Merge pull request #1101 from peastman/multipoles

Implemented spherical harmonics for multipoles

plugins/amoeba/platforms/cuda/src/AmoebaCudaKernels.cpp

@@ -806,8 +806,8 @@ private:
 
 CudaCalcAmoebaMultipoleForceKernel::CudaCalcAmoebaMultipoleForceKernel(std::string name, const Platform& platform, CudaContext& cu, const System& system) : 
         CalcAmoebaMultipoleForceKernel(name, platform), cu(cu), system(system), hasInitializedScaleFactors(false), hasInitializedFFT(false), multipolesAreValid(false),
-        multipoleParticles(NULL), molecularDipoles(NULL), molecularQuadrupoles(NULL), labFrameDipoles(NULL), labFrameQuadrupoles(NULL), fracDipoles(NULL),
-        fracQuadrupoles(NULL), field(NULL), fieldPolar(NULL), inducedField(NULL), inducedFieldPolar(NULL), torque(NULL), dampingAndThole(NULL), inducedDipole(NULL),
+        multipoleParticles(NULL), molecularDipoles(NULL), molecularQuadrupoles(NULL), labFrameDipoles(NULL), labFrameQuadrupoles(NULL), sphericalDipoles(NULL), sphericalQuadrupoles(NULL),
+        fracDipoles(NULL), fracQuadrupoles(NULL), field(NULL), fieldPolar(NULL), inducedField(NULL), inducedFieldPolar(NULL), torque(NULL), dampingAndThole(NULL), inducedDipole(NULL),
         diisCoefficients(NULL), inducedDipolePolar(NULL), inducedDipoleErrors(NULL), prevDipoles(NULL), prevDipolesPolar(NULL), prevDipolesGk(NULL),
         prevDipolesGkPolar(NULL), prevErrors(NULL), diisMatrix(NULL), polarizability(NULL), covalentFlags(NULL), polarizationGroupFlags(NULL),
         pmeGrid(NULL), pmeBsplineModuliX(NULL), pmeBsplineModuliY(NULL), pmeBsplineModuliZ(NULL), pmeIgrid(NULL), pmePhi(NULL),
@@ -826,6 +826,10 @@ CudaCalcAmoebaMultipoleForceKernel::~CudaCalcAmoebaMultipoleForceKernel() {
         delete labFrameDipoles;
     if (labFrameQuadrupoles != NULL)
         delete labFrameQuadrupoles;
+    if (sphericalDipoles != NULL)
+        delete sphericalDipoles;
+    if (sphericalQuadrupoles != NULL)
+        delete sphericalQuadrupoles;
     if (fracDipoles != NULL)
         delete fracDipoles;
     if (fracQuadrupoles != NULL)
@@ -985,6 +989,8 @@ void CudaCalcAmoebaMultipoleForceKernel::initialize(const System& system, const
     int elementSize = (cu.getUseDoublePrecision() ? sizeof(double) : sizeof(float));
     labFrameDipoles = new CudaArray(cu, 3*paddedNumAtoms, elementSize, "labFrameDipoles");
     labFrameQuadrupoles = new CudaArray(cu, 5*paddedNumAtoms, elementSize, "labFrameQuadrupoles");
+    sphericalDipoles = new CudaArray(cu, 3*paddedNumAtoms, elementSize, "sphericalDipoles");
+    sphericalQuadrupoles = new CudaArray(cu, 5*paddedNumAtoms, elementSize, "sphericalQuadrupoles");
     fracDipoles = new CudaArray(cu, 3*paddedNumAtoms, elementSize, "fracDipoles");
     fracQuadrupoles = new CudaArray(cu, 6*paddedNumAtoms, elementSize, "fracQuadrupoles");
     field = new CudaArray(cu, 3*paddedNumAtoms, sizeof(long long), "field");
@@ -1144,6 +1150,7 @@ void CudaCalcAmoebaMultipoleForceKernel::initialize(const System& system, const
     if (maxInducedIterations > 0) {
         defines["THREAD_BLOCK_SIZE"] = cu.intToString(inducedFieldThreads);
         defines["MAX_PREV_DIIS_DIPOLES"] = cu.intToString(MaxPrevDIISDipoles);
+        defines["USE_MUTUAL_POLARIZATION"] = "1";
         module = cu.createModule(CudaKernelSources::vectorOps+CudaAmoebaKernelSources::multipoleInducedField, defines);
         computeInducedFieldKernel = cu.getKernel(module, "computeInducedField");
         updateInducedFieldKernel = cu.getKernel(module, "updateInducedFieldByDIIS");
@@ -1151,33 +1158,13 @@ void CudaCalcAmoebaMultipoleForceKernel::initialize(const System& system, const
         buildMatrixKernel = cu.getKernel(module, "computeDIISMatrix");
     }
     stringstream electrostaticsSource;
-    if (usePME) {
-        electrostaticsSource << CudaKernelSources::vectorOps;
+    electrostaticsSource << CudaKernelSources::vectorOps;
+    electrostaticsSource << CudaAmoebaKernelSources::sphericalMultipoles;
+    if (usePME)
         electrostaticsSource << CudaAmoebaKernelSources::pmeMultipoleElectrostatics;
-        electrostaticsSource << (hasQuadrupoles ? CudaAmoebaKernelSources::pmeElectrostaticPairForce : CudaAmoebaKernelSources::pmeElectrostaticPairForceNoQuadrupoles);
-        electrostaticsSource << "#define APPLY_SCALE\n";
-        electrostaticsSource << (hasQuadrupoles ? CudaAmoebaKernelSources::pmeElectrostaticPairForce : CudaAmoebaKernelSources::pmeElectrostaticPairForceNoQuadrupoles);
-        electrostaticsThreadMemory = 24*elementSize+3*sizeof(float)+3*sizeof(int)/(double) cu.TileSize;
-        if (!useShuffle)
-            electrostaticsThreadMemory += 3*elementSize;
-    }
-    else {
-        electrostaticsSource << CudaKernelSources::vectorOps;
+    else
         electrostaticsSource << CudaAmoebaKernelSources::multipoleElectrostatics;
-        electrostaticsSource << "#define F1\n";
-        electrostaticsSource << (hasQuadrupoles ? CudaAmoebaKernelSources::electrostaticPairForce : CudaAmoebaKernelSources::electrostaticPairForceNoQuadrupoles);
-        electrostaticsSource << "#undef F1\n";
-        electrostaticsSource << "#define T1\n";
-        electrostaticsSource << (hasQuadrupoles ? CudaAmoebaKernelSources::electrostaticPairForce : CudaAmoebaKernelSources::electrostaticPairForceNoQuadrupoles);
-        electrostaticsSource << "#undef T1\n";
-        electrostaticsSource << "#define T3\n";
-        electrostaticsSource << (hasQuadrupoles ? CudaAmoebaKernelSources::electrostaticPairForce : CudaAmoebaKernelSources::electrostaticPairForceNoQuadrupoles);
-        electrostaticsThreadMemory = 21*elementSize+2*sizeof(float)+3*sizeof(int)/(double) cu.TileSize;
-        if (!useShuffle)
-            electrostaticsThreadMemory += 3*elementSize;
-        if (gk != NULL)
-            electrostaticsThreadMemory += 4*elementSize;
-    }
+    electrostaticsThreadMemory = 24*elementSize+3*sizeof(float)+3*sizeof(int)/(double) cu.TileSize;
     electrostaticsThreads = min(maxThreads, cu.computeThreadBlockSize(electrostaticsThreadMemory));
     defines["THREAD_BLOCK_SIZE"] = cu.intToString(electrostaticsThreads);
     module = cu.createModule(electrostaticsSource.str(), defines);
@@ -1433,7 +1420,8 @@ double CudaCalcAmoebaMultipoleForceKernel::execute(ContextImpl& context, bool in
 
     void* computeMomentsArgs[] = {&cu.getPosq().getDevicePointer(), &multipoleParticles->getDevicePointer(),
         &molecularDipoles->getDevicePointer(), &molecularQuadrupoles->getDevicePointer(),
-        &labFrameDipoles->getDevicePointer(), &labFrameQuadrupoles->getDevicePointer()};
+        &labFrameDipoles->getDevicePointer(), &labFrameQuadrupoles->getDevicePointer(),
+        &sphericalDipoles->getDevicePointer(), &sphericalQuadrupoles->getDevicePointer()};
     cu.executeKernel(computeMomentsKernel, computeMomentsArgs, cu.getNumAtoms());
     int startTileIndex = nb.getStartTileIndex();
     int numTileIndices = nb.getNumTiles();
@@ -1497,8 +1485,8 @@ double CudaCalcAmoebaMultipoleForceKernel::execute(ContextImpl& context, bool in
         void* electrostaticsArgs[] = {&cu.getForce().getDevicePointer(), &torque->getDevicePointer(), &cu.getEnergyBuffer().getDevicePointer(),
             &cu.getPosq().getDevicePointer(), &covalentFlags->getDevicePointer(), &polarizationGroupFlags->getDevicePointer(),
             &nb.getExclusionTiles().getDevicePointer(), &startTileIndex, &numTileIndices,
-            &labFrameDipoles->getDevicePointer(), &labFrameQuadrupoles->getDevicePointer(), &inducedDipole->getDevicePointer(),
-            &inducedDipolePolar->getDevicePointer(), &dampingAndThole->getDevicePointer()};
+            &sphericalDipoles->getDevicePointer(), &sphericalQuadrupoles->getDevicePointer(),
+            &inducedDipole->getDevicePointer(), &inducedDipolePolar->getDevicePointer(), &dampingAndThole->getDevicePointer()};
         cu.executeKernel(electrostaticsKernel, electrostaticsArgs, numForceThreadBlocks*electrostaticsThreads, electrostaticsThreads);
         if (gkKernel != NULL)
             gkKernel->finishComputation(*torque, *labFrameDipoles, *labFrameQuadrupoles, *inducedDipole, *inducedDipolePolar, *dampingAndThole, *covalentFlags, *polarizationGroupFlags);
@@ -1652,8 +1640,8 @@ double CudaCalcAmoebaMultipoleForceKernel::execute(ContextImpl& context, bool in
             &nb.getInteractingTiles().getDevicePointer(), &nb.getInteractionCount().getDevicePointer(),
             cu.getPeriodicBoxSizePointer(), cu.getInvPeriodicBoxSizePointer(), cu.getPeriodicBoxVecXPointer(), cu.getPeriodicBoxVecYPointer(), cu.getPeriodicBoxVecZPointer(),
             &maxTiles, &nb.getBlockCenters().getDevicePointer(), &nb.getInteractingAtoms().getDevicePointer(),
-            &labFrameDipoles->getDevicePointer(), &labFrameQuadrupoles->getDevicePointer(), &inducedDipole->getDevicePointer(),
-            &inducedDipolePolar->getDevicePointer(), &dampingAndThole->getDevicePointer()};
+            &sphericalDipoles->getDevicePointer(), &sphericalQuadrupoles->getDevicePointer(),
+            &inducedDipole->getDevicePointer(), &inducedDipolePolar->getDevicePointer(), &dampingAndThole->getDevicePointer()};
         cu.executeKernel(electrostaticsKernel, electrostaticsArgs, numForceThreadBlocks*electrostaticsThreads, electrostaticsThreads);
         void* pmeTransformInducedPotentialArgs[] = {&pmePhidp->getDevicePointer(), &pmeCphi->getDevicePointer(), recipBoxVectorPointer[0], recipBoxVectorPointer[1], recipBoxVectorPointer[2]};
         cu.executeKernel(pmeTransformPotentialKernel, pmeTransformInducedPotentialArgs, cu.getNumAtoms());

