
{"id":1851,"date":"2025-05-22T10:39:22","date_gmt":"2025-05-22T07:39:22","guid":{"rendered":"https:\/\/www.ucy.ac.cy\/biophysmolphys\/?page_id=1851"},"modified":"2025-05-22T10:39:22","modified_gmt":"2025-05-22T07:39:22","slug":"ctrate-m","status":"publish","type":"page","link":"https:\/\/www.ucy.ac.cy\/biophysmolphys\/ctrate-m\/","title":{"rendered":"CTrate.m"},"content":{"rendered":"<p>1\u00a0\u00a0\u00a0\u00a0 clear<\/p>\n<p>2\u00a0\u00a0\u00a0\u00a0 % This program computes the overall donor-to-acceptor<\/p>\n<p>3\u00a0\u00a0\u00a0\u00a0 % transfer time<\/p>\n<p>4\u00a0\u00a0\u00a0\u00a0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n<p>5\u00a0\u00a0\u00a0\u00a0 % Inputs related to building rate matrix<\/p>\n<p>6\u00a0\u00a0\u00a0\u00a0 hbar=0.6582*10^(-3); % in eV psec<\/p>\n<p>7\u00a0\u00a0\u00a0\u00a0 kb=0.02586\/300;\u00a0\u00a0\u00a0\u00a0\u00a0 % in eV\/Kelvin<\/p>\n<p>8\u00a0\u00a0\u00a0\u00a0 n=5;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % number of states<\/p>\n<p>9\u00a0\u00a0\u00a0\u00a0 % temperature index to pick temp from temprange vector<\/p>\n<p>10\u00a0\u00a0\u00a0 tempindex=3;<\/p>\n<p>11\u00a0\u00a0\u00a0 ened=0;\u00a0\u00a0\u00a0\u00a0\u00a0 % donor (d) site energy (eV)<\/p>\n<p>12\u00a0\u00a0\u00a0 enea=ened;\u00a0\u00a0 % unbiased acceptor (a) site energy (eV)<\/p>\n<p>13\u00a0\u00a0\u00a0 enebr=0.2;\u00a0\u00a0 % unbiazed bridge site energy (eV)<\/p>\n<p>14\u00a0\u00a0\u00a0 vdb=0.1;\u00a0\u00a0\u00a0\u00a0 % donor-bridge electronic coupling (eV)<\/p>\n<p>15\u00a0\u00a0\u00a0 vba=vdb;\u00a0\u00a0\u00a0\u00a0 % acceptor-bridge electronic coupling (eV)<\/p>\n<p>16\u00a0\u00a0\u00a0 vbb=0.01;\u00a0\u00a0\u00a0 % bridge-bridge electronic coupling (eV)<\/p>\n<p>17\u00a0\u00a0\u00a0 dgda=0.0;\u00a0\u00a0\u00a0 % overal free energy bias between d and a (eV)<\/p>\n<p>18\u00a0\u00a0\u00a0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n<p>19\u00a0\u00a0\u00a0 % Inputs related to time evolution<\/p>\n<p>20\u00a0\u00a0\u00a0 nt=10^(6);\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % number of time steps<\/p>\n<p>21\u00a0\u00a0\u00a0 tin=0.0;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % initial time<\/p>\n<p>22\u00a0\u00a0\u00a0 tfinalfact=1*10^(5); % determines tfinal<\/p>\n<p>23\u00a0\u00a0\u00a0 % initial probability distribution vector vec(P)(t=0)<\/p>\n<p>24\u00a0\u00a0\u00a0 p0=zeros(n,1);<\/p>\n<p>25\u00a0\u00a0\u00a0 % Set initial condition P_i(t=0)=delta_i,a<\/p>\n<p>26\u00a0\u00a0\u00a0 p0(1)=1.;<\/p>\n<p>27\u00a0\u00a0\u00a0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n<p>28\u00a0\u00a0\u00a0 % Initializing variables to build the rate matrix<\/p>\n<p>29\u00a0\u00a0\u00a0 ene=zeros(1,n);\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % unbiased site-energies vector<\/p>\n<p>30\u00a0\u00a0\u00a0 voltbias=zeros(1,n);\u00a0\u00a0 % voltage bias profile