Added spherical harmonic multipoles.

o Permanent and induced moment energies, forces and torques are implemented, for PME direct space.
o The code is activated by a preprocessor macro at the top of AmoebaReferenceMultipoleForce.h, and can be completely disabled.
o Currently, the Cartesian momenents are stored alongside the spherical harmonic moments, but these can eventually be removed when the reciprocal and self terms have been adapted to use spherical harmonics (in progress) and the non-PME routines have been coded.

plugins/amoeba/platforms/reference/src/SimTKReference/AmoebaReferenceMultipoleForce.h

@@ -24,6 +24,9 @@
 #ifndef __AmoebaReferenceMultipoleForce_H__
 #define __AmoebaReferenceMultipoleForce_H__
 
+#define SPHERICAL_MULTIPOLES 1
+#define DEBUG_MULTIPOLES 0
+
 #include "RealVec.h"
 #include "openmm/AmoebaMultipoleForce.h"
 #include "AmoebaReferenceGeneralizedKirkwoodForce.h"
@@ -37,6 +40,19 @@ typedef std::map< unsigned int, RealOpenMM> MapIntRealOpenMM;
 typedef MapIntRealOpenMM::iterator MapIntRealOpenMMI;
 typedef MapIntRealOpenMM::const_iterator MapIntRealOpenMMCI;
 
+
+#if SPHERICAL_MULTIPOLES
+// A few useful constants for the spherical harmonic multipole code.
+const RealOpenMM oneThird = 1.0/3.0;
+const RealOpenMM twoThirds = 2.0/3.0;
+const RealOpenMM fourThirds = 4.0/3.0;
+const RealOpenMM fourSqrtOneThird = 4.0/sqrt(3.0);
+const RealOpenMM oneNinth = 1.0/9.0;
+const RealOpenMM fourOverFortyFive = 4.0/45.0;
+const RealOpenMM fourOverFifteen = 4.0/15.0;
+#endif
+
+
 /**
  * 2-dimensional int vector
  */
@@ -589,6 +605,10 @@ protected:
             RealOpenMM charge;
             RealVec dipole;
             RealOpenMM quadrupole[6];
+#if SPHERICAL_MULTIPOLES
+            RealVec sphericalDipole;
+            RealOpenMM sphericalQuadrupole[5];
+#endif
             RealOpenMM thole;
             RealOpenMM dampingFactor;
             RealOpenMM polarity;
@@ -795,6 +815,31 @@ protected:
                                        const MultipoleParticleData& particleX,
                                              MultipoleParticleData* particleY, int axisType) const;
 
+#if SPHERICAL_MULTIPOLES
+    /**
+     * Forms the rotation matrix for the quasi-internal coordinate system,
+     * which is the rotation matrix that describes the orientation of the
+     * internuclear vector for a given pair (I,J) in lab frame.
+     *
+     * @param particleI             particleI data
+     * @param particleJ             particleJ data
+     * @param r                     the bond length between atoms I and J
+     * @param rotationmatrix        the output rotation matrix for a 3-vector
+     */
+    void formQIRotationMatrix(const MultipoleParticleData& particleI,
+                              const MultipoleParticleData& particleJ,
+                              RealOpenMM r,
+                              RealOpenMM (&rotationMatrix)[3][3]) const;
+
+    /**
+     * Constructs a rotation matrix for spherical harmonic quadrupoles, using the dipole rotation matrix.
+     *
+     * @param D1                    The input spherical harmonic dipole rotation matrix
+     * @param D2                    The output spherical harmonic quadrupole rotation matrix
+     */
+     void buildSphericalQuadrupoleMatrix(const RealOpenMM (&D1)[3][3], RealOpenMM (&D2)[5][5]) const;
+#endif
+
     /**
      * Apply rotation matrix to molecular dipole/quadrupoles to get corresponding lab frame values.
      *