plugins/amoeba/platforms/cuda/src/AmoebaCudaKernels.h

@@ -392,6 +392,8 @@ private:
     CudaArray* molecularQuadrupoles;
     CudaArray* labFrameDipoles;
     CudaArray* labFrameQuadrupoles;
+    CudaArray* sphericalDipoles;
+    CudaArray* sphericalQuadrupoles;
     CudaArray* fracDipoles;
     CudaArray* fracQuadrupoles;
     CudaArray* field;

plugins/amoeba/platforms/cuda/src/kernels/electrostaticPairForceNoQuadrupoles.cu

-/**
- * This defines three different closely related functions, depending on which constant (F1, T1, or T3) is defined.
- */
-
-#if defined F1
-__device__ void computeOneInteractionF1(AtomData& atom1, volatile AtomData& atom2, float dScale, float pScale, float mScale, real& energy, real3& outputForce) {
-#elif defined T1
-__device__ void computeOneInteractionT1(AtomData& atom1, volatile AtomData& atom2, float dScale, float pScale, float mScale, real3& outputForce) {
-#else
-__device__ void computeOneInteractionT3(AtomData& atom1, volatile AtomData& atom2, float dScale, float pScale, float mScale, real3& outputForce) {
-#endif
-    
-#ifdef F1
-    const float uScale = 1;
-    real ddsc3_0 = 0;
-    real ddsc3_1 = 0;
-    real ddsc3_2 = 0;
-
-    real ddsc5_0 = 0;
-    real ddsc5_1 = 0;
-    real ddsc5_2 = 0;
-
-    real ddsc7_0 = 0;
-    real ddsc7_1 = 0;
-    real ddsc7_2 = 0;
-#endif
-
-    real xr = atom2.posq.x - atom1.posq.x;
-    real yr = atom2.posq.y - atom1.posq.y;
-    real zr = atom2.posq.z - atom1.posq.z;
-    
-    real r2 = xr*xr + yr*yr + zr*zr;
-    real r = SQRT(r2);
-    real rr1 = RECIP(r);
-    real rr2 = rr1*rr1;
-    real rr3 = rr1*rr2;
-    real rr5 = 3*rr3*rr2;
-    real rr7 = 5*rr5*rr2;
-    real rr9 = 7*rr7*rr2;
-#ifdef F1
-    real rr11 = 9*rr9*rr2;
-#endif
-
-    real scale3 = 1;
-    real scale5 = 1;
-    real scale7 = 1;
-
-    real pdamp = atom1.damp*atom2.damp;
-    if (pdamp != 0) {
-   
-        real ratio = r/pdamp;
-        float pGamma = atom2.thole > atom1.thole ? atom1.thole : atom2.thole;
-
-        real damp = ratio*ratio*ratio*pGamma;
-        real dampExp = EXP(-damp);
-        real damp1 = damp + 1;
-        real damp2 = damp*damp;
-
-        scale3 = 1 - dampExp;
-        scale5 = 1 - damp1*dampExp;
-        scale7 = 1 - (damp1 + 0.6f*damp2)*dampExp;
-
-#ifdef F1
-        real factor = 3*damp*dampExp*rr2;
-        real factor7 = -0.2f + 0.6f*damp;
-        
-        ddsc3_0 = factor*xr;
-        ddsc5_0 = ddsc3_0*damp;
-        ddsc7_0 = ddsc5_0*factor7;
-
-        ddsc3_1 = factor*yr;
-        ddsc5_1 = ddsc3_1*damp;
-        ddsc7_1 = ddsc5_1*factor7;
-
-        ddsc3_2 = factor*zr;
-        ddsc5_2 = ddsc3_2*damp;
-        ddsc7_2 = ddsc5_2*factor7;
-#endif
-
-    }
-      
-#if defined F1
-    real scale3i = rr3*scale3*uScale;
-    real scale5i = rr5*scale5*uScale;
-#endif
-    real dsc3 = rr3*scale3*dScale;
-    real psc3 = rr3*scale3*pScale;
-
-    real dsc5 = rr5*scale5*dScale;
-    real psc5 = rr5*scale5*pScale;
-
-    real dsc7 = rr7*scale7*dScale;
-    real psc7 = rr7*scale7*pScale;
-
-#if defined F1
-    real sc2 = atom1.dipole.x*atom2.dipole.x + atom1.dipole.y*atom2.dipole.y + atom1.dipole.z*atom2.dipole.z;
-#endif
-#if defined F1 || defined T1
-    real sc4 = atom2.dipole.x*xr + atom2.dipole.y*yr + atom2.dipole.z*zr;
-#endif
-
-#if defined F1 || defined T3
-    real sc3 = atom1.dipole.x*xr + atom1.dipole.y*yr + atom1.dipole.z*zr;
-#endif
-    
-#if defined F1
-    real sci1 = atom1.inducedDipole.x*atom2.dipole.x + atom1.inducedDipole.y*atom2.dipole.y + atom1.inducedDipole.z*atom2.dipole.z +
-                atom2.inducedDipole.x*atom1.dipole.x + atom2.inducedDipole.y*atom1.dipole.y + atom2.inducedDipole.z*atom1.dipole.z;
-#endif
-        
-#if defined F1 || defined T3
-    real sci3 = atom1.inducedDipole.x*xr + atom1.inducedDipole.y*yr + atom1.inducedDipole.z*zr;
-#endif
-#if defined F1 || defined T1
-    real sci4 = atom2.inducedDipole.x*xr + atom2.inducedDipole.y*yr + atom2.inducedDipole.z*zr;
-#endif
-    
-#if defined F1
-    real scip1 = atom1.inducedDipolePolar.x*atom2.dipole.x + atom1.inducedDipolePolar.y*atom2.dipole.y + atom1.inducedDipolePolar.z*atom2.dipole.z +
-                 atom2.inducedDipolePolar.x*atom1.dipole.x + atom2.inducedDipolePolar.y*atom1.dipole.y + atom2.inducedDipolePolar.z*atom1.dipole.z;
-
-    real scip2 = atom1.inducedDipole.x*atom2.inducedDipolePolar.x + atom1.inducedDipole.y*atom2.inducedDipolePolar.y + atom1.inducedDipole.z*atom2.inducedDipolePolar.z +
-                 atom2.inducedDipole.x*atom1.inducedDipolePolar.x + atom2.inducedDipole.y*atom1.inducedDipolePolar.y + atom2.inducedDipole.z*atom1.inducedDipolePolar.z;
-
-#endif
-    
-#if defined F1 || defined T3
-    real scip3 = ((atom1.inducedDipolePolar.x)*(xr) + (atom1.inducedDipolePolar.y)*(yr) + (atom1.inducedDipolePolar.z)*(zr));
-#endif
-#if defined F1 || defined T1
-    real scip4 = ((atom2.inducedDipolePolar.x)*(xr) + (atom2.inducedDipolePolar.y)*(yr) + (atom2.inducedDipolePolar.z)*(zr));
-#endif
-
-#ifdef F1
-    real gli1 = atom2.posq.w*sci3 - atom1.posq.w*sci4;
-    
-    real gli6 = sci1;
-    real glip1 = atom2.posq.w*scip3 - atom1.posq.w*scip4;
-    real glip6 = scip1;
-    real gli2 = -sc3*sci4 - sci3*sc4;
-    
-    real glip2 = -sc3*scip4 - scip3*sc4;
-    real factor3 = rr3*((gli1  +  gli6)*pScale + (glip1  + glip6)*dScale);
-    real factor5 = rr5*(gli2*pScale + glip2*dScale);
-    
-    real ftm2i_0 = -0.5f*(factor3*ddsc3_0 + factor5*ddsc5_0);
-    real ftm2i_1 = -0.5f*(factor3*ddsc3_1 + factor5*ddsc5_1);
-    real ftm2i_2 = -0.5f*(factor3*ddsc3_2 + factor5*ddsc5_2);
-      
-    real gl0 = atom1.posq.w*atom2.posq.w;
-    real gl1 = atom2.posq.w*sc3 - atom1.posq.w*sc4;
-    real gl2 = -sc3*sc4;
-    real gl6 = sc2;
-    
-    real gf1 = rr3*gl0 + rr5*(gl1+gl6) + rr7*gl2;
-#endif
-#if defined F1 || defined T1
-    real gf2 = -atom2.posq.w*rr3 + sc4*rr5;
-    real gf5 = 2*(-atom2.posq.w*rr5+sc4*rr7);
-#endif
-#if defined F1 || defined T3
-    real gf3 =  atom1.posq.w*rr3 + sc3*rr5;
-    real gf6 = 2*(-atom1.posq.w*rr5-sc3*rr7);
-#endif
-
-#ifdef F1
-    real em = mScale*(rr1*gl0 + rr3*(gl1+gl6) + rr5*gl2);
-    real ei = 0.5f*((gli1+gli6)*psc3 + gli2*psc5);
-    energy = em+ei;
-#endif
-    
-#ifdef F1
-    real ftm2_0 = mScale*(gf1*xr + gf2*atom1.dipole.x + gf3*atom2.dipole.x);
-    real ftm2_1 = mScale*(gf1*yr + gf2*atom1.dipole.y + gf3*atom2.dipole.y);
-    real ftm2_2 = mScale*(gf1*zr + gf2*atom1.dipole.z + gf3*atom2.dipole.z);
-
-    real gfi1 = rr2*(1.5f*((gli1+gli6)*psc3 + (glip1+glip6)*dsc3 + scip2*scale3i) + 2.5f*(gli2*psc5 + glip2*dsc5 - (sci3*scip4+scip3*sci4)*scale5i));
-    ftm2i_0 += gfi1*xr;
-    ftm2i_1 += gfi1*yr;
-    ftm2i_2 += gfi1*zr;
-#endif
-
-#if defined F1 || defined T1
-    real gfi5 = (sci4*psc7 + scip4*dsc7);
-#endif
-#if defined F1 || defined T3