vector<\/p>\n<p>31\u00a0\u00a0\u00a0 % biased site-energies vector = unbiased + voltage bias<\/p>\n<p>32\u00a0\u00a0\u00a0 enebias=zeros(1,n);<\/p>\n<p>33\u00a0\u00a0\u00a0 % dgnn(i)=enebias(i+1)-enebias(i) nn&#8217;site enrgy gap vector<\/p>\n<p>34\u00a0\u00a0\u00a0 dgnn=zeros(1,n-1);<\/p>\n<p>35\u00a0\u00a0\u00a0 coupl=zeros(1,n-1);\u00a0\u00a0\u00a0 % nearest-neighbor couplings<\/p>\n<p>36\u00a0\u00a0\u00a0 kforw=zeros(1,n-1);\u00a0\u00a0\u00a0 % quantum forward rates vector<\/p>\n<p>37\u00a0\u00a0\u00a0 kbackw=zeros(1,n-1);\u00a0\u00a0 % quantum\u00a0 backward rates vector<\/p>\n<p>38\u00a0\u00a0\u00a0 clkforw=zeros(1,n-1);\u00a0 % clasical forward rates\u00a0 vector<\/p>\n<p>39\u00a0\u00a0\u00a0 clkbackw=zeros(1,n-1); % classical\u00a0 backward rates vector<\/p>\n<p>40\u00a0\u00a0\u00a0 kforwda=zeros(1,n-1);<\/p>\n<p>41\u00a0\u00a0\u00a0 kbackwda=zeros(1,n-1);<\/p>\n<p>42\u00a0\u00a0\u00a0 clkforwda=zeros(1,n-1);<\/p>\n<p>43\u00a0\u00a0\u00a0 clkbackwda=zeros(1,n-1);<\/p>\n<p>44\u00a0\u00a0\u00a0 % index used to pick energy gap values hbarw=dgnn(i) and<\/p>\n<p>45\u00a0\u00a0\u00a0 % corresponding FC factors at dgnn(i) (quantum and<\/p>\n<p>46\u00a0\u00a0\u00a0 % clasical) from fcond &amp; fcondcl files produced by<\/p>\n<p>47\u00a0\u00a0\u00a0 % FCprodOCT21.m program<\/p>\n<p>48\u00a0\u00a0\u00a0 indexe=zeros(1,n-1);<\/p>\n<p>49\u00a0\u00a0\u00a0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n<p>50\u00a0\u00a0\u00a0 % Initalizing variables\u00a0 related to time evolution of<\/p>\n<p>51\u00a0\u00a0\u00a0 % probabilities<\/p>\n<p>52\u00a0\u00a0\u00a0 tvec=zeros(1,nt);\u00a0\u00a0\u00a0\u00a0\u00a0 % time vector given nt<\/p>\n<p>53\u00a0\u00a0\u00a0 pvec=zeros(1,nt);\u00a0\u00a0\u00a0\u00a0\u00a0 % 1st (d) state time-dep prob P_d(t)<\/p>\n<p>54\u00a0\u00a0\u00a0 p2vec=zeros(1,nt);\u00a0\u00a0\u00a0\u00a0 % nth (a) state time-dep prob P_a(t)<\/p>\n<p>55\u00a0\u00a0\u00a0 pt=zeros(n,1);\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % time dep prob distr vect vec(P)(t)<\/p>\n<p>56\u00a0\u00a0\u00a0 w=zeros(n,n);\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % Initializing rate matrix<\/p>\n<p>57\u00a0\u00a0\u00a0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n<p>58\u00a0\u00a0\u00a0 % Hamiltonian parameters given inputs<\/p>\n<p>59\u00a0\u00a0\u00a0 ene(1)=ened;<\/p>\n<p>60\u00a0\u00a0\u00a0 ene(n)=enea;<\/p>\n<p>61\u00a0\u00a0\u00a0 ene(2:n-1)=enebr;<\/p>\n<p>62\u00a0\u00a0\u00a0 coupl(1)=vdb;<\/p>\n<p>63\u00a0\u00a0\u00a0 coupl(n-1)=vba;<\/p>\n<p>64\u00a0\u00a0\u00a0 coupl(2:n-2)=vbb;<\/p>\n<p>65\u00a0\u00a0\u00a0 for i=2:n<\/p>\n<p>66\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 bias(i)=(i-1)*dgda\/(n-1);<\/p>\n<p>67\u00a0\u00a0\u00a0 end<\/p>\n<p>68\u00a0\u00a0\u00a0 enebias=ene+bias;<\/p>\n<p>69\u00a0\u00a0\u00a0 for i=1:n-1<\/p>\n<p>70\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 