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1808 2662 l 1829 2732 l 1850 2804 l 1871 2879 l 1893 2955 l 1916 3033 l 1939 3110 l 1962 3188 l 1985 3266 l 2007 3342 l 2030 3418 l 2052 3492 l 2074 3565 l 2096 3635 l 2117 3704 l 2138 3771 l 2158 3836 l 2177 3899 l 2197 3960 l 2216 4018 l 2234 4075 l 2252 4130 l 2270 4183 l 2287 4234 l 2304 4284 l 2321 4332 l 2337 4379 l 2354 4424 l 2370 4469 l 2386 4512 l 2402 4554 l 2418 4596 l 2434 4636 l 2450 4676 l 2466 4716 l 2483 4755 l 2503 4803 l 2523 4850 l 2544 4897 l 2565 4944 l 2586 4990 l 2608 5037 l 2629 5083 l 2652 5129 l 2674 5174 l 2697 5220 l 2720 5265 l 2744 5311 l 2768 5356 l 2792 5400 l 2816 5445 l 2840 5489 l 2865 5532 l 2890 5575 l 2914 5618 l 2939 5660 l 2964 5701 l 2988 5741 l 3013 5781 l 3037 5819 l 3061 5857 l 3085 5894 l 3109 5930 l 3132 5964 l 3155 5998 l 3177 6030 l 3199 6062 l 3221 6092 l 3242 6121 l 3263 6149 l 3283 6176 l 3303 6202 l 3322 6227 l 3341 6251 l 3359 6274 l 3377 6296 l 3395 6317 l 3413 6338 l 3440 6369 l 3467 6399 l 3493 6428 l 3519 6455 l 3545 6481 l 3571 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l 5762 5050 l 5786 5043 l 5811 5037 l 5837 5032 l 5864 5026 l 5891 5021 l 5920 5016 l 5950 5011 l 5981 5007 l 6013 5002 l 6046 4998 l 6080 4994 l 6115 4991 l 6151 4987 l 6188 4984 l 6226 4981 l 6265 4978 l 6305 4976 l 6345 4973 l 6386 4971 l 6428 4969 l 6470 4968 l 6512 4966 l 6556 4965 l 6599 4963 l 6644 4962 l 6688 4961 l 6734 4960 l 6780 4960 l 6826 4959 l 6874 4958 l 6923 4958 l 6958 4957 l 6993 4957 l 7030 4956 l 7068 4956 l 7106 4956 l 7146 4955 l 7187 4955 l 7229 4955 l 7273 4954 l 7319 4954 l 7366 4954 l 7415 4954 l 7467 4953 l 7520 4953 l 7576 4953 l 7633 4953 l 7694 4952 l 7756 4952 l 7821 4952 l 7888 4952 l 7958 4952 l 8029 4952 l 8103 4951 l 8178 4951 l 8254 4951 l 8331 4951 l 8409 4951 l 8486 4951 l 8563 4951 l 8639 4951 l 8713 4951 l 8784 4950 l 8851 4950 l 8915 4950 l 8974 4950 l 9028 4950 l 9077 4950 l 9120 4950 l 9157 4950 l 9188 4950 l 9214 4950 l 9234 4950 l 9248 4950 l 9259 4950 l 9265 4950 l 9269 4950 l 9270 4950 l gs col11 s gr % adsobate groundstate % Polyline n 1665 1260 m 1665 1261 l 1666 1264 l 1668 1270 l 1670 1279 l 1674 1291 l 1679 1308 l 1685 1330 l 1693 1358 l 1702 1390 l 1713 1428 l 1725 1472 l 1739 1520 l 1754 1574 l 1771 1633 l 1789 1695 l 1808 1762 l 1829 1832 l 1850 1904 l 1871 1979 l 1893 2055 l 1916 2133 l 1939 2210 l 1962 2288 l 1985 2366 l 2007 2442 