-    real gfi6 = -(sci3*psc7 + scip3*dsc7);
-#endif
-
-#ifdef F1
-    ftm2i_0 += 0.5f*(-atom2.posq.w*(atom1.inducedDipole.x*psc3 + atom1.inducedDipolePolar.x*dsc3) +
-               sc4*(atom1.inducedDipole.x*psc5 + atom1.inducedDipolePolar.x*dsc5)) +
-      
-               0.5f*(atom1.posq.w*(atom2.inducedDipole.x*psc3+atom2.inducedDipolePolar.x*dsc3) +
-               sc3*(atom2.inducedDipole.x*psc5 +atom2.inducedDipolePolar.x*dsc5)) +
-
-               scale5i*(sci4*atom1.inducedDipolePolar.x+scip4*atom1.inducedDipole.x +
-                        sci3*atom2.inducedDipolePolar.x+scip3*atom2.inducedDipole.x)*0.5f +
-      
-               0.5f*(sci4*psc5+scip4*dsc5)*atom1.dipole.x +
-               0.5f*(sci3*psc5+scip3*dsc5)*atom2.dipole.x;
-      
-    ftm2i_1 += 0.5f*(-atom2.posq.w*(atom1.inducedDipole.y*psc3 + atom1.inducedDipolePolar.y*dsc3) +
-               sc4*(atom1.inducedDipole.y*psc5 + atom1.inducedDipolePolar.y*dsc5)) +
-
-               (atom1.posq.w*(atom2.inducedDipole.y*psc3+atom2.inducedDipolePolar.y*dsc3) +
-                    sc3*(atom2.inducedDipole.y*psc5+atom2.inducedDipolePolar.y*dsc5))*0.5f +
-                    scale5i*(sci4*atom1.inducedDipolePolar.y+scip4*atom1.inducedDipole.y + sci3*atom2.inducedDipolePolar.y+scip3*atom2.inducedDipole.y)*0.5f +
-
-               0.5f*(sci4*psc5+scip4*dsc5)*atom1.dipole.y +
-               0.5f*(sci3*psc5+scip3*dsc5)*atom2.dipole.y;
-      
-    ftm2i_2 += 0.5f*(-atom2.posq.w*(atom1.inducedDipole.z*psc3 + atom1.inducedDipolePolar.z*dsc3) +
-               sc4*(atom1.inducedDipole.z*psc5 + atom1.inducedDipolePolar.z*dsc5)) +
-
-               (atom1.posq.w*(atom2.inducedDipole.z*psc3+atom2.inducedDipolePolar.z*dsc3) +
-                    sc3*(atom2.inducedDipole.z*psc5+atom2.inducedDipolePolar.z*dsc5))*0.5f +
-                    scale5i*(sci4*atom1.inducedDipolePolar.z+scip4*atom1.inducedDipole.z +
-                    sci3*atom2.inducedDipolePolar.z+scip3*atom2.inducedDipole.z)*0.5f +
-
-               0.5f*(sci4*psc5+scip4*dsc5)*atom1.dipole.z +
-               0.5f*(sci3*psc5+scip3*dsc5)*atom2.dipole.z;
-
-#ifdef DIRECT_POLARIZATION
-    real gfd = 0.5*(3*rr2*scip2*scale3i - 5*rr2*(scip3*sci4+sci3*scip4)*scale5i);
-    real temp5 = 0.5*scale5i;
-    real fdir_0 = gfd*xr + temp5*(sci4*atom1.inducedDipolePolar.x + scip4*atom1.inducedDipole.x + sci3*atom2.inducedDipolePolar.x + scip3*atom2.inducedDipole.x);
-    real fdir_1 = gfd*yr + temp5*(sci4*atom1.inducedDipolePolar.y + scip4*atom1.inducedDipole.y + sci3*atom2.inducedDipolePolar.y + scip3*atom2.inducedDipole.y);
-    real fdir_2 = gfd*zr + temp5*(sci4*atom1.inducedDipolePolar.z + scip4*atom1.inducedDipole.z + sci3*atom2.inducedDipolePolar.z + scip3*atom2.inducedDipole.z);
-    ftm2i_0 -= fdir_0;
-    ftm2i_1 -= fdir_1;
-    ftm2i_2 -= fdir_2;
-#else
-    real scaleF = 0.5f*uScale;
-    real inducedFactor3 = scip2*rr3*scaleF;
-    real inducedFactor5 = (sci3*scip4+scip3*sci4)*rr5*scaleF;
-    real findmp_0 = inducedFactor3*ddsc3_0 - inducedFactor5*ddsc5_0;
-    real findmp_1 = inducedFactor3*ddsc3_1 - inducedFactor5*ddsc5_1;
-    real findmp_2 = inducedFactor3*ddsc3_2 - inducedFactor5*ddsc5_2;
-    ftm2i_0 -= findmp_0;
-    ftm2i_1 -= findmp_1;
-    ftm2i_2 -= findmp_2;
-#endif
-#endif
-
-#if defined T1
-    real gti2 = 0.5f*(sci4*psc5+scip4*dsc5);
-    real gti5 = gfi5;
-#endif
-#if defined T3
-    real gti3 = 0.5f*(sci3*psc5+scip3*dsc5);
-    real gti6 = gfi6;
-#endif
-
-#if defined T1 || defined T3
-    real dixdk_0 = atom1.dipole.y*atom2.dipole.z - atom1.dipole.z*atom2.dipole.y;
-    real dixdk_1 = atom1.dipole.z*atom2.dipole.x - atom1.dipole.x*atom2.dipole.z;
-    real dixdk_2 = atom1.dipole.x*atom2.dipole.y - atom1.dipole.y*atom2.dipole.x;
-
-#if defined T1
-    real dixuk_0 = atom1.dipole.y*atom2.inducedDipole.z - atom1.dipole.z*atom2.inducedDipole.y;
-    real dixuk_1 = atom1.dipole.z*atom2.inducedDipole.x - atom1.dipole.x*atom2.inducedDipole.z;
-    real dixuk_2 = atom1.dipole.x*atom2.inducedDipole.y - atom1.dipole.y*atom2.inducedDipole.x;
-#endif
-#endif
-
-#ifdef T1
-    real dixukp_0 = atom1.dipole.y*atom2.inducedDipolePolar.z - atom1.dipole.z*atom2.inducedDipolePolar.y;
-    real dixukp_1 = atom1.dipole.z*atom2.inducedDipolePolar.x - atom1.dipole.x*atom2.inducedDipolePolar.z;
-    real dixukp_2 = atom1.dipole.x*atom2.inducedDipolePolar.y - atom1.dipole.y*atom2.inducedDipolePolar.x;
-#endif
-
-#ifdef T1
-    real dixr_0 = atom1.dipole.y*zr - atom1.dipole.z*yr;
-    real dixr_1 = atom1.dipole.z*xr - atom1.dipole.x*zr;
-    real dixr_2 = atom1.dipole.x*yr - atom1.dipole.y*xr;
-#endif
-
-#ifdef T1
-    real ttm2_0 = -rr3*dixdk_0 + gf2*dixr_0;
-    real ttm2_1 = -rr3*dixdk_1 + gf2*dixr_1;
-    real ttm2_2 = -rr3*dixdk_2 + gf2*dixr_2;
-
-    real ttm2i_0 = -(dixuk_0*psc3+dixukp_0*dsc3)*0.5f + gti2*dixr_0;
-    real ttm2i_1 = -(dixuk_1*psc3+dixukp_1*dsc3)*0.5f + gti2*dixr_1;
-    real ttm2i_2 = -(dixuk_2*psc3+dixukp_2*dsc3)*0.5f + gti2*dixr_2;
-#endif
-
-#ifdef T3
-    real dkxr_0 = atom2.dipole.y*zr - atom2.dipole.z*yr;
-    real dkxr_1 = atom2.dipole.z*xr - atom2.dipole.x*zr;
-    real dkxr_2 = atom2.dipole.x*yr - atom2.dipole.y*xr;
-
-    real dkxui_0 = atom2.dipole.y*atom1.inducedDipole.z - atom2.dipole.z*atom1.inducedDipole.y;
-    real dkxui_1 = atom2.dipole.z*atom1.inducedDipole.x - atom2.dipole.x*atom1.inducedDipole.z; 
-    real dkxui_2 = atom2.dipole.x*atom1.inducedDipole.y - atom2.dipole.y*atom1.inducedDipole.x;
-
-    real dkxuip_0 = atom2.dipole.y*atom1.inducedDipolePolar.z - atom2.dipole.z*atom1.inducedDipolePolar.y;
-    real dkxuip_1 = atom2.dipole.z*atom1.inducedDipolePolar.x - atom2.dipole.x*atom1.inducedDipolePolar.z;
-    real dkxuip_2 = atom2.dipole.x*atom1.inducedDipolePolar.y - atom2.dipole.y*atom1.inducedDipolePolar.x;
-
-    real ttm3_0 =  rr3*dixdk_0 + gf3*dkxr_0;
-    real ttm3_1 =  rr3*dixdk_1 + gf3*dkxr_1;
-    real ttm3_2 =  rr3*dixdk_2 + gf3*dkxr_2;
-
-    real ttm3i_0 = -(dkxui_0*psc3+ dkxuip_0*dsc3)*0.5f + gti3*dkxr_0;
-    real ttm3i_1 = -(dkxui_1*psc3+ dkxuip_1*dsc3)*0.5f + gti3*dkxr_1;
-    real ttm3i_2 = -(dkxui_2*psc3+ dkxuip_2*dsc3)*0.5f + gti3*dkxr_2;
-#endif
-
-    if (mScale < 1) {
-#ifdef T1
-        ttm2_0 *= mScale;
-        ttm2_1 *= mScale;
-        ttm2_2 *= mScale;
-#endif
-        
-#ifdef T3
-        ttm3_0 *= mScale;
-        ttm3_1 *= mScale;
-        ttm3_2 *= mScale;
-#endif
-    }
-
-#ifdef F1
-    outputForce.x = -(ftm2_0+ftm2i_0);
-    outputForce.y = -(ftm2_1+ftm2i_1);
-    outputForce.z = -(ftm2_2+ftm2i_2);
-#endif
-    
-#ifdef T1
-    outputForce.x = (ttm2_0 + ttm2i_0);
-    outputForce.y = (ttm2_1 + ttm2i_1);
-    outputForce.z = (ttm2_2 + ttm2i_2);
-#endif
-
-#ifdef T3
-    outputForce.x = (ttm3_0 + ttm3i_0);
-    outputForce.y = (ttm3_1 + ttm3i_1);
-    outputForce.z = (ttm3_2 + ttm3i_2);
-#endif
-}

