simple.h

大型并行量子化学软件；支持密度泛函（DFT）。可以进行各种量子化学计算。支持CHARMM并行计算。非常具有应用价值。

\f[ \bar{u}_{ab} = \frac{\bar{r}_a - \bar{r}_b}{\| \bar{r}_a - \bar{r}_b \|}\f]
\f[ \bar{u}_{cb} = \frac{\bar{r}_c - \bar{r}_b}{\| \bar{r}_c - \bar{r}_b \|}\f]
\f[ \bar{u}_{cd} = \frac{\bar{r}_c - \bar{r}_d}{\| \bar{r}_c - \bar{r}_b \|}\f]
\f[ \bar{n}_{abc}= \frac{\bar{u}_{ab} \times \bar{u}_{cb}}
                       {\| \bar{u}_{ab} \times \bar{u}_{cb} \|} \f]
\f[ \bar{n}_{bcd}= \frac{\bar{u}_{cd} \times \bar{u}_{bc}}
                       {\| \bar{u}_{cd} \times \bar{u}_{bc} \|} \f]
\f[ s = \left\{
    \begin{array}{ll}
        1 & \mbox{if $(\bar{n}_{abc}\times\bar{n}_{bcd}) \cdot \bar{u}_{cb}
                  > 0;$} \\
       -1 & \mbox{otherwise}
    \end{array} \right.
 \f]
\f[ \tau         = s \arccos ( - \bar{n}_{abc} \cdot \bar{n}_{bcd} ) \f]

*/
class TorsSimpleCo : public SimpleCo { 
SimpleCo_DECLARE(TorsSimpleCo)
  public:
    TorsSimpleCo();
    TorsSimpleCo(const TorsSimpleCo&);
    /** This constructor takes a string containing a label, and four
     integers a, b, c, and d which give the indices of the atoms involved in
     the torsion angle abcd. Atom numbering begins at atom 1, not atom 0. */
    TorsSimpleCo(const char *refr, int, int, int, int);
    /** The KeyVal constructor.  This calls the
        SimpleCo keyval constructor with an integer argument of 4. */
    TorsSimpleCo(const Ref<KeyVal>&);

    ~TorsSimpleCo();

    /// Always returns the string "TORS".
    const char * ctype() const;
    
    /// Returns the value of the angle abc in radians.
    double radians() const;
    /// Returns the value of the angle abc in degrees.
    double degrees() const;
    /// Returns the value of the angle abc in degrees.
    double preferred_value() const;
  };

typedef TorsSimpleCo Tors;

// ///////////////////////////////////////////////////////////////////////

/**
The ScaledTorsSimpleCo class describes an scaled torsion internal
coordinate of a molecule.  The scaled torsion is more stable that ordinary
torsions (see the TorsSimpleCo class) in describing situations
where one of the torsions plane's is given by three near linear atoms.

Designating the four atoms as \f$a\f$, \f$b\f$, \f$c\f$, and \f$d\f$ and
their cartesian positions as \f$\bar{r}_a\f$, \f$\bar{r}_b\f$,
\f$\bar{r}_c\f$, and \f$\bar{r}_d\f$, the value of the coordinate,
\f$\tau_s\f$, is given by

\f[ \bar{u}_{ab} = \frac{\bar{r}_a - \bar{r}_b}{\| \bar{r}_a - \bar{r}_b \|}\f]
\f[ \bar{u}_{cb} = \frac{\bar{r}_c - \bar{r}_b}{\| \bar{r}_c - \bar{r}_b \|}\f]
\f[ \bar{u}_{cd} = \frac{\bar{r}_c - \bar{r}_d}{\| \bar{r}_c - \bar{r}_b \|}\f]
\f[ \bar{n}_{abc}= \frac{\bar{u}_{ab} \times \bar{u}_{cb}}
                       {\| \bar{u}_{ab} \times \bar{u}_{cb} \|}\f]
\f[ \bar{n}_{bcd}= \frac{\bar{u}_{cd} \times \bar{u}_{cb}}
                       {\| \bar{u}_{cd} \times \bar{u}_{cb} \|}\f]
\f[ s = \left\{
    \begin{array}{ll}
      -1 & \mbox{if $(\bar{n}_{abc}\times\bar{n}_{bcd})
                                  \cdot \bar{u}_{cb} > 0$} \\
       1 & \mbox{otherwise}
    \end{array}
    \right.
\f]
\f[ \tau_s       = s \sqrt{\left(1-(\bar{u}_{ab} \cdot \bar{u}_{cb}\right)^2)
                        \left(1-(\bar{u}_{cb} \cdot \bar{u}_{cd}\right)^2)}
                  \arccos ( - \bar{n}_{abc} \cdot \bar{n}_{bcd} )\f]