l 2030 2518 l 2052 2592 l 2074 2665 l 2096 2735 l 2117 2804 l 2138 2871 l 2158 2936 l 2177 2999 l 2197 3060 l 2216 3118 l 2234 3175 l 2252 3230 l 2270 3283 l 2287 3334 l 2304 3384 l 2321 3432 l 2337 3479 l 2354 3524 l 2370 3569 l 2386 3612 l 2402 3654 l 2418 3696 l 2434 3736 l 2450 3776 l 2466 3816 l 2483 3855 l 2503 3903 l 2523 3950 l 2544 3997 l 2565 4044 l 2586 4090 l 2608 4137 l 2629 4183 l 2652 4229 l 2674 4274 l 2697 4320 l 2720 4365 l 2744 4411 l 2768 4456 l 2792 4500 l 2816 4545 l 2840 4589 l 2865 4632 l 2890 4675 l 2914 4718 l 2939 4760 l 2964 4801 l 2988 4841 l 3013 4881 l 3037 4919 l 3061 4957 l 3085 4994 l 3109 5030 l 3132 5064 l 3155 5098 l 3177 5130 l 3199 5162 l 3221 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1753 y(b)r(ers)26 b(1{5)g(indicate)h(the)e(\014v)n(e)g(steps)h(of)g (the)f(desorption)h(pro)r(cess.)2042 2017 y Fu(a)31 b(few)h(adsorbate)e (states,)i(whic)n(h)g(ha)n(v)n(e)e(to)i(b)r(e)g(tak)n(en)f(in)n(to)g (ac-)2042 2112 y(coun)n(t.)76 b(But)41 b(the)h(main)e(e\013ect)i(of)e (the)i(substrate)e(states)g(of)2042 2207 y(coupling)35 b(di\013eren)n(t)g(adsorbate)f(states)h(either)g(to)g(eac)n(h)g(other) 2042 2303 y(or)40 b(to)g(an)g(external)g(electromagnetic)f(\014eld)i (can)g(b)r(e)g(treated)2042 2398 y(collectiv)n(ely)-7 b(.)41 b(T)-7 b(o)29 b(mo)r(del)g(this)g(e\013ect)h(w)n(e)f(com)n(bine) g(ideas)g(from)2042 2494 y(T)-7 b(ully's)37 b(few)n(est)f(switc)n(hing) g(algorithm)g([11)o(])h(and)g(generalized)2042 2589 y(surface)h (hopping)g(metho)r(d)h([12)o(])g(with)g(those)g(of)f(Brenig)g([13)o(]) 2042 2685 y(and)33 b(Saalfrank)f([14)o(])h(who)g(in)n(tro)r(duced)g (optical)g(p)r(oten)n(tials)g(in)2042 2780 y(the)25 b(description)g(of) g(DIET)g(pro)r(cesses.)35 b(First)25 b(w)n(e)g(separate)f(the)2042 2876 y(n)n(uclear)32 b(from)h(the)g(electronic)g(degrees)f(of)h (freedom,)h(i.e.)54 b(the)2042 2971 y(Hamilton)30 b(op)r(erator)e Fm(H)36 b Fu(is)30 b(split)g(in)n(to)f(the)i(kinetic)f(energy)e Fm(T)4030 2983 y Fl(R)2042 3067 y Fu(of)33 b(the)g(n)n(uclear)f(co)r (ordinates)g Fm(R)h Fu(and)g(an)g(electronic)f(part)g Fm(H)4048 3079 y Fl(e)2042 3162 y Fu(dep)r(ending)d(explicitly)g(on)g (the)g(electronic)f(co)r(ordinates)g Fm(r)j Fu(and)2042 3258 y(parametrically)25 b(on)j(the)g(p)r(osition)f(of)h(the)g(n)n (uclei)f Fm(R)q Fu(.)2615 3416 y Fm(H)7 b Fu(\()p Fm(r)n(;)14 b(R)q Fu(\))23 b(=)g Fm(T)3051 3428 y Fl(R)3123 3416 y Fu(+)18 b Fm(H)3275 3428 y