plugins/amoeba/platforms/cuda/src/kernels/multipoles.cu

 extern "C" __global__ void computeLabFrameMoments(real4* __restrict__ posq, int4* __restrict__ multipoleParticles, float* __restrict__ molecularDipoles,
-        float* __restrict__ molecularQuadrupoles, real* __restrict__ labFrameDipoles, real* __restrict__ labFrameQuadrupoles) {
-    // get coordinates of this atom and the z & x axis atoms
-    // compute the vector between the atoms and 1/sqrt(d2), d2 is distance between
-    // this atom and the axis atom
- 
-    // this atom is referred to as the k-atom in notes below
- 
-    // code common to ZThenX and Bisector
-    
+        float* __restrict__ molecularQuadrupoles, real* __restrict__ labFrameDipoles, real* __restrict__ labFrameQuadrupoles,
+        real* __restrict__ sphericalDipoles, real* __restrict__ sphericalQuadrupoles) {
     for (int atom = blockIdx.x*blockDim.x+threadIdx.x; atom < NUM_ATOMS; atom += gridDim.x*blockDim.x) {
+        // Load the spherical multipoles.
+        
+        int offset = 3*atom;
+        sphericalDipoles[offset+0] = molecularDipoles[offset+2]; // z -> Q_10
+        sphericalDipoles[offset+1] = molecularDipoles[offset+0]; // x -> Q_11c
+        sphericalDipoles[offset+2] = molecularDipoles[offset+1]; // y -> Q_11s
+        offset = 5*atom;
+        sphericalQuadrupoles[offset+0] = -3.0f*(molecularQuadrupoles[offset+0]+molecularQuadrupoles[offset+3]); // zz -> Q_20
+        sphericalQuadrupoles[offset+1] = (2*SQRT((real) 3))*molecularQuadrupoles[offset+2]; // xz -> Q_21c
+        sphericalQuadrupoles[offset+2] = (2*SQRT((real) 3))*molecularQuadrupoles[offset+4]; // yz -> Q_21s
+        sphericalQuadrupoles[offset+3] = SQRT((real) 3)*(molecularQuadrupoles[offset+0]-molecularQuadrupoles[offset+3]); // xx-yy -> Q_22c
+        sphericalQuadrupoles[offset+4] = (2*SQRT((real) 3))*molecularQuadrupoles[offset+1]; // xy -> Q_22s
+        
+        // get coordinates of this atom and the z & x axis atoms
+        // compute the vector between the atoms and 1/sqrt(d2), d2 is distance between
+        // this atom and the axis atom
+
+        // this atom is referred to as the k-atom in notes below
+
+        // code common to ZThenX and Bisector
+        
         int4 particles = multipoleParticles[atom];
         if (particles.x >= 0 && particles.z >= 0) {
             real4 thisParticlePos = posq[atom];
@@ -149,7 +163,7 @@ extern "C" __global__ void computeLabFrameMoments(real4* __restrict__ posq, int4
         
             // Transform the dipole
             
-            unsigned int offset = 3*atom;
+            offset = 3*atom;
             real molDipole[3];
             molDipole[0] = molecularDipoles[offset];
             molDipole[1] = molecularDipoles[offset+1];
@@ -192,6 +206,67 @@ extern "C" __global__ void computeLabFrameMoments(real4* __restrict__ posq, int4
             labFrameQuadrupoles[offset+4] = vectorX.y*(vectorX.z*mPoleXX + vectorY.z*mPoleXY + vectorZ.z*mPoleXZ)
                                         + vectorY.y*(vectorX.z*mPoleXY + vectorY.z*mPoleYY + vectorZ.z*mPoleYZ)
                                         + vectorZ.y*(vectorX.z*mPoleXZ + vectorY.z*mPoleYZ + vectorZ.z*mPoleZZ);
+            
+            // ---------------------------------------------------------------------------------------
+            
+            // Now transform the spherical multipoles.  First do the dipoles.
+
+            offset = 3*atom;
+            real sphericalDipole[3];
+            sphericalDipole[0] = sphericalDipoles[offset];
+            sphericalDipole[1] = sphericalDipoles[offset+1];
+            sphericalDipole[2] = sphericalDipoles[offset+2];
+            if (reverse)
+                sphericalDipole[2] *= -1;
+            sphericalDipoles[offset] = sphericalDipole[0]*vectorZ.z + sphericalDipole[1]*vectorX.z + sphericalDipole[2]*vectorY.z;
+            sphericalDipoles[offset+1] = sphericalDipole[0]*vectorZ.x + sphericalDipole[1]*vectorX.x + sphericalDipole[2]*vectorY.x;
+            sphericalDipoles[offset+2] = sphericalDipole[0]*vectorZ.y + sphericalDipole[1]*vectorX.y + sphericalDipole[2]*vectorY.y;
+            
+            // Now the quadrupoles.
+
+            offset = 5*atom;
+            real sphericalQuadrupole[5];
+            sphericalQuadrupole[0] = sphericalQuadrupoles[offset];
+            sphericalQuadrupole[1] = sphericalQuadrupoles[offset+1];
+            sphericalQuadrupole[2] = sphericalQuadrupoles[offset+2];
+            sphericalQuadrupole[3] = sphericalQuadrupoles[offset+3];
+            sphericalQuadrupole[4] = sphericalQuadrupoles[offset+4];
+            if (reverse) {
+                sphericalQuadrupole[2] *= -1;
+                sphericalQuadrupole[4] *= -1;
+            }
+            real rotatedQuadrupole[5] = {0, 0, 0, 0, 0};
+            real sqrtThree = SQRT((real) 3);
+            rotatedQuadrupole[0] += sphericalQuadrupole[0]*0.5f*(3.0f*vectorZ.z*vectorZ.z - 1.0f) +
+                                    sphericalQuadrupole[1]*sqrtThree*vectorZ.z*vectorX.z +
+                                    sphericalQuadrupole[2]*sqrtThree*vectorZ.z*vectorY.z +
+                                    sphericalQuadrupole[3]*0.5f*sqrtThree*(vectorX.z*vectorX.z - vectorY.z*vectorY.z) +
+                                    sphericalQuadrupole[4]*sqrtThree*vectorX.z*vectorY.z;
+            rotatedQuadrupole[1] += sphericalQuadrupole[0]*sqrtThree*vectorZ.z*vectorZ.x +
+                                    sphericalQuadrupole[1]*(vectorZ.x*vectorX.z + vectorZ.z*vectorX.x) +
+                                    sphericalQuadrupole[2]*(vectorZ.x*vectorY.z + vectorZ.z*vectorY.x) +
+                                    sphericalQuadrupole[3]*(vectorX.z*vectorX.x - vectorY.z*vectorY.x) +
+                                    sphericalQuadrupole[4]*(vectorX.x*vectorY.z + vectorX.z*vectorY.x);
+            rotatedQuadrupole[2] += sphericalQuadrupole[0]*sqrtThree*vectorZ.z*vectorZ.y +
+                                    sphericalQuadrupole[1]*(vectorZ.y*vectorX.z + vectorZ.z*vectorX.y) +
+                                    sphericalQuadrupole[2]*(vectorZ.y*vectorY.z + vectorZ.z*vectorY.y) +
+                                    sphericalQuadrupole[3]*(vectorX.z*vectorX.y - vectorY.z*vectorY.y) +
+                                    sphericalQuadrupole[4]*(vectorX.y*vectorY.z + vectorX.z*vectorY.y);
+            rotatedQuadrupole[3] += sphericalQuadrupole[0]*0.5f*sqrtThree*(vectorZ.x*vectorZ.x - vectorZ.y*vectorZ.y) +
+                                    sphericalQuadrupole[1]*(vectorZ.x*vectorX.x - vectorZ.y*vectorX.y) +
+                                    sphericalQuadrupole[2]*(vectorZ.x*vectorY.x - vectorZ.y*vectorY.y) +
+                                    sphericalQuadrupole[3]*0.5f*(vectorX.x*vectorX.x - vectorX.y*vectorX.y - vectorY.x*vectorY.x + vectorY.y*vectorY.y) +
+                                    sphericalQuadrupole[4]*(vectorX.x*vectorY.x - vectorX.y*vectorY.y);
+            rotatedQuadrupole[4] += sphericalQuadrupole[0]*sqrtThree*vectorZ.x*vectorZ.y +
+                                    sphericalQuadrupole[1]*(vectorZ.y*vectorX.x + vectorZ.x*vectorX.y) +
+                                    sphericalQuadrupole[2]*(vectorZ.y*vectorY.x + vectorZ.x*vectorY.y) +
+                                    sphericalQuadrupole[3]*(vectorX.x*vectorX.y - vectorY.x*vectorY.y) +
+                                    sphericalQuadrupole[4]*(vectorX.y*vectorY.x + vectorX.x*vectorY.y);
+            sphericalQuadrupoles[offset] = rotatedQuadrupole[0];
+            sphericalQuadrupoles[offset+1] = rotatedQuadrupole[1];
+            sphericalQuadrupoles[offset+2] = rotatedQuadrupole[2];
+            sphericalQuadrupoles[offset+3] = rotatedQuadrupole[3];
+            sphericalQuadrupoles[offset+4] = rotatedQuadrupole[4];
         }
         else {
             labFrameDipoles[3*atom] = molecularDipoles[3*atom];