dgnn(i)=enebias(i+1)-enebias(i);<\/p>\n<p>71\u00a0\u00a0\u00a0 end<\/p>\n<p>72\u00a0\u00a0\u00a0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n<p>73<\/p>\n<p>74\u00a0\u00a0\u00a0 % Loading temperatures, and precomputed 2*pi*hbar*FC<\/p>\n<p>75\u00a0\u00a0\u00a0 mydata=load(&#8216;temperature.mat&#8217;,&#8217;temprange&#8217;);<\/p>\n<p>76\u00a0\u00a0\u00a0 temprange=mydata.temprange;<\/p>\n<p>77\u00a0\u00a0\u00a0 % precomputed quantum 2*pi*hbar*FC to be used for computing<\/p>\n<p>78\u00a0\u00a0\u00a0 % bridge-bridge quantum rate, donor=bridge molecule,<\/p>\n<p>79\u00a0\u00a0\u00a0 % acceptor=bridge molecule<\/p>\n<p>80\u00a0\u00a0\u00a0 mydata2=load(&#8216;fc_bb_hbgamma0point001.mat&#8217;,&#8217;fcond&#8217;);<\/p>\n<p>81\u00a0\u00a0\u00a0 fcondbb=mydata2.fcond;<\/p>\n<p>82\u00a0\u00a0\u00a0 % precomputed classical 2*pi*hbar*FC(classical) to be used<\/p>\n<p>83\u00a0\u00a0\u00a0 % for computing bridge-bridge classical rate<\/p>\n<p>84\u00a0\u00a0\u00a0 mydata3=load(&#8216;fccl_bb_hbgamma0point001.mat&#8217;,&#8217;fcondcl&#8217;);<\/p>\n<p>85\u00a0\u00a0\u00a0 fcondclbb=mydata3.fcondcl;<\/p>\n<p>86\u00a0\u00a0\u00a0 % precomputed quantum 2*pi*hbar*FC, to be used<\/p>\n<p>87\u00a0\u00a0\u00a0 % for donor-acceptor rates<\/p>\n<p>88\u00a0\u00a0\u00a0 mydata4=load(&#8216;fc_da_hbgamma0point001.mat&#8217;,&#8217;fcond&#8217;);<\/p>\n<p>89\u00a0\u00a0\u00a0 fcondda=mydata4.fcond;<\/p>\n<p>90\u00a0\u00a0\u00a0 % precomputed classical 2*pi*hbar*FC, to be used<\/p>\n<p>91\u00a0\u00a0\u00a0 % for donor-acceptor rates<\/p>\n<p>92\u00a0\u00a0\u00a0 mydata5=load(&#8216;fccl_da_hbgamma0point001.mat&#8217;,&#8217;fcondcl&#8217;);<\/p>\n<p>93\u00a0\u00a0\u00a0 fcondclda=mydata5.fcondcl;<\/p>\n<p>94\u00a0\u00a0\u00a0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n<p>95<\/p>\n<p>96\u00a0\u00a0\u00a0 % forward quantum and classical rates for all site to site<\/p>\n<p>97\u00a0\u00a0\u00a0 % energy gaps defined in dgnn<\/p>\n<p>98\u00a0\u00a0\u00a0 % BRIDGE &#8211; BRIDGE RATES<\/p>\n<p>99\u00a0\u00a0\u00a0 hbarw_bb = fcondbb(1,:);<\/p>\n<p>100\u00a0\u00a0 for i=2:n-2<\/p>\n<p>101\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % pick dgnn values for hbarw which corresponds to the<\/p>\n<p>102\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % energy gap between each bridge site and also extract<\/p>\n<p>103\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % 2*pi*hbar*FC factors for the dgnn(i) and compute<\/p>\n<p>104\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % corresponding rates<\/p>\n<p>105\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 [abs1,indexe(i-1)] = min(abs(hbarw_bb &#8211; dgnn(i)));<\/p>\n<p>106\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % quantum rates at temperature picked by tempindex<\/p>\n<p>107\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 