Fl(e)3311 3416 y Fu(\()p Fm(r)n(;)c(R)q Fu(\))467 b(\(1\))2042 3574 y(The)28 b(electronic)g(w)n (a)n(v)n(e)f(function)i(\010)f(is)h(expanded)f(in)n(to)g(the)h(ex-)2042 3670 y(plicitly)h(treated)f(excited)h(adsorbate)e(states)h Fm(\036)3565 3682 y Fl(i)3623 3670 y Fu(and)h(a)f(collec-)2042 3765 y(tiv)n(e)37 b(state)h Fm( )j Fu(con)n(taining)c(the)h(molecular)e (ground)h(state)h(to-)2042 3861 y(gether)27 b(with)h(the)g(con)n(tin)n (uum)f(of)h(substrate)f(excitations.)2347 4035 y(\010\()p Fm(r)n(;)14 b(R)q(;)g(t)p Fu(\))23 b(=)2784 3956 y Fk(X)2833 4133 y Fl(i)2918 4035 y Fm(c)2954 4047 y Fl(i)2982 4035 y Fu(\()p Fm(t)p Fu(\))p Fm(\036)3125 4047 y Fl(i)3153 4035 y Fu(\()p Fm(r)n(;)14 b(R)q Fu(\))19 b(+)f Fm( )s Fu(\()p Fm(r)n(;)c(R)q(;)g(t)p Fu(\))2042 4270 y(The)28 b(in\015uence)h(of)f(the)h(collectiv)n(e)f(state)g Fm( )k Fu(can)c(b)r(e)h(tak)n(en)e(in)n(to)2042 4365 y(accoun)n(t)i(b)n(y)g (an)g(e\013ectiv)n(e)h(non-Hermitian)f(Hamiltonian)g(\(see)2042 4461 y(c)n(hapter)e(16)f(in)i([24)o(]\))2343 4619 y Fm(H)2412 4631 y Fl(ef)7 b(f)2525 4619 y Fu(\()p Fm(r)n(;)14 b(R)q Fu(\))23 b(=)g Fm(T)2885 4631 y Fl(e)2939 4619 y Fu(+)18 b Fm(V)3070 4631 y Fl(ef)7 b(f)3183 4619 y Fu(\()p Fm(r)n(;)14 b(R)q Fu(\))19 b(+)f Fm(i)p Fu(\001\()p Fm(r)n(;)c(R)q Fu(\))195 b(\(2\))2042 4777 y(where)25 b Fm(T)2329 4789 y Fl(e)2390 4777 y Fu(is)g(the)h(kinetic)g(energy)e(op)r(erator)g(for)h (the)h(electrons.)2042 4873 y(The)j(e\013ectiv)n(e)h(p)r(oten)n(tial)f Fm(V)2937 4885 y Fl(ef)7 b(f)3080 4873 y Fu(and)30 b(the)g(optical)f(p) r(oten)n(tial)g(\001)2042 4968 y(are)22 b(real)g(functions)i(of)f Fm(r)k Fu(and)c Fm(R)q Fu(.)35 b(In)23 b(a)g(Newns-Andersson)f(pic-) 2042 5064 y(ture)e(\001)g(is)g(related)f(to)h(the)g(lifetime)h (broadening)d(of)i(a)g(resonance)2042 5159 y(state)27 b(whic)n(h)h(can)f(b)r(e)h(determined)g(via)f([25)o(])2502 5338 y(\001\()p Fm(E)5 b Fu(\))52 b(=)e Fm(\031)2960 5259 y Fk(X)3000 5438 y Fj(k)3094 5338 y Fi(j)p Fm(V)3165 5350 y Fj(k)3209 5338 y Fi(j)3232 5304 y Ft(2)3269 5338 y Fm(\016)s Fu(\()p Fm(E)24 b Fi(\000)18 b Fm(")3548 5350 y Fj(k)3592 5338 y Fu(\))354 b(\(3\))p eop %%Page: 3 3 3 2 bop 4043 -299 a Fu(3)-150 -83 y(With)57 b(the)g(e\013ectiv)n(e)f (Hamiltonian)g(and)f(a)h(diabatic)g(\(i.e.)