plugins/amoeba/platforms/cuda/src/kernels/pmeElectrostaticPairForceNoQuadrupoles.cu

-__device__ void
-#ifdef APPLY_SCALE
-computeOneInteractionF1(
-#else
-computeOneInteractionF1NoScale(
-#endif
-        AtomData& atom1, volatile AtomData& atom2, real4 delta, real4 bn, real bn5, float forceFactor,
-#ifdef APPLY_SCALE
-        float dScale, float pScale, float mScale,
-#endif
-        real3& force, real& energy) {
-    real xr = delta.x;
-    real yr = delta.y;
-    real zr = delta.z;
-#ifdef APPLY_SCALE
-    real rr1 = delta.w;
-#endif
-
-    // set the permanent multipole and induced dipole values;
-
-    real ci = atom1.q;
-
-    real di1 = atom1.dipole.x;
-    real di2 = atom1.dipole.y;
-    real di3 = atom1.dipole.z;
-
-    real ck = atom2.q;
-    real dk1 = atom2.dipole.x;
-    real dk2 = atom2.dipole.y;
-    real dk3 = atom2.dipole.z;
-
-    real bn1 = bn.x;
-    real bn2 = bn.y;
-    real bn3 = bn.z;
-    real bn4 = bn.w;
-
-#ifdef APPLY_SCALE
-    real offset = 1-mScale;
-    real rr3 = rr1*rr1*rr1;
-    real gf4 = 2*(bn2 - 3*offset*rr3*rr1*rr1);
-#else
-    real gf4 = 2*bn2;
-#endif
-    real ftm21 = 0;
-    real ftm22 = 0;
-    real ftm23 = 0;
-
-    // calculate the scalar products for permanent components
-
-    real gl6 = di1*dk1 + di2*dk2 + di3*dk3;
-    real sc3 = di1*xr + di2*yr + di3*zr;
-    real sc4 = dk1*xr + dk2*yr + dk3*zr;
-
-    real gl0 = ci*ck;
-    real gl1 = ck*sc3 - ci*sc4;
-    real gl2 = -sc3*sc4;
-
-#ifdef APPLY_SCALE
-    energy += forceFactor*(-offset*rr1*gl0 + (bn1-offset*rr3)*(gl1+gl6) + (bn2-offset*(3*rr3*rr1*rr1))*gl2);
-#else
-    energy += forceFactor*(bn1*(gl1+gl6) + bn2*gl2);
-    
-#endif
-
-    real gf1 = bn1*gl0 + bn2*(gl1+gl6) + bn3*gl2;
-#ifdef APPLY_SCALE
-    gf1 -= offset*(rr3*gl0 + (3*rr3*rr1*rr1)*(gl1+gl6) + (15*rr3*rr3*rr1)*gl2);
-#endif
-    ftm21 += gf1*xr;
-    ftm22 += gf1*yr;
-    ftm23 += gf1*zr;
-
-#ifdef APPLY_SCALE
-    real gf2 = -ck*bn1 + sc4*bn2 - offset*(-ck*rr3 + sc4*(3*rr3*rr1*rr1));
-#else
-    real gf2 = -ck*bn1 + sc4*bn2;
-#endif
-    ftm21 += gf2*di1;
-    ftm22 += gf2*di2;
-    ftm23 += gf2*di3;
-
-#ifdef APPLY_SCALE
-    real gf3 = ci*bn1 + sc3*bn2 - offset*(ci*rr3 + sc3*(3*rr3*rr1*rr1));
-#else
-    real gf3 = ci*bn1 + sc3*bn2;
-#endif
-    ftm21 += gf3*dk1;
-    ftm22 += gf3*dk2;
-    ftm23 += gf3*dk3;
-
-    force.x = ftm21;
-    force.y = ftm22;
-    force.z = ftm23;
-}
-
-
-__device__ void
-#ifdef APPLY_SCALE
-computeOneInteractionF2(
-#else
-computeOneInteractionF2NoScale(
-#endif
-        AtomData& atom1, volatile AtomData& atom2, real4 delta, real4 bn, float forceFactor,
-#ifdef APPLY_SCALE
-        float dScale, float pScale, float mScale,
-#endif
-        real3& force, real& energy) {
-    const float uScale = 1;
-    real xr = delta.x;
-    real yr = delta.y;
-    real zr = delta.z;
-    real rr1 = delta.w;
-
-    // set the permanent multipole and induced dipole values;
-
-    real ci = atom1.q;
-
-    real di1 = atom1.dipole.x;
-    real di2 = atom1.dipole.y;
-    real di3 = atom1.dipole.z;
-
-    real bn1 = bn.x;
-    real bn2 = bn.y;
-    real bn3 = bn.z;
-    real bn4 = bn.w;
-
-    real damp = atom1.damp*atom2.damp;
-    if (damp != 0) {
-        real pgamma = atom1.thole < atom2.thole ? atom1.thole : atom2.thole;
-        real ratio = RECIP(rr1*damp);
-        damp = -pgamma*ratio*ratio*ratio;
-    }
-
-    real scale5 = (damp == 0) ? 1 : (1 - (1-damp)*EXP(damp));
-    real rr5 = rr1*rr1;
-          rr5 = 3*rr1*rr5*rr5;
-#ifdef APPLY_SCALE
-    real psc5 = rr5*(1 - scale5*pScale);
-    real dsc5 = rr5*(1 - scale5*dScale);
-    real usc5 = rr5*(1 - scale5*uScale);
-#else
-    real psc5 = rr5*(1 - scale5);
-#endif
-
-    real ftm21 = 0;
-    real ftm22 = 0;
-    real ftm23 = 0;
-
-    real expdamp = EXP(damp);
-    real scale3 = (damp == 0) ? 1 : (1 - expdamp);
-    real rr3 = rr1*rr1*rr1;
-
-#ifdef APPLY_SCALE
-    real psc3 = rr3*(1 - scale3*pScale);
-    real dsc3 = rr3*(1 - scale3*dScale);
-    real usc3 = rr3*(1 - scale3*uScale);
-#else
-    real psc3 = rr3*(1 - scale3);
-#endif
-
-    real scale7 = (damp == 0) ? 1 : (1 - (1-damp+0.6f*damp*damp)*expdamp);
-
-#ifdef APPLY_SCALE
-    real psc7 = (15*rr3*rr3*rr1)*(1 - scale7*pScale);
-    real dsc7 = (15*rr3*rr3*rr1)*(1 - scale7*dScale);
-#else
-    real psc7 = (15*rr3*rr3*rr1)*(1 - scale7);
-#endif
-
-    real sc3 = di1*xr + di2*yr + di3*zr;
-    real gfi3 = ci*bn1 + sc3*bn2;
-
-    real prefactor1;
-    prefactor1 = 0.5f*(ci*psc3 + sc3*psc5 - gfi3);
-    ftm21 -= prefactor1*atom2.inducedDipole.x;
-    ftm22 -= prefactor1*atom2.inducedDipole.y;
-    ftm23 -= prefactor1*atom2.inducedDipole.z;
-
-#ifdef APPLY_SCALE
-    prefactor1 = 0.5f*(ci*dsc3 + sc3*dsc5 - gfi3);
-#endif
-    ftm21 -= prefactor1*atom2.inducedDipolePolar.x;
-    ftm22 -= prefactor1*atom2.inducedDipolePolar.y;
-    ftm23 -= prefactor1*atom2.inducedDipolePolar.z;
-
-    real sci4 = atom2.inducedDipole.x*xr + atom2.inducedDipole.y*yr + atom2.inducedDipole.z*zr;
-    energy += forceFactor*0.5f*sci4*((psc3-bn1)*ci + (psc5-bn2)*sc3);
-
-    real scip4 = atom2.inducedDipolePolar.x*xr + atom2.inducedDipolePolar.y*yr + atom2.inducedDipolePolar.z*zr;
-#ifndef DIRECT_POLARIZATION
-#ifdef APPLY_SCALE
-    prefactor1 = 0.5f*(bn2 - usc5);
-#else
-    prefactor1 = 0.5f*(bn2 - psc5);
-#endif
-    ftm21 += prefactor1*((sci4*atom1.inducedDipolePolar.x + scip4*atom1.inducedDipole.x));
-    ftm22 += prefactor1*((sci4*atom1.inducedDipolePolar.y + scip4*atom1.inducedDipole.y));
-    ftm23 += prefactor1*((sci4*atom1.inducedDipolePolar.z + scip4*atom1.inducedDipole.z));
-#endif
-
-#ifdef APPLY_SCALE
-    prefactor1 = 0.5f*(bn2*(sci4+scip4) - (sci4*psc5+scip4*dsc5)); 
-#else
-    sci4 += scip4;
-    prefactor1 = 0.5f*sci4*(bn2 - psc5); 
-#endif
-
-    ftm21 += prefactor1*di1;
-    ftm22 += prefactor1*di2;
-    ftm23 += prefactor1*di3;
-
-#ifdef APPLY_SCALE
