GeometryOptimization - Maple Help

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QuantumChemistry

 GeometryOptimization
 compute the optimized geometry

 Calling Sequence GeometryOptimization(molecule, method, options)

Parameters

 molecule - list of lists; each list has 4 elements, the string of an atom's symbol and atom's x, y, and z coordinates method - name/procedure where name is one of 'HartreeFock', 'DensityFunctional', $'\mathrm{ActiveSpaceCI}',$ options - (optional) equation(s) of the form option = value where option is optimization, optimalitytolerance, or any valid option of the chosen method

Description

 • GeometryOptimization optimizes the molecular geometry to minimize the total energy.
 • The optimization searches for a first-order stationary point on the potential energy surface,
 • The stationary point may be either a local minimum or a saddle point (transition state).
 • The optional optimization keyword selects the type of optimization.  If the keyword is set to "analytical" (default), then GeometryOptimization will use analytical gradients where available in a quasi-Newton algorithm.  If analytical derivatives are not available, then the derivatives with respect to nuclear displacement are computed by numerical centered finite differences.  If the keyword is set to "newton", then numerical gradients are used in a second-order Newton-Raphson algorithm, and if the keyword is set to "quasi-newton", then numerical gradients are used in a quasi-Newton algorithm.
 • Analytical nuclear gradients are implemented on the MacOS X and Linux platforms for all spin states of HartreeFock and DensityFunctional as well as the singlet states of ActiveSpaceCI, ActiveSpaceSCF, CoupledCluster, FullCI, MP2, Variational2RDM, and Parametric2RDM.
 • The optional optimalitytolerance keyword can be set to a float which sets the convergence tolerance.
 • The output of the procedure is a Maple sequence.  The first element in the sequence is the optimized geometry as a Maple list of lists in the same format as the input argument molecule.  The second element is the output table of the given method evaluated for the optimized geometry.

Examples

 > $\mathrm{with}\left(\mathrm{QuantumChemistry}\right):$
 >
 ${\mathrm{molecule}}{≔}\left[\left[{"H"}{,}{0}{,}{0}{,}{-0.55000000}\right]{,}\left[{"F"}{,}{0}{,}{0}{,}{0.55000000}\right]\right]$ (1)
 >
 $\left[\left[{"H"}{,}{0}{,}{0}{,}{-0.55000000}\right]{,}\left[{"F"}{,}{-2.53109794}{}{{10}}^{{-11}}{,}{-1.91734444}{}{{10}}^{{-10}}{,}{0.36963639}\right]\right]{,}{table}\left(\left[{\mathrm{aolabels}}{=}\begin{array}{c}\left[\begin{array}{c}{"0 H 1s"}\\ {"0 H 2s"}\\ {"1 F 1s"}\\ {"1 F 2s"}\\ {"1 F 3s"}\\ {"1 F 4s"}\\ {⋮}\end{array}\right]\\ \hfill {\text{12 element Vector[column]}}\end{array}{,}{\mathrm{mo_coeff}}{=}\begin{array}{c}\left[\begin{array}{ccccccc}{-0.00001998}& {0.13319634}& {-0.28714486}& {0.}& {0.}& {0.09830711}& {\dots }\\ {-0.00014381}& {0.00152251}& {-0.08533694}& {0.}& {0.}& {1.46588020}& {\dots }\\ {0.57990096}& {-0.14056678}& {-0.03785850}& {0.}& {0.}& {0.03649391}& {\dots }\\ {0.46217976}& {-0.19296525}& {-0.05191157}& {0.}& {0.}& {0.04818272}& {\dots }\\ {-0.00020089}& {0.56385489}& {0.15693243}& {0.}& {0.}& {-0.08564130}& {\dots }\\ {0.00167921}& {0.48362336}& {0.21684512}& {0.}& {0.}& {-0.79644632}& {\dots }\\ {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {}\end{array}\right]\\ \hfill {\text{12 × 12 Matrix}}\end{array}{,}{\mathrm{rdm1}}{=}\begin{array}{c}\left[\begin{array}{ccccccc}{0.20038687}& {0.04941372}& {-0.01572739}& {-0.02161072}& {0.06008214}& {0.00430173}& {\dots }\\ {0.04941372}& {0.01456946}& {0.00586664}& {0.00813944}& {-0.02506726}& {-0.03553764}& {\dots }\\ {-0.01572739}& {0.00586664}& {0.71495481}& {0.59421657}& {-0.17063399}& {-0.15043406}& {\dots }\\ {-0.02161072}& {0.00813944}& {0.59421657}& {0.50708106}& {-0.23408772}& {-0.20760635}& {\dots }\\ {0.06008214}& {-0.02506726}& {-0.17063399}& {-0.23408772}& {0.68512033}& {0.61344619}& {\dots }\\ {0.00430173}& {-0.03553764}& {-0.15043406}& {-0.20760635}& {0.61344619}& {0.56183236}& {\dots }\\ {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {⋮}& {}\end{array}\right]\\ \hfill {\text{12 × 12 Matrix}}\end{array}{,}{\mathrm{group}}{=}{"C1"}{,}{\mathrm{charges}}{=}\left[\begin{array}{c}{0.48429455}\\ {-0.48429455}\end{array}\right]{,}{\mathrm{converged}}{=}{1}{,}{\mathrm{populations}}{=}\begin{array}{c}\left[\begin{array}{c}{0.45802135}\\ {0.05768410}\\ {1.13084493}\\ {0.86372312}\\ {1.00575255}\\ {0.95167518}\\ {⋮}\end{array}\right]\\ \hfill {\text{12 element Vector[column]}}\end{array}{,}{\mathrm{mo_energy}}{=}\begin{array}{c}\left[\begin{array}{c}{-26.28790303}\\ {-1.60084552}\\ {-0.75208982}\\ {-0.64277497}\\ {-0.64277497}\\ {0.21220910}\\ {⋮}\end{array}\right]\\ \hfill {\text{12 element Vector[column]}}\end{array}{,}{\mathrm{mo_occ}}{=}\begin{array}{c}\left[\begin{array}{c}{2.00000000}\\ {2.00000000}\\ {2.00000000}\\ {2.00000000}\\ {2.00000000}\\ {0.}\\ {⋮}\end{array}\right]\\ \hfill {\text{12 element Vector[column]}}\end{array}{,}{\mathrm{dipole}}{=}\left[\begin{array}{c}{6.55819768}{}{{10}}^{{-11}}\\ {4.96783738}{}{{10}}^{{-10}}\\ {-2.38277661}\end{array}\right]{,}{\mathrm{e_tot}}{=}{-100.02197906}{,}{\mathrm{mo_symmetry}}{=}\begin{array}{c}\left[\begin{array}{c}{"A"}\\ {"A"}\\ {"A"}\\ {"A"}\\ {"A"}\\ {"A"}\\ {⋮}\end{array}\right]\\ \hfill {\text{12 element Vector[column]}}\end{array}\right]\right)$ (2)
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