-150 12 y Fi(r)-81 24 y Fl(R)-26 12 y Fm(\036)23 24 y Fl(i)85 12 y Fu(=)33 b(0\))h(represen)n(tation)f(of)h(the)h(w)n(a)n(v)n(e)d (functions)j Fm(\036)1715 24 y Fl(i)1777 12 y Fu(the)-150 108 y(electronic)27 b(Sc)n(hr\177)-42 b(odinger)26 b(equation)h(has)g (the)h(follo)n(wing)e(form)304 309 y(_)-34 b Fm(c)329 321 y Fl(j)387 309 y Fu(=)22 b Fi(\000)557 253 y Fm(i)p 549 290 45 4 v 549 366 a Fh(~)617 230 y Fk(X)666 407 y Fl(i)751 309 y Fm(c)787 321 y Fl(i)815 309 y Fm(V)863 321 y Fl(j)s(i)940 309 y Fu(+)1035 253 y(1)p 1033 290 V 1033 366 a Fh(~)1102 230 y Fk(X)1150 407 y Fl(i)1235 309 y Fm(c)1271 321 y Fl(i)1299 309 y Fu(\001)1368 321 y Fl(j)s(i)1427 309 y Fm(;)336 b Fu(\(4\))-150 546 y(where)27 b(the)h(matrix)f(elemen)n(ts)h Fm(V)891 558 y Fl(ij)977 546 y Fu(and)g(\001)1208 558 y Fl(j)s(i)1294 546 y Fu(are)f(de\014ned)g (as)321 707 y Fm(V)369 719 y Fl(j)s(i)478 707 y Fi(\021)49 b(h)q Fm(\036)674 719 y Fl(j)p 723 731 4 87 v 740 707 a Fm(T)789 719 y Fl(e)843 707 y Fu(+)18 b Fm(V)974 719 y Fl(ef)7 b(f)1087 707 y Fu(\()p Fm(r)n(;)14 b(R)q Fu(\))p 1301 731 V 32 w Fm(\036)1368 719 y Fl(i)1396 707 y Fi(i)300 828 y Fu(\001)369 840 y Fl(j)s(i)478 828 y Fi(\021)49 b(h)q Fm(\036)674 840 y Fl(j)p 723 851 V 740 828 a Fu(\001\()p Fm(r)n(;)14 b(R)q Fu(\))p 1023 851 V 32 w Fm(\036)1090 840 y Fl(i)1118 828 y Fi(i)41 b Fm(;)572 b Fu(\(5\))-150 989 y(resp)r(ectiv)n(ely)-7 b(.)71 b(F)-7 b(or)38 b(the)i(diagonal)e (elemen)n(ts)h(of)g(the)h(densit)n(y)-150 1084 y(matrix)27 b Fm(a)164 1096 y Fl(j)s(i)245 1084 y Fi(\021)c Fm(c)369 1054 y Fl(?)369 1106 y(j)407 1084 y Fm(c)443 1096 y Fl(i)498 1084 y Fu(this)28 b(leads)f(to)314 1300 y(_)-33 b Fm(a)348 1312 y Fl(j)s(j)436 1300 y Fu(=)524 1221 y Fk(X)572 1398 y Fl(i)658 1300 y Fm(b)694 1312 y Fl(j)s(i)770 1300 y Fu(+)853 1221 y Fk(X)902 1398 y Fl(i)999 1244 y Fu(2)p 997 1281 45 4 v 997 1357 a Fh(~)1052 1300 y Fi(<)14 b Fu([)p Fm(a)1193 1312 y Fl(j)s(i)1251 1300 y Fu(\001)1320 1312 y Fl(j)s(i)1379 1300 y Fu(])g Fm(;)347 b Fu(\(6\))-150 1550 y(with)30 b Fm(b)77 1562 y Fl(j)s(i)162 1550 y Fi(\021)265 1518 y Ft(2)p 263 1532 37 4 v 263 1579 a Fg(~)310 1550 y Fi(=)14 b Fu([)p Fm(a)451 1562 y Fl(j)s(i)509 1550 y Fm(V)557 1562 y Fl(j)s(i)616 1550 y Fu(].)43 b(Note)30 b(that)g(for)f(a)g(normalized)g(w)n(a)n(v)n(e)-150 1646 y(function)h(\010)g(the)g(o)r(ccupation)g(probabilit)n(y)e Fm(a)1307 1658 y Fl(cc)1400 1646 y Fu(for)i(the)g(\\rest")-150 1741 y(is)d(simply)h(giv)n(en)f(b)n(y)g Fm(a)575 1753 y Fl(cc)662 1741 y Fi(\021)22 b Fu(1)c Fi(\000)892 1679 y Fk(P)980 1766 y Fl(j)1029 1741 y Fm(a)1073 1753 y Fl(j)s(j)1166 1741 y Fu(leading)27 b(to)224 1961 