-    real gli1 = -ci*sci4;
-    real gli2 = -sc3*sci4;
-    real glip1 = -ci*scip4;
-    real glip2 = -sc3*scip4;
-#else
-    real gli1 = -ci*sci4;
-    real gli2 = -sc3*sci4;
-#endif
-
-#ifdef APPLY_SCALE
-    real gfi1 = (bn2*(gli1+glip1) + bn3*(gli2+glip2));
-    gfi1 -= (rr1*rr1)*(3*(gli1*psc3 + glip1*dsc3) + 5*(gli2*psc5 + glip2*dsc5));
-#else
-    real gfi1 = bn2*gli1 + bn3*gli2;
-    gfi1 -= (rr1*rr1)*(3*gli1*psc3 + 5*gli2*psc5);
-#endif
-    gfi1 *= 0.5f;
-    ftm21 += gfi1*xr;
-    ftm22 += gfi1*yr;
-    ftm23 += gfi1*zr;
-
-    {
-        real expdamp = EXP(damp);
-        real temp3 = -1.5f*damp*expdamp*rr1*rr1;
-        real temp5 = -damp;
-        real temp7 = -0.2f - 0.6f*damp;
-
-        real ddsc31 = temp3*xr;
-        real ddsc32 = temp3*yr;
-        real ddsc33 = temp3*zr;
-
-        real ddsc51 = temp5*ddsc31;
-        real ddsc52 = temp5*ddsc32;
-        real ddsc53 = temp5*ddsc33;
-
-        real ddsc71 = temp7*ddsc51;
-        real ddsc72 = temp7*ddsc52;
-        real ddsc73 = temp7*ddsc53;
-
-        real rr3 = rr1*rr1*rr1;
-#ifdef APPLY_SCALE
-        temp3 = (gli1*pScale + glip1*dScale);
-        temp5 = (3*rr1*rr1)*(gli2*pScale + glip2*dScale);
-#else
-        temp3 = gli1;
-        temp5 = (3*rr1*rr1)*gli2;
-#endif
-        ftm21 -= rr3*(temp3*ddsc31 + temp5*ddsc51);
-        ftm22 -= rr3*(temp3*ddsc32 + temp5*ddsc52);
-        ftm23 -= rr3*(temp3*ddsc33 + temp5*ddsc53);
-    }
-
-//K
-    real dk1 = atom2.dipole.x;
-    real dk2 = atom2.dipole.y;
-    real dk3 = atom2.dipole.z;
-
-    real sc4 =  dk1*xr +  dk2*yr +  dk3*zr;
-
-    real ck = atom2.q;
-    real gfi2 = (-ck*bn1 + sc4*bn2);
-
-    prefactor1 = 0.5f*(ck*psc3 - sc4*psc5 + gfi2);
-    ftm21 += prefactor1*atom1.inducedDipole.x;
-    ftm22 += prefactor1*atom1.inducedDipole.y;
-    ftm23 += prefactor1*atom1.inducedDipole.z;
-
-#ifdef APPLY_SCALE
-    prefactor1 = 0.5f*(ck*dsc3 - sc4*dsc5 + gfi2);
-#endif
-    ftm21 += prefactor1*atom1.inducedDipolePolar.x;
-    ftm22 += prefactor1*atom1.inducedDipolePolar.y;
-    ftm23 += prefactor1*atom1.inducedDipolePolar.z;
-
-    real sci3 = atom1.inducedDipole.x*xr + atom1.inducedDipole.y*yr + atom1.inducedDipole.z*zr;
-    energy += forceFactor*0.5f*sci3*(ck*(bn1-psc3) - sc4*(bn2-psc5));
-    real scip3 = atom1.inducedDipolePolar.x*xr + atom1.inducedDipolePolar.y*yr + atom1.inducedDipolePolar.z*zr;
-
-#ifndef DIRECT_POLARIZATION
-#ifdef APPLY_SCALE
-    prefactor1 = 0.5f*(bn2 - usc5);
-#else
-    prefactor1 = 0.5f*(bn2 - psc5);
-#endif
-
-    ftm21 += prefactor1*(sci3*atom2.inducedDipolePolar.x + scip3*atom2.inducedDipole.x);
-    ftm22 += prefactor1*(sci3*atom2.inducedDipolePolar.y + scip3*atom2.inducedDipole.y);
-    ftm23 += prefactor1*(sci3*atom2.inducedDipolePolar.z + scip3*atom2.inducedDipole.z);
-    
-    real sci34;
-    sci4 = atom2.inducedDipole.x*xr + atom2.inducedDipole.y*yr + atom2.inducedDipole.z*zr;
-    scip4 = atom2.inducedDipolePolar.x*xr + atom2.inducedDipolePolar.y*yr + atom2.inducedDipolePolar.z*zr;
-    sci34 = (sci3*scip4+scip3*sci4);
-
-#ifdef APPLY_SCALE
-    gfi1 = sci34*(usc5*(5*rr1*rr1) -bn3);
-#else
-    gfi1 = sci34*(psc5*(5*rr1*rr1) -bn3);
-#endif
-#else
-    gfi1 = 0;
-#endif
-    
-#ifdef APPLY_SCALE
-    prefactor1 = 0.5f*(bn2*(sci3+scip3) - (sci3*psc5+scip3*dsc5));
-#else
-    sci3 += scip3;
-    prefactor1 = 0.5f*sci3*(bn2 - psc5);
-#endif
-    ftm21 += prefactor1*dk1;
-    ftm22 += prefactor1*dk2;
-    ftm23 += prefactor1*dk3;
-
-#ifdef APPLY_SCALE
-    real gfi6 = -bn3*(sci3+scip3) + (sci3*psc7+scip3*dsc7);
-#else
-    real gfi6 = sci3*(psc7 - bn3);
-#endif
-
-    real sci1 = atom1.inducedDipole.x*dk1 + atom1.inducedDipole.y*dk2 + atom1.inducedDipole.z*dk3 + di1*atom2.inducedDipole.x + di2*atom2.inducedDipole.y + di3*atom2.inducedDipole.z;
-    energy += forceFactor*0.5f*(sci1*(bn1-psc3));
-
-    real scip1 = atom1.inducedDipolePolar.x*dk1 + atom1.inducedDipolePolar.y*dk2 + atom1.inducedDipolePolar.z*dk3 + di1*atom2.inducedDipolePolar.x + di2*atom2.inducedDipolePolar.y + di3*atom2.inducedDipolePolar.z;
-#ifndef APPLY_SCALE
-        sci1 += scip1;
-#endif
-
-    real scip2 = atom1.inducedDipole.x*atom2.inducedDipolePolar.x +
-                                  atom1.inducedDipole.y*atom2.inducedDipolePolar.y +
-                                  atom1.inducedDipole.z*atom2.inducedDipolePolar.z +
-                                  atom2.inducedDipole.x*atom1.inducedDipolePolar.x +
-                                  atom2.inducedDipole.y*atom1.inducedDipolePolar.y +
-                                  atom2.inducedDipole.z*atom1.inducedDipolePolar.z;
-
-           gli1 = ck*sci3 + sci1;
-           gli2 = -sci3*sc4;
-#ifdef APPLY_SCALE
-          glip1 = ck*scip3 + scip1;
-          glip2 = -scip3*sc4;
-#endif
-
-
-#ifdef APPLY_SCALE
-    gfi1 += (bn2*(gli1+glip1) + bn3*(gli2+glip2));
-    gfi1 -= (rr1*rr1)*(3*(gli1*psc3 + glip1*dsc3) + 5*(gli2*psc5 + glip2*dsc5));
-#else
-    gfi1 += (bn2*gli1 + bn3*gli2);
-    gfi1 -= (rr1*rr1)*(3*gli1*psc3 + 5*gli2*psc5);
-#endif
-    
-#ifndef DIRECT_POLARIZATION
-#ifdef APPLY_SCALE
-    gfi1 += scip2*(bn2 - (3*rr1*rr1)*usc3);
-#else
-    gfi1 += scip2*(bn2 - (3*rr1*rr1)*psc3);
-#endif
-#endif
-    
-    gfi1 *= 0.5f;
-
-    ftm21 += gfi1*xr;
-    ftm22 += gfi1*yr;
-    ftm23 += gfi1*zr;
-
-    {
-        real expdamp = EXP(damp);
-        real temp3 = -1.5f*damp*expdamp*rr1*rr1;
-        real temp5 = -damp;
-        real temp7 = -0.2f - 0.6f*damp;
-
-        real ddsc31 = temp3*xr;
-        real ddsc32 = temp3*yr;
-        real ddsc33 = temp3*zr;
-
-        real ddsc51 = temp5*ddsc31;
-        real ddsc52 = temp5*ddsc32;
-        real ddsc53 = temp5*ddsc33;
-
-        real ddsc71 = temp7*ddsc51;
-        real ddsc72 = temp7*ddsc52;
-        real ddsc73 = temp7*ddsc53;
-
-        real rr3 = rr1*rr1*rr1;
-
-#ifdef APPLY_SCALE
-        temp3 = gli1*pScale + glip1*dScale;