 */
class ScaledTorsSimpleCo : public SimpleCo { 
SimpleCo_DECLARE(ScaledTorsSimpleCo)
  private:
    double old_torsion_;
  public:
    ScaledTorsSimpleCo();
    ScaledTorsSimpleCo(const ScaledTorsSimpleCo&);
    /** This constructor takes a string containing a label, and four
     integers a, b, c, and d which give the indices of the atoms involved in
     the torsion angle abcd. Atom numbering begins at atom 1, not atom 0. */
    ScaledTorsSimpleCo(const char *refr, int, int, int, int);
    /** The KeyVal constructor.  This calls the
        SimpleCo keyval constructor with an integer argument of 4. */
    ScaledTorsSimpleCo(const Ref<KeyVal>&);

    ~ScaledTorsSimpleCo();

    /// Always returns the string "TORS".
    const char * ctype() const;
    
    /// Returns the value of the angle abc in radians.
    double radians() const;
    /// Returns the value of the angle abc in degrees.
    double degrees() const;
    /// Returns the value of the angle abc in degrees.
    double preferred_value() const;
  };

typedef ScaledTorsSimpleCo ScaledTors;

// ///////////////////////////////////////////////////////////////////////

/*
The OutSimpleCo class describes an out-of-plane internal coordinate
of a molecule.  The input is described in the documentation of its parent
class SimpleCo.

Designating the four atoms as \f$a\f$, \f$b\f$, \f$c\f$, and \f$d\f$ and
their cartesian positions as \f$\bar{r}_a\f$, \f$\bar{r}_b\f$,
\f$\bar{r}_c\f$, and \f$\bar{r}_d\f$, the value of the coordinate,
\f$\tau\f$, is given by

\f[ \bar{u}_{ab} = \frac{\bar{r}_a - \bar{r}_b}{\| \bar{r}_a - \bar{r}_b \|}\f]
\f[ \bar{u}_{cb} = \frac{\bar{r}_b - \bar{r}_c}{\| \bar{r}_c - \bar{r}_b \|}\f]
\f[ \bar{u}_{db} = \frac{\bar{r}_c - \bar{r}_d}{\| \bar{r}_c - \bar{r}_b \|}\f]
\f[ \bar{n}_{bcd}= \frac{\bar{u}_{cb} \times \bar{u}_{db}}
                     {\| \bar{u}_{cb} \times \bar{u}_{db} \|}\f]
\f[ \phi         = \arcsin ( \bar{u}_{ab} \cdot \bar{n}_{bcd} )\f]

*/
class OutSimpleCo : public SimpleCo { 
SimpleCo_DECLARE(OutSimpleCo)
  public:
    OutSimpleCo();
    OutSimpleCo(const OutSimpleCo&);
    /** This constructor takes a string containing a label, and four
     integers a, b, c, and d which give the indices of the atoms involved in
     the out-of-plane angle abcd. Atom numbering begins at atom 1, not
     atom 0. */
    OutSimpleCo(const char *refr, int, int, int, int);
    /** The KeyVal constructor.  This calls the SimpleCo keyval
        constructor with an integer argument of 4. */
    OutSimpleCo(const Ref<KeyVal>&);

    ~OutSimpleCo();

    /// Always returns the string "OUT".
    const char * ctype() const;
    
    /// Returns the value of the angle abc in radians.
    double radians() const;
    /// Returns the value of the angle abc in degrees.
    double degrees() const;
    /// Returns the value of the angle abc in degrees.
    double preferred_value() const;
  };

typedef OutSimpleCo Out;

// ///////////////////////////////////////////////////////////////////////

/** The LinIPSimpleCo class describes an in-plane component of a linear
bend internal coordinate of a molecule.  The input is described in the
documentation of its parent class SimpleCo.  A vector, \f$\bar{u}\f$, given
as the keyword u, that is not colinear with either \f$\bar{r}_a -
\bar{r}_b\f$ or \f$\bar{r}_b - \bar{r}_c\f$ must be provided, where
\f$\bar{r}_a\f$, \f$\bar{r}_b\f$, and \f$\bar{r}_c\f$ are the positions of
the first, second, and third atoms, respectively.

  Usually, LinIPSimpleCo is used with a corresponding LinOPSimpleCo, which
is given exactly the same u.