y(_)-33 b Fm(a)258 1973 y Fl(cc)344 1961 y Fu(=)23 b Fi(\000)511 1882 y Fk(X)555 2059 y Fl(j)655 1961 y Fu(_)-34 b Fm(a)688 1973 y Fl(j)s(j)777 1961 y Fu(=)23 b Fi(\000)942 1905 y Fu(2)p 940 1942 45 4 v 940 2018 a Fh(~)1008 1882 y Fk(X)1041 2059 y Fl(ij)1142 1961 y Fi(<)14 b Fu([)o Fm(a)1282 1973 y Fl(j)s(i)1341 1961 y Fu(\001)1410 1973 y Fl(j)s(i)1468 1961 y Fu(])g Fm(;)258 b Fu(\(7\))-150 2215 y(since)51 2152 y Fk(P)139 2239 y Fl(j)s(i)211 2215 y Fm(b)247 2227 y Fl(j)s(i)328 2215 y Fu(=)23 b(0.)35 b(The)25 b(n)n(uclear)f(co)r (ordinates)g Fm(R)i Fu(are)e(treated)-150 2310 y(classically)i(and)h (ob)r(ey)h(the)g(Newtonian)f(equation)g(of)h(motion)359 2499 y(\177)341 2520 y Fm(R)c Fu(=)526 2464 y Fi(\000)p Fu(1)p 526 2501 107 4 v 534 2577 a Fm(M)642 2520 y Fi(r)725 2403 y Fk(\024)778 2464 y Fi(h)q Fm( )865 2476 y Fl(occ)p 975 2485 4 84 v 992 2464 a Fm(H)1061 2476 y Fl(e)p 1111 2485 V 1128 2464 a Fm( )1182 2476 y Fl(occ)1278 2464 y Fi(i)p 778 2501 532 4 v 846 2577 a(h)q Fm( )933 2589 y Fl(occ)p 1043 2598 4 84 v 1060 2577 a Fm( )1114 2589 y Fl(occ)1210 2577 y Fi(i)1320 2403 y Fk(\025)1378 2520 y Fm(;)385 b Fu(\(8\))-150 2731 y(where)34 b Fm( )151 2743 y Fl(occ)282 2731 y Fu(is)g(the)h(curren)n(tly)e(o)r(ccupied)h (state.)57 b(Using)34 b(clas-)-150 2826 y(sical)h(equations)f(of)i (motion)f(for)g(the)h(n)n(uclei)f(is)g(a)g(reasonable)-150 2921 y(appro)n(ximation)26 b(as)h(long)g(as)f(h)n(ydrogen)g(is)i(not)g (in)n(v)n(olv)n(ed.)-67 3017 y(These)61 b(equations)f(are)f(equiv)-5 b(alen)n(t)61 b(to)g(the)g(ones)f(that)-150 3112 y(ha)n(v)n(e)44 b(b)r(een)i(deriv)n(ed)f(in)g(the)h(generalized)e(surface)h(hopping) -150 3208 y(metho)r(d)38 b([12)o(].)66 b(In)37 b(our)g(scenario,)h(ho)n (w)n(ev)n(er,)f(up)r(on)h(a)e(transi-)-150 3303 y(tion)g(to)g(the)g (con)n(tin)n(uum)f(state)h(w)n(e)f(assume)h(that)g(the)g(whole)-150 3399 y(excess)31 b(energy)f(is)h(tak)n(en)g(up)h(b)n(y)g(the)g (substrate)e(electrons,)i(as)-150 3494 y(it)21 b(is)f(usually)g(done)g (in)g(the)h(mo)r(deling)f(of)h(laser-induced)e(desorp-)-150 3590 y(tion)i([8].)34 b(This)21 b(means)g(that)g(up)r(on)g(a)g(switc)n (h)f(to)h(the)h(con)n(tin)n(uum)-150 3685 y(state)32 b(w)n(e)f(just)i(mak)n(e)e(a)h(F)-7 b(ranc)n(k-Condon)29 b(transition,)k(i.e.)50 b(w)n(e)-150 3781 y(transfer)28 b(the)h(molecule)f(to)h(the)g(ground)f(state)g(p)r(oten)n(tial)h(with) -150 3876 y(its)f(kinetic)h(energy)e(preserv)n(ed)f(and)j(p)r(erform)e (ordinary)g(Born-)-150 3972 y(Opp)r(enheimer)32 b(molecular)e(dynamics) h(un)n(til)h(the)g(\014nal)g(fate)f(of)-150 4067 y(the)d(molecule)f (has)g(b)r(een)h(determined.)