-        temp5 = (3*rr1*rr1)*(gli2*pScale + glip2*dScale);
-#else
-        temp3 = gli1;
-        temp5 = (3*rr1*rr1)*gli2;
-#endif
-
-        ftm21 -= rr3*(temp3*ddsc31 + temp5*ddsc51);
-        ftm22 -= rr3*(temp3*ddsc32 + temp5*ddsc52);
-        ftm23 -= rr3*(temp3*ddsc33 + temp5*ddsc53);
-
-#ifndef DIRECT_POLARIZATION
-#ifdef APPLY_SCALE
-        temp3 =  uScale*scip2;
-        temp5 = -(3*rr1*rr1)*uScale*sci34;
-#else
-        temp3 =  scip2;
-        temp5 = -(3*rr1*rr1)*sci34;
-#endif
-        ftm21 -= rr3*(temp3*ddsc31 + temp5*ddsc51);
-        ftm22 -= rr3*(temp3*ddsc32 + temp5*ddsc52);
-        ftm23 -= rr3*(temp3*ddsc33 + temp5*ddsc53);
-#endif
-    }
-
-    force.x += ftm21;
-    force.y += ftm22;
-    force.z += ftm23;
-}
-
-
-__device__ void
-#ifdef APPLY_SCALE
-computeOneInteractionT1(
-#else
-computeOneInteractionT1NoScale(
-#endif
-        AtomData& atom1, volatile AtomData& atom2, const real4 delta, const real4 bn
-#ifdef APPLY_SCALE
-        , float dScale, float pScale, float mScale
-#endif
-        ) {
-
-    real xr = delta.x;
-    real yr = delta.y;
-    real zr = delta.z;
-#ifdef APPLY_SCALE
-    real rr1 = delta.w;
-#endif
-
-    // set the permanent multipole and induced dipole values;
-
-    real di1 = atom1.dipole.x;
-    real di2 = atom1.dipole.y;
-    real di3 = atom1.dipole.z;
-
-    real ck = atom2.q;
-
-    real dk1 = atom2.dipole.x;
-    real dk2 = atom2.dipole.y;
-    real dk3 = atom2.dipole.z;
-
-    real bn1 = bn.x;
-    real bn2 = bn.y;
-    real bn3 = bn.z;
-    real bn4 = bn.w;
-
-    // apply Thole polarization damping to scale factors
-
-#ifdef APPLY_SCALE
-    real rr2 = rr1*rr1;
-    real rr3 = rr1*rr2;
-    real rr5 = 3*rr3*rr2;
-    real rr7 = 5*rr5*rr2;
-    real rr9 = 7*rr7*rr2;
-
-    real scale = 1-mScale;
-    real prefactor = scale*rr3 - bn1;
-#else
-    real prefactor = -bn1;
-#endif
-    real dixdk1 = di2*dk3 - di3*dk2;
-    real ttm21 = prefactor*dixdk1;
-
-    real dixdk2 = di3*dk1 - di1*dk3;
-    real ttm22 = prefactor*dixdk2;
-
-    real dixdk3 = di1*dk2 - di2*dk1;
-    real ttm23 = prefactor*dixdk3;
-
-    real sc4 = dk1*xr + dk2*yr + dk3*zr;
-    real sc6 = 0;
-
-    real gf2 = -ck*bn1 + sc4*bn2;
-#ifdef APPLY_SCALE
-    real gfr2 = -ck*rr3 + sc4*rr5;
-    prefactor = (gf2 - scale*gfr2);
-#else
-    prefactor = gf2;
-#endif
-    ttm21 += prefactor*(di2*zr - di3*yr);
-    ttm22 += prefactor*(di3*xr - di1*zr);
-    ttm23 += prefactor*(di1*yr - di2*xr);
-
-    atom1.torque.x += ttm21;
-    atom1.torque.y += ttm22;
-    atom1.torque.z += ttm23;
-}
-
-
-__device__ void
-#ifdef APPLY_SCALE
-computeOneInteractionT2(
-#else
-computeOneInteractionT2NoScale(
-#endif
-        AtomData& atom1, volatile AtomData& atom2, const real4 delta, const real4 bn
-#ifdef APPLY_SCALE
-        , float dScale, float pScale, float mScale
-#endif
-        ) {
-
-    real xr = delta.x;
-    real yr = delta.y;
-    real zr = delta.z;
-    real rr1 = delta.w;
-
-    // set the permanent multipole and induced dipole values;
-
-    real di1 = atom1.dipole.x;
-    real di2 = atom1.dipole.y;
-    real di3 = atom1.dipole.z;
-
-    real bn1 = bn.x;
-    real bn2 = bn.y;
-    real bn3 = bn.z;
-
-    // apply Thole polarization damping to scale factors
-
-    real scale3 = 1;
-    real scale5 = 1;
-    real scale7 = 1;
-
-    real damp = atom1.damp*atom2.damp;
-    if (damp != 0) {
-        real pgamma = atom1.thole < atom2.thole ? atom1.thole : atom2.thole;
-        real ratio = RECIP(rr1*damp);
-        damp = -pgamma*ratio*ratio*ratio;
-        real expdamp = EXP(damp);
-        scale3 = 1 - expdamp;
-        scale5 = 1 - (1-damp)*expdamp;
-        scale7 = 1 - (1-damp+0.6f*damp*damp)*expdamp;
-    }
-
-    real rr3 = rr1*rr1*rr1;
-#ifdef APPLY_SCALE
-    real dsc3 = rr3*(1 - scale3*dScale);
-    real dsc5 = (3*rr3*rr1*rr1)* (1 - scale5*dScale);
-    real dsc7 = (15*rr3*rr3*rr1)*(1 - scale7*dScale);
-
-    real psc3 = rr3*(1 - scale3*pScale);
-    real psc5 = (3*rr3*rr1*rr1)*(1 - scale5*pScale);
-    real psc7 = (15*rr3*rr3*rr1)*(1 - scale7*pScale);
-#else
-    real psc3 = rr3*(1 - scale3);
-    real psc5 = (3*rr3*rr1*rr1)*(1 - scale5);
-    real psc7 = (15*rr3*rr3*rr1)*(1 - scale7);
-#endif
-
-    real prefactor1 = 0.5f*(psc3 - bn1);
-#ifdef APPLY_SCALE
-    real prefactor2 = 0.5f*(dsc3 - bn1);
-#endif
-
-    real dixuk1 = di2*atom2.inducedDipole.z - di3*atom2.inducedDipole.y;
-    real dixukp1 = di2*atom2.inducedDipolePolar.z - di3*atom2.inducedDipolePolar.y;
-
-#ifdef APPLY_SCALE
-    real ttm2i1 = prefactor1*dixuk1 + prefactor2*dixukp1;
-#else
-    real ttm2i1 = prefactor1*(dixuk1 + dixukp1);
-#endif
-
-    real dixuk2 = di3*atom2.inducedDipole.x - di1*atom2.inducedDipole.z;
-    real dixukp2 = di3*atom2.inducedDipolePolar.x - di1*atom2.inducedDipolePolar.z;
-
-#ifdef APPLY_SCALE
-    real ttm2i2 = prefactor1*dixuk2 + prefactor2*dixukp2;
-#else
-    real ttm2i2 = prefactor1*(dixuk2 + dixukp2);
-#endif
-
-    real dixuk3 = di1*atom2.inducedDipole.y - di2*atom2.inducedDipole.x;
-    real dixukp3 = di1*atom2.inducedDipolePolar.y - di2*atom2.inducedDipolePolar.x;
-#ifdef APPLY_SCALE
-    real ttm2i3 = prefactor1*dixuk3 + prefactor2*dixukp3;
-#else
-    real ttm2i3 = prefactor1*(dixuk3 + dixukp3);
-#endif
-
-    real sci4 = atom2.inducedDipole.x*xr + atom2.inducedDipole.y*yr + atom2.inducedDipole.z*zr;
-    real scip4 = atom2.inducedDipolePolar.x*xr + atom2.inducedDipolePolar.y*yr + atom2.inducedDipolePolar.z*zr;
-    real gti2 = bn2*(sci4+scip4);
-#ifdef APPLY_SCALE
-    real gtri2 = (sci4*psc5+scip4*dsc5);
-#else
-    real gtri2 = psc5*(sci4+scip4);
-#endif
-    prefactor1 = 0.5f*(gti2 - gtri2);
-
-    ttm2i1 += prefactor1*(di2*zr - di3*yr);
-    ttm2i2 += prefactor1*(di3*xr - di1*zr);
-    ttm2i3 += prefactor1*(di1*yr - di2*xr);
-
-    atom1.torque.x += ttm2i1;
-    atom1.torque.y += ttm2i2;
-    atom1.torque.z += ttm2i3;
-}