kforw(i)=((coupl(i)\/hbar)^2)*&#8230;<\/p>\n<p>108\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (fcondbb(tempindex+1,indexe(i-1)));<\/p>\n<p>109\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 kbackw(i)=kforw(i)*(exp(dgnn(i)\/&#8230;<\/p>\n<p>110\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (kb*temprange(tempindex))));<\/p>\n<p>111\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % classical marcus rates at temp picked by tempindex<\/p>\n<p>112\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 clkforw(i)=((coupl(i)\/hbar)^2)*&#8230;<\/p>\n<p>113\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (fcondclbb(tempindex+1,indexe(i-1)));<\/p>\n<p>114\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 clkbackw(i)=clkforw(i)*(exp(dgnn(i)\/&#8230;<\/p>\n<p>115\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (kb*temprange(tempindex))));<\/p>\n<p>116\u00a0\u00a0 end<\/p>\n<p>117\u00a0\u00a0 % DONOR-BRIDGE quantum rates<\/p>\n<p>118\u00a0\u00a0 hbarw_db = fcondda(1,:);<\/p>\n<p>119\u00a0\u00a0 % pick dgnn values for hbarw which corresponds to the<\/p>\n<p>120\u00a0\u00a0 % energy gap between donor &amp; bridge site<\/p>\n<p>121\u00a0\u00a0 [abs2,indexe2] = min(abs(hbarw_db-dgnn(1)));<\/p>\n<p>122\u00a0\u00a0 kforwdb=((coupl(1)\/hbar)^2)*(fcondda(tempindex+1,indexe2));<\/p>\n<p>123\u00a0\u00a0 kbackwdb=kforwdb*(exp(dgnn(1)\/(kb*temprange(tempindex))));<\/p>\n<p>124\u00a0\u00a0 % BRIDGE-ACCEPTOR quantum rates<\/p>\n<p>125\u00a0\u00a0 % pick dgnn values for hbarw which corresponds to the<\/p>\n<p>126\u00a0\u00a0 % energy gap between bridge &amp; acceptor site<\/p>\n<p>127\u00a0\u00a0 [abs3,indexe3] = min(abs(hbarw_db-dgnn(n-1)));<\/p>\n<p>128\u00a0\u00a0 kforwba=((coupl(n-1)\/hbar)^2)*&#8230;<\/p>\n<p>129\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (fcondda(tempindex+1,indexe3));<\/p>\n<p>130\u00a0\u00a0 kbackwba=kforwba*(exp(dgnn(n-1)\/&#8230;<\/p>\n<p>131\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (kb*temprange(tempindex))));<\/p>\n<p>132\u00a0\u00a0 % DONOR-BRIDGE classical rates<\/p>\n<p>133\u00a0\u00a0 hbarw_db_cl = fcondclda(1,:);<\/p>\n<p>134\u00a0\u00a0 [abs4,indexe4] = min(abs(hbarw_db-dgnn(1)));<\/p>\n<p>135\u00a0\u00a0 clkforwdb=((coupl(1)\/hbar)^2)*&#8230;<\/p>\n<p>136\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (fcondclda(tempindex+1,indexe4));<\/p>\n<p>137\u00a0\u00a0 clkbackwdb=clkforwdb*(exp(dgnn(1)\/&#8230;<\/p>\n<p>138\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (kb*temprange(tempindex))));<\/p>\n<p>139\u00a0\u00a0 % BRIDGE-ACCEPTOR classical<\/p>\n<p>140\u00a0\u00a0 [abs5,indexe5] = min(abs(hbarw_db-dgnn(n-1)));<\/p>\n<p>141\u00a0\u00a0 clkforwba=((coupl(n-1)\/hbar)^2)*&#8230;<\/p>\n<p>142\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (fcondclda(tempindex+1,indexe5));<\/p>\n<p>143\u00a0\u00a0 