600 +1  119.2494590 +1  150.0224060 +1     3     2     1
C         1.53154900 +1  110.2108510 +1 -122.9442610 +1     2     1     3
S         1.81497400 +1  108.2495690 +1 -116.9760990 +1     5     2     1
H         1.09144500 +1  107.8966510 +1  117.4730020 +1     2     1     3
H         1.09439500 +1  110.6252580 +1  125.3849350 +1     5     2     1
H         1.09375800 +1  111.5846500 +1    4.2686790 +1     5     2     1
H         1.37249300 +1  102.4190520 +1 -179.3933780 +1     6     5     2
H         1.01203000 +1  116.9993300 +1  127.1027860 +1     1     2     3
H         1.01203000 +1  116.9993300 +1 -127.1027860 +1     1     2     3
N         1.41779186 +1    2.3818640 +1   -0.5930817 +1
C         1.96005201 +1    3.7395708 +1   -0.5873182 +1
C         0.87144992 +1    4.6925379 +1   -0.0859199 +1
O        -0.30894710 +1    4.3852105 +1   -0.2277412 +1
C         2.58984680 +1    4.0757744 +1   -1.9613244 +1
C         3.95504011 +1    3.4174209 +1   -2.2109945 +1
C         5.13263384 +1    4.0760823 +1   -1.8023387 +1
C         6.39390379 +1    3.5338821 +1   -2.0746443 +1
C         6.51251534 +1    2.3040175 +1   -2.7409980 +1
C         5.35236761 +1    1.6339502 +1   -3.1585724 +1
C         4.08327785 +1    2.1864831 +1   -2.9055825 +1
H         2.75184646 +1    3.8479695 +1    0.1426395 +1
H         2.74129210 +1    5.1566073 +1   -1.9998683 +1
H         1.90797747 +1    3.8313152 +1   -2.7790034 +1
H         5.07815939 +1    5.0182815 +1   -1.2765870 +1
H         7.28256125 +1    4.0711027 +1   -1.8000485 +1
H         3.20599873 +1    1.6658896 +1   -3.2578962 +1
H         5.45626342 +1    0.6951745 +1   -3.6940611 +1
H         7.49097179 +1    1.8927662 +1   -2.9377954 +1
H         0.46717507 +1    2.2471723 +1   -0.9238687 +1
N         1.33611900 +1  118.9784180 +1  152.6871430 +1    15    14    13
C         1.45816400 +1  122.1765280 +1  173.0360570 +1    33    15    14
C         1.54029400 +1  106.1916250 +1  -98.1274360 +1    34    33    15
O         1.22473500 +1  118.4172840 +1  -38.7329790 +1    35    34    33
C         1.54046400 +1  112.6361960 +1  139.8205900 +1    34    33    15
C         1.53533100 +1  115.3620840 +1  -28.7237370 +1    37    34    33
C         1.52273000 +1  109.3021640 +1  175.4610420 +1    38    37    34
O         1.24543100 +1  114.2017740 +1  -65.1675870 +1    39    38    37
O         1.25543200 +1  119.1622320 +1  113.3463330 +1    39    38    37
H         1.08372800 +1  109.7991700 +1   24.1081960 +1    34    33    15
H         1.09211200 +1  107.8205160 +1 -148.0829980 +1    37    34    33
H         1.09379600 +1  109.2718540 +1   94.4693220 +1    37    34    33
H         1.08910800 +1  109.7719310 +1   58.7340750 +1    38    37    34
H         1.08916200 +1  111.1381130 +1  -61.8510410 +1    38    37    34
H         0.90000000 +1  120.0000000 +1 -179.9999990 +1    40    39    38
H         1.01192900 +1  119.8483270 +1   10.8020530 +1    33    15    14
H         1.34588100 +1  121.3449610 +1  139.3147470 +1    35    34    33
```