plugins/amoeba/platforms/cuda/src/kernels/sphericalMultipoles.cu

+__device__ void buildQIRotationMatrix(real3 deltaR, real rInv, real (&rotationMatrix)[3][3]) {
+    real3 vectorZ = deltaR*rInv;
+    real3 vectorX = vectorZ;
+    if (deltaR.y != 0 || deltaR.z != 0)
+        vectorX.x += 1;
+    else
+        vectorX.y += 1;
+
+    vectorX -= vectorZ*dot(vectorX, vectorZ);
+    vectorX = normalize(vectorX);
+    real3 vectorY = cross(vectorZ, vectorX);
+
+    // Reorder the Cartesian {x,y,z} dipole rotation matrix, to account
+    // for spherical harmonic ordering {z,x,y}.
+    rotationMatrix[0][0] = vectorZ.z;
+    rotationMatrix[0][1] = vectorZ.x;
+    rotationMatrix[0][2] = vectorZ.y;
+    rotationMatrix[1][0] = vectorX.z;
+    rotationMatrix[1][1] = vectorX.x;
+    rotationMatrix[1][2] = vectorX.y;
+    rotationMatrix[2][0] = vectorY.z;
+    rotationMatrix[2][1] = vectorY.x;
+    rotationMatrix[2][2] = vectorY.y;
+}
+
+__device__ real3 rotateDipole(real3& dipole, const real (&rotationMatrix)[3][3]) {
+    return make_real3(rotationMatrix[0][0]*dipole.x + rotationMatrix[0][1]*dipole.y + rotationMatrix[0][2]*dipole.z,
+                      rotationMatrix[1][0]*dipole.x + rotationMatrix[1][1]*dipole.y + rotationMatrix[1][2]*dipole.z,
+                      rotationMatrix[2][0]*dipole.x + rotationMatrix[2][1]*dipole.y + rotationMatrix[2][2]*dipole.z);
+}
+
+
+__device__ void rotateQuadupoles(const real (&rotationMatrix)[3][3], const real* quad1, const real* quad2, real* rotated1, real* rotated2) {
+    real sqrtThree = SQRT((real) 3);
+    real element;
+    element = 0.5f*(3.0f*rotationMatrix[0][0]*rotationMatrix[0][0] - 1.0f);
+    rotated1[0] += quad1[0]*element;
+    rotated2[0] += quad2[0]*element;
+    element = sqrtThree*rotationMatrix[0][0]*rotationMatrix[0][1];
+    rotated1[0] += quad1[1]*element;
+    rotated2[0] += quad2[1]*element;
+    element = sqrtThree*rotationMatrix[0][0]*rotationMatrix[0][2];
+    rotated1[0] += quad1[2]*element;
+    rotated2[0] += quad2[2]*element;
+    element = 0.5f*sqrtThree*(rotationMatrix[0][1]*rotationMatrix[0][1] - rotationMatrix[0][2]*rotationMatrix[0][2]);
+    rotated1[0] += quad1[3]*element;
+    rotated2[0] += quad2[3]*element;
+    element = sqrtThree*rotationMatrix[0][1]*rotationMatrix[0][2];
+    rotated1[0] += quad1[4]*element;
+    rotated2[0] += quad2[4]*element;
+    element = sqrtThree*rotationMatrix[0][0]*rotationMatrix[1][0];
+    rotated1[1] += quad1[0]*element;
+    rotated2[1] += quad2[0]*element;
+    element = rotationMatrix[1][0]*rotationMatrix[0][1] + rotationMatrix[0][0]*rotationMatrix[1][1];
+    rotated1[1] += quad1[1]*element;
+    rotated2[1] += quad2[1]*element;
+    element = rotationMatrix[1][0]*rotationMatrix[0][2] + rotationMatrix[0][0]*rotationMatrix[1][2];
+    rotated1[1] += quad1[2]*element;
+    rotated2[1] += quad2[2]*element;
+    element = rotationMatrix[0][1]*rotationMatrix[1][1] - rotationMatrix[0][2]*rotationMatrix[1][2];
+    rotated1[1] += quad1[3]*element;
+    rotated2[1] += quad2[3]*element;
+    element = rotationMatrix[1][1]*rotationMatrix[0][2] + rotationMatrix[0][1]*rotationMatrix[1][2];
+    rotated1[1] += quad1[4]*element;
+    rotated2[1] += quad2[4]*element;
+    element = sqrtThree*rotationMatrix[0][0]*rotationMatrix[2][0];
+    rotated1[2] += quad1[0]*element;
+    rotated2[2] += quad2[0]*element;
+    element = rotationMatrix[2][0]*rotationMatrix[0][1] + rotationMatrix[0][0]*rotationMatrix[2][1];
+    rotated1[2] += quad1[1]*element;
+    rotated2[2] += quad2[1]*element;
+    element = rotationMatrix[2][0]*rotationMatrix[0][2] + rotationMatrix[0][0]*rotationMatrix[2][2];
+    rotated1[2] += quad1[2]*element;
+    rotated2[2] += quad2[2]*element;
+    element = rotationMatrix[0][1]*rotationMatrix[2][1] - rotationMatrix[0][2]*rotationMatrix[2][2];
+    rotated1[2] += quad1[3]*element;
+    rotated2[2] += quad2[3]*element;
+    element = rotationMatrix[2][1]*rotationMatrix[0][2] + rotationMatrix[0][1]*rotationMatrix[2][2];
+    rotated1[2] += quad1[4]*element;
+    rotated2[2] += quad2[4]*element;
+    element = 0.5f*sqrtThree*(rotationMatrix[1][0]*rotationMatrix[1][0] - rotationMatrix[2][0]*rotationMatrix[2][0]);
+    rotated1[3] += quad1[0]*element;
+    rotated2[3] += quad2[0]*element;
+    element = rotationMatrix[1][0]*rotationMatrix[1][1] - rotationMatrix[2][0]*rotationMatrix[2][1];
+    rotated1[3] += quad1[1]*element;
+    rotated2[3] += quad2[1]*element;
+    element = rotationMatrix[1][0]*rotationMatrix[1][2] - rotationMatrix[2][0]*rotationMatrix[2][2];
+    rotated1[3] += quad1[2]*element;
+    rotated2[3] += quad2[2]*element;
+    element = 0.5f*(rotationMatrix[1][1]*rotationMatrix[1][1] - rotationMatrix[2][1]*rotationMatrix[2][1] - rotationMatrix[1][2]*rotationMatrix[1][2] + rotationMatrix[2][2]*rotationMatrix[2][2]);
+    rotated1[3] += quad1[3]*element;
+    rotated2[3] += quad2[3]*element;
+    element = rotationMatrix[1][1]*rotationMatrix[1][2] - rotationMatrix[2][1]*rotationMatrix[2][2];
+    rotated1[3] += quad1[4]*element;
+    rotated2[3] += quad2[4]*element;
+    element = sqrtThree*rotationMatrix[1][0]*rotationMatrix[2][0];
+    rotated1[4] += quad1[0]*element;
+    rotated2[4] += quad2[0]*element;
+    element = rotationMatrix[2][0]*rotationMatrix[1][1] + rotationMatrix[1][0]*rotationMatrix[2][1];
+    rotated1[4] += quad1[1]*element;
+    rotated2[4] += quad2[1]*element;
+    element = rotationMatrix[2][0]*rotationMatrix[1][2] + rotationMatrix[1][0]*rotationMatrix[2][2];
+    rotated1[4] += quad1[2]*element;
+    rotated2[4] += quad2[2]*element;
+    element = rotationMatrix[1][1]*rotationMatrix[2][1] - rotationMatrix[1][2]*rotationMatrix[2][2];
+    rotated1[4] += quad1[3]*element;
+    rotated2[4] += quad2[3]*element;
+    element = rotationMatrix[2][1]*rotationMatrix[1][2] + rotationMatrix[1][1]*rotationMatrix[2][2];
+    rotated1[4] += quad1[4]*element;
+    rotated2[4] += quad2[4]*element;
+}

plugins/amoeba/platforms/cuda/tests/TestCudaAmoebaGeneralizedKirkwoodForce.cpp

@@ -6980,7 +6980,7 @@ static void compareForcesEnergy(std::string& testName, double expectedEnergy, do
                                 const std::vector<Vec3>& expectedForces,
                                 const std::vector<Vec3>& forces, double tolerance) {
     for (unsigned int ii = 0; ii < forces.size(); ii++) {
-        ASSERT_EQUAL_VEC_MOD(expectedForces[ii], forces[ii], tolerance, testName);
+        ASSERT_EQUAL_VEC(expectedForces[ii], forces[ii], tolerance);
     }
     ASSERT_EQUAL_TOL_MOD(expectedEnergy, energy, tolerance, testName);
 }

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

@@ -37,6 +37,20 @@ typedef std::map< unsigned int, RealOpenMM> MapIntRealOpenMM;
 typedef MapIntRealOpenMM::iterator MapIntRealOpenMMI;
 typedef MapIntRealOpenMM::const_iterator MapIntRealOpenMMCI;
 
+
+// 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 sqrtFourThirds = 2.0/sqrt(3.0);
+const RealOpenMM sqrtOneThird = 1.0/sqrt(3.0);
+const RealOpenMM sqrtThree = sqrt(3.0);
+const RealOpenMM oneNinth = 1.0/9.0;
+const RealOpenMM fourOverFortyFive = 4.0/45.0;
+const RealOpenMM fourOverFifteen = 4.0/15.0;
+
+
 /**
  * 2-dimensional int vector
  */
@@ -589,6 +603,8 @@ protected:
             RealOpenMM charge;
             RealVec dipole;
             RealOpenMM quadrupole[6];
+            RealVec sphericalDipole;
+            RealOpenMM sphericalQuadrupole[5];
             RealOpenMM thole;
             RealOpenMM dampingFactor;
             RealOpenMM polarity;
@@ -795,6 +811,41 @@ protected:
                                        const MultipoleParticleData& particleX,
                                              MultipoleParticleData* particleY, int axisType) const;
 
+    /**
+     * 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 position
+     * @param particleJ             particleJ position
+     * @param deltaR                the internuclear vector, corrected for periodic boundary conditions
+     * @param r                     the bond length between atoms I and J
+     * @param rotationmatrix        the output rotation matrix for a 3-vector
+     */
+    void formQIRotationMatrix(const RealVec& iPosition,
+                              const RealVec& jPosition,
+                              const RealVec &deltaR,
+                              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 buildSphericalQuadrupoleRotationMatrix(const RealOpenMM (&D1)[3][3], RealOpenMM (&D2)[5][5]) const;
+
+     /**
+      * Constructs a rotation matrix for spherical harmonic quadrupoles, using the dipole rotation matrix.
+      * Only the m={0,1c,1s} terms are constructed; these are the only terms needed to evaluate the field.
+      *
+      * @param D1                    The input spherical harmonic dipole rotation matrix
+      * @param D2                    The output spherical harmonic quadrupole rotation matrix
+      */
+      void buildPartialSphericalQuadrupoleRotationMatrix(const RealOpenMM (&D1)[3][3], RealOpenMM (&D2)[3][5]) const;
+
     /**
      * Apply rotation matrix to molecular dipole/quadrupoles to get corresponding lab frame values.
      * 

plugins/amoeba/platforms/reference/tests/TestReferenceAmoebaGeneralizedKirkwoodForce.cpp

@@ -6983,7 +6983,7 @@ static void compareForcesEnergy(std::string& testName, double expectedEnergy, do
                                 const std::vector<Vec3>& forces, double tolerance) {
     for (unsigned int ii = 0; ii < forces.size(); ii++) {
-        ASSERT_EQUAL_VEC_MOD(expectedForces[ii], forces[ii], tolerance, testName);
+        ASSERT_EQUAL_VEC(expectedForces[ii], forces[ii], tolerance);
     }
     ASSERT_EQUAL_TOL_MOD(expectedEnergy, energy, tolerance, testName);
 }