clkbackwba=clkforwba*(exp(dgnn(n-1)\/&#8230;<\/p>\n<p>144\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (kb*temprange(tempindex))));<\/p>\n<p>145\u00a0\u00a0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n<p>146<\/p>\n<p>147\u00a0\u00a0 % Kinetic matrix (W)<\/p>\n<p>148\u00a0\u00a0 % Nonzero off-diagonal elements<\/p>\n<p>149\u00a0\u00a0 for j=1:n-1<\/p>\n<p>150\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 w(j+1,j) = kforw(j);<\/p>\n<p>151\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 w(j,j+1) = kbackw(j);<\/p>\n<p>152\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % w(j+1,j) = clkforw(j);<\/p>\n<p>153\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 % w(j,j+1) = clkbackw(j);<\/p>\n<p>154\u00a0\u00a0 end<\/p>\n<p>155\u00a0\u00a0 % overwriting with d-b\/b0a rates<\/p>\n<p>156\u00a0\u00a0 w(2,1)=kforwdb;<\/p>\n<p>157\u00a0\u00a0 w(1,2)=kbackwdb;<\/p>\n<p>158\u00a0\u00a0 w(n,n-1)=kforwba;<\/p>\n<p>159\u00a0\u00a0 w(n-1,n)=kbackwba;<\/p>\n<p>160\u00a0\u00a0 % w(2,1)=clkforwdb;<\/p>\n<p>161\u00a0\u00a0 % w(1,2)=clkbackwdb;<\/p>\n<p>162\u00a0\u00a0 % w(n,n-1)=clkforwba;<\/p>\n<p>163\u00a0\u00a0 % w(n-1,n)=clkbackwba;<\/p>\n<p>164\u00a0\u00a0 % diagonal elements<\/p>\n<p>165\u00a0\u00a0 for j=2:n-1<\/p>\n<p>166\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 w(j,j) = -w(j+1,j)-w(j-1,j);<\/p>\n<p>167\u00a0\u00a0 end<\/p>\n<p>168\u00a0\u00a0 w(1,1)= -w(2,1);<\/p>\n<p>169\u00a0\u00a0 w(n,n)= -w(n-1,n);<\/p>\n<p>170\u00a0\u00a0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n<p>171\u00a0\u00a0 % find the eigevectors &amp; eigenvalues of rate matrix<\/p>\n<p>172\u00a0\u00a0 [V,D]=eig(w);<\/p>\n<p>173\u00a0\u00a0 s=diag(D);<\/p>\n<p>174\u00a0\u00a0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n<p>175\u00a0\u00a0 % final time in multiples of timescale kfdb^-1<\/p>\n<p>176\u00a0\u00a0 tfin=tfinalfact\/kforwdb;<\/p>\n<p>177\u00a0\u00a0 % 1st choice for timestep = Total time interval\/number<\/p>\n<p>178\u00a0\u00a0 % of time steps<\/p>\n<p>179\u00a0\u00a0 dt=(tfin-tin)\/nt;<\/p>\n<p>180\u00a0\u00a0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%<\/p>\n<p>181\u00a0\u00a0 for i=1:nt<\/p>\n<p>182\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 t=tin+(i-1)*dt; tvec(i)=t;<\/p>\n<p>183\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 pt= V*diag(exp(t*s))*inv(V)*p0;<\/p>\n<p>184\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 pvec(i)=pt(1);\u00a0 % 1st state time-dep prob<\/p>\n<p>185\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 p2vec(i)=pt(n); % last state time-dep prob<\/p>\n<p>186\u00a0\u00a0 end<\/p>\n<p>187<\/p>\n<p>188\u00a0\u00a0 plot(10^(-3)*tvec,p2vec,10^(-3)*tvec,pvec)<\/p>\n<p>189\u00a0\u00a0 xlabel(&#8216;$t(ns)$&#8217;,&#8217;interpreter&#8217;,&#8217;latex&#8217;)<\/p>\n<p>190\u00a0\u00a0 ylabel(&#8216;$P_{i}(t)$&#8217;,&#8217;interpreter&#8217;,&#8217;latex&#8217;)<\/p>\n<p>191\u00a0\u00a0 