Designating the three atoms as \f$a\f$, \f$b\f$, and \f$c\f$ and their
cartesian positions as \f$\bar{r}_a\f$, \f$\bar{r}_b\f$, and
\f$\bar{r}_c\f$, the value of the coordinate, \f$\theta_i\f$, is given by

\f[ \bar{u}_{ab} = \frac{\bar{r}_a - \bar{r}_b}{\| \bar{r}_a - \bar{r}_b \|}\f]
\f[ \bar{u}_{cb} = \frac{\bar{r}_b - \bar{r}_c}{\| \bar{r}_c - \bar{r}_b \|}\f]
\f[ \theta_i     = \pi - \arccos ( \bar{u}_{ab} \cdot \bar{u} )
                    - \arccos ( \bar{u}_{cb} \cdot \bar{u} )\f]

*/
class LinIPSimpleCo : public SimpleCo { 
SimpleCo_DECLARE(LinIPSimpleCo)
  private:
    SCVector3 u2;
  public:
    LinIPSimpleCo();
    LinIPSimpleCo(const LinIPSimpleCo&);
    /** This constructor takes a string containing a label, and three
     integers a, b, and d which give the indices of the atoms involved in
     the linear angle abc.  The last argument, u, is a unit vector
     used to defined the direction in which distortion is measured.
     Atom numbering begins at atom 1, not atom 0. */
    LinIPSimpleCo(const char *refr, int, int, int, const SCVector3 &u);
    /** The KeyVal constructor.  This calls the SimpleCo keyval
        constructor with an integer argument of 3. */
    LinIPSimpleCo(const Ref<KeyVal>&);

    ~LinIPSimpleCo();

    /// Always returns the string "LINIP".
    const char * ctype() const;

    /// Returns the value of the angle abc in radians.
    double radians() const;
    /// Returns the value of the angle abc in degrees.
    double degrees() const;
    /// Returns the value of the angle abc in degrees.
    double preferred_value() const;
  };

typedef LinIPSimpleCo LinIP;

// ///////////////////////////////////////////////////////////////////////

/** The LinOPSimpleCo class describes an out-of-plane component of a linear
bend internal coordinate of a molecule.  The input is described in the
documentation of its parent class SimpleCo.  A vector, \f$\bar{u}\f$, given
as the keyword u, that is not colinear with either \f$\bar{r}_a -
\bar{r}_b\f$ or \f$\bar{r}_b - \bar{r}_c\f$ must be provided, where
\f$\bar{r}_a\f$, \f$\bar{r}_b\f$, and \f$\bar{r}_c\f$ are the positions of
the first, second, and third atoms, respectively.

  Usually, LinOPSimpleCo is used with a corresponding LinIPSimpleCo, which
is given exactly the same u.

Designating the three atoms as \f$a\f$, \f$b\f$, and \f$c\f$ and their
cartesian positions as \f$\bar{r}_a\f$, \f$\bar{r}_b\f$, and
\f$\bar{r}_c\f$, the value of the coordinate, \f$\theta_o\f$, is given by


\f[ \bar{u}_{ab} = \frac{\bar{r}_a - \bar{r}_b}{\| \bar{r}_a - \bar{r}_b \|}\f]
\f[ \bar{u}_{cb} = \frac{\bar{r}_b - \bar{r}_c}{\| \bar{r}_c - \bar{r}_b \|}\f]
\f[ \bar{n}      = \frac{\bar{u} \times \bar{u}_{ab}}
                       {\| \bar{u} \times \bar{u}_{ab} \|}\f]
\f[ \theta_o     = \pi - \arccos ( \bar{u}_{ab} \cdot \bar{n} )
                      - \arccos ( \bar{u}_{cb} \cdot \bar{n} )\f]

*/
class LinOPSimpleCo : public SimpleCo { 
SimpleCo_DECLARE(LinOPSimpleCo)
  private:
    SCVector3 u2;
  public:
    LinOPSimpleCo();
    LinOPSimpleCo(const LinOPSimpleCo&);
    /** This constructor takes a string containing a label, and three
     integers a, b, and c which give the indices of the atoms involved in
     the linear angle abc.  The last argument, u, is a unit vector used to
     defined the direction perpendicular to the direction in which
     distortion is measured.  Atom numbering begins at atom 1, not atom 0. */
    LinOPSimpleCo(const char *refr, int, int, int, const SCVector3 &u);
    /** The KeyVal constructor.  This calls the
        SimpleCo keyval constructor with an integer argument of 3. */
    LinOPSimpleCo(const Ref<KeyVal>&);

    ~LinOPSimpleCo();

    /// Always returns the string "LINIP".
    const char * ctype() const;

    /// Returns the value of the angle abc in radians.
    double radians() const;
    /// Returns the value of the angle abc in degrees.
    double degrees() const;
    /// Returns the value of the angle abc in degrees.
    double preferred_value() const;
  };

typedef LinOPSimpleCo LinOP;

}

#endif /* _intco_simple_h */

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