legend(&#8216;$P_{N+2}(t)$&#8217;,&#8217;$P_{1}(t)$&#8217;,&#8217;interpreter&#8217;,&#8217;latex&#8217;)<\/p>\n<p>192<\/p>\n<p>193\u00a0\u00a0 % finding equilibrium values of site probabilities<\/p>\n<p>194\u00a0\u00a0 peq=zeros(1,n);<\/p>\n<p>195\u00a0\u00a0 normpeq=zeros(1,n);<\/p>\n<p>196\u00a0\u00a0 for k=1:n<\/p>\n<p>197\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 peq(k)=exp(-enebias(k)\/(kb*temprange(tempindex)));<\/p>\n<p>198\u00a0\u00a0 end<\/p>\n<p>199<\/p>\n<p>200\u00a0\u00a0 % fprintf(&#8216;zero bias energy gap (ev)\u00a0 %f\\n&#8217;, dgnn(1));<\/p>\n<p>201\u00a0\u00a0 % fprintf(&#8216;temperature (Kelvin) %f\\n&#8217;,temprange(tempindex));<\/p>\n<p>202\u00a0\u00a0 % fprintf(&#8216;kforwbb (psec)\u00a0 %f\\n&#8217;,1\/kforw(2));<\/p>\n<p>203\u00a0\u00a0 % fprintf(&#8216;1\/kforwbb (nsec) %f\\n&#8217;,(1\/kforw(2))*(10^(-3)));<\/p>\n<p>204\u00a0\u00a0 % fprintf(&#8216;1\/kforwba (nsec) %f\\n&#8217;,(1\/kforwba)*(10^(-3)));<\/p>\n<p>205\u00a0\u00a0 % fprintf(&#8216;1\/kforwdb (psec) %f\\n&#8217;,1\/kforwdb);<\/p>\n<p>206\u00a0\u00a0 % fprintf(&#8216;1\/kforwdb (nsec) %f\\n&#8217;,(1\/kforwdb)*(10^(-3)));<\/p>\n<p>207<\/p>\n<p>208\u00a0\u00a0 stath=sum(peq);<\/p>\n<p>209\u00a0\u00a0 normpeq=(1\/stath)*peq;<\/p>\n<p>210\u00a0\u00a0 tolerance=0.1;<\/p>\n<p>211\u00a0\u00a0 [avte,vadoum]=min(abs(p2vec-(normpeq(n)*(0.8))));<\/p>\n<p>212\u00a0\u00a0 if min(abs(p2vec-(normpeq(n)*(0.8)))) &lt;=tolerance;<\/p>\n<p>213\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 fprintf(&#8216;transfer time in psec %f\\n&#8217;, tvec(vadoum));<\/p>\n<p>214\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 fprintf(&#8216;transfer time in nsec %f\\n&#8217;, tvec(vadoum)*&#8230;<\/p>\n<p>215\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (10^(-3)));<\/p>\n<p>216\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 fprintf(&#8216;Transfer time in units of 1\/kforwardb %f\\n&#8217;,&#8230;<\/p>\n<p>217\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 tvec(vadoum));<\/p>\n<p>218\u00a0\u00a0 else<\/p>\n<p>219\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 fprintf(&#8216;Run for longer times&#8217;)<\/p>\n<p>220\u00a0\u00a0 end<\/p>\n","protected":false},"excerpt":{"rendered":"<p>1\u00a0\u00a0\u00a0\u00a0 clear 2\u00a0\u00a0\u00a0\u00a0 % This program computes the overall donor-to-acceptor 3\u00a0\u00a0\u00a0\u00a0 % transfer time 4\u00a0\u00a0\u00a0\u00a0 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 5\u00a0\u00a0\u00a0\u00a0 % Inputs related to building rate matrix 6\u00a0\u00a0\u00a0\u00a0 hbar=0.6582*10^(-3);<span class=\"excerpt-hellip\"> [\u2026]<\/span><\/p>\n","protected":false},"author":48,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"class_list":["post-1851","page","type-page","status-publish","hentry"],"publishpress_future_action":{"enabled":false,"date":"2026-06-22 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