-67 4163 y(If)40 b(just)g(one)f (electronically)f(excited)h(state)g(is)g(considered,)-150 4258 y(then)31 b(the)g(equations)f(b)r(ecome)h(m)n(uc)n(h)f(simpler.)46 b(According)30 b(to)-150 4354 y(Eqs.)d(6)g(and)g(7,)h(the)g (de-excitation)e(rate)h(is)h(directly)f(giv)n(en)g(b)n(y)185 4556 y(_)-33 b Fm(a)219 4568 y Ft(11)340 4556 y Fu(=)50 b Fi(\000)10 b Fu(_)-33 b Fm(a)564 4568 y Fl(cc)678 4556 y Fu(=)61 b(_)-34 b Fm(c)829 4568 y Ft(1)866 4556 y Fm(c)902 4522 y Ff(\003)902 4577 y Ft(1)959 4556 y Fu(+)18 b Fm(c)1078 4568 y Ft(1)1126 4556 y Fu(_)-34 b Fm(c)1151 4522 y Ff(\003)1151 4577 y Ft(1)1212 4556 y Fu(=)1310 4500 y(2)p Fm(a)1396 4512 y Ft(11)1465 4500 y Fu(\001)p 1310 4537 225 4 v 1400 4613 a Fh(~)1545 4556 y Fm(:)218 b Fu(\(9\))-150 4745 y(In)41 b(fact,)i(for)d(suc)n(h)g(a)g(situation)g(no)h(electronic) e(Sc)n(hr\177)-42 b(odinger)-150 4840 y(equation)27 b(has)g(to)h(b)r(e) g(in)n(tegrated.)-67 4936 y(Our)e(metho)r(d)i(could)f(in)g(principle)g (also)f(b)r(e)i(extended)f(in)h(or-)-150 5031 y(der)h(to)f(include)i (the)f(excitation)f(pro)r(cess.)40 b(F)-7 b(urthermore,)28 b(tak-)-150 5127 y(ing)20 b(explicit)h(time)h(dep)r(endence)f(in)n(to)f (accoun)n(t)g(is)g(also)g(straigh)n(t-)-150 5222 y(forw)n(ard.)66 b(This)37 b(could)h(b)r(e)g(used,)j(e.g.,)f(to)d(mo)r(del)h(the)g (pulse)-150 5318 y(shap)r(e)33 b(of)h(the)g(exciting)f(laser)f(or)h (the)g(thermalization)g(of)g(hot)-150 5413 y(electrons)27 b(in)g(the)h(case)f(of)h(an)f(indirect)h(pro)r(cess.)2776 -83 y Fo(B.)88 b(Pro)r(cedure)2125 139 y Fu(W)-7 b(e)39 b(start)g(our)g(tra)5 b(jectories)37 b(in)j(the)f(excited)h(state)f (where)2042 234 y(they)28 b(mo)n(v)n(e)e(classically)g(for)h(a)h (certain)f(time.)37 b(After)28 b(a)g(F)-7 b(ranc)n(k-)2042 330 y(Condon)27 b(transition)g(the)h(mo)n(v)n(emen)n(t)e(of)i(the)g (molecule)f(is)h(con-)2042 425 y(tin)n(ued)c(on)f(the)h(ground)e(state) i(p)r(oten)n(tial)f(for)g(a)g(maximal)g(prop-)2042 521 y(agation)18 b(time)j(or)e(un)n(til)h(it)h(reac)n(hes)d(a)i(certain)f (distance)h Fm(Z)3854 533 y Fl(C)t(utof)7 b(f)2042 616 y Fu(from)27 b(the)h(surface)f(and)g(is)h(considered)e(desorb)r(ed.) 2125 720 y(The)f(tra)5 b(jectories)23 b(are)h(started)h(around)f(the)i (p)r(osition)f(of)g(the)2042 815 y(ground)d(state)h(minim)n(um)h (assuming)f(a)g(Gaussian)f(distribution)2042 911 y(in)38 b(p)r(osition)f(and)g(momen)n(tum)h(according)e(to)h(the)h(curv)-5 b(ature)2042 1006 y(of)34 b(the)g(ground)f(state)h(p)r(oten)n(tial)g (energy)e(surface.)56 b(This)34 b(cor-)2042 1102 y(resp)r(onds)29 b(to)h(a)f(harmonic)g(appro)n(ximation)f(for)h(the)h(p)r(oten)n(tial) 2042 1197 y(at)h(the)g(minim)n(um)h(p)r(osition.)47 b(In)32 b(principle)f(the)g(distributions)2042 1293 y(should)d(b)r(e)h(giv)n (en)e(b)n(y)h(the)h(true)f(ground)g(state)g(w)n(a)n(v)n(e)f(function,) 2042 1388 y(but)21 b(since)g(the)g(masses)f(of)h(the)h(n)n(uclei)f(are) f(rather)f(large)h(and)h(the)2042 1484 y(anharmonicit)n(y)g(of)h(the)h (p)r(oten)n(tial)f(is)g(small,)h(this)g(is)f(a)g(go)r(o)r(d)g(ap-)2042 1579 y(pro)n(ximation.)2125 1683 y(After)28 b(eac)n(h)e(in)n(tegration) g(step)i(in)f(the)h(excited)f(state)g(w)n(e)g(de-)2042 1791 y(cide,)44 b(according)c(to)h(the)h(deca)n(y)e(probabilit)n(y)g Fm(p)45 b Fu(=)3802 1751 y Ft(2\001\()p Fl(R)p Ft(\))p Fl(dt)p 3802 1772 250 4 v 3908 1820 a Fg(~)4061 1791 y Fu(,)2042 1886 y(whether)27 b(to)h(con)n(tin)n(ue)f(in)h(the)g (excited)f(or)g(the)h(ground)f(state.)2125 1990 y(F)-7 b(or)44 b(constan)n(t)g(\001)h(this)g(pro)r(cedure)e(is)i(equiv)-5 b(alen)n(t)44 b(to)h(the)2042 2086 y(Gadzuk)29 b(sc)n(heme)f([26)o(]\)) i(as)f(used)g(in)g([17)o(].)42 b(In)30 b(this)f(sc)n(heme)g(the)2042 2181 y(residence)36 b(times)h(are)f(k)n(ept)h(\014xed)g(and)g(the)g(o)n (v)n(erall)e(result)h(is)2042 2276 y(obtained)29 b(b)n(y)h(a)n(v)n (eraging)d(o)n(v)n(er)h(the)i(di\013eren)n(t)g(residence)f(times)2042 2372 y(with)41 b(w)n(eigh)n(t)e(function)i Fm(w)2916 2384 y Fl(\034)2958 2372 y Fu(\()p Fm(t)p Fu(\))k(=)3217 2339 y Ft(1)p 3215 2353 38 4 v 3215 2401 a Fl(\034)3276 2372 y Fu(exp\()p Fi(\000)p Fm(t=\034)9 b Fu(\),)44 b(where)c(the)2042 2467 y(a)n(v)n(erage)28 b(residence)j(time)h(or)e(resonance)g(lifetime) i Fm(\034)41 b Fu(is)32 b(an)f(ad-)2042 2563 y(justable)d(parameter)f (directly)h(connected)g(to)g(the)g(strength)g(of)2042 2658 y(the)g(optical)f(p)r(oten)n(tial)2908 2895 y Fm(\034)33 b Fu(=)3107 2839 y Fh(~)p 3074 2876 111 4 v 3074 2952 a Fu(2\001)3195 2895 y Fm(:)719 b Fu(\(10\))2782 3245 y Fo(C.)88 b(P)n(oten)n(tials)2125 3467 y Fu(The)41 b(p)r(oten)n(tial)g (energy)f(surfaces)g(w)n(e)g(used)h(in)g(our)g(sim)n(u-)2042 3562 y(lation)35 b(are)g(based)h(on)g(t)n(w)n(o)f(t)n(w)n (o-dimensional)f(p)r(oten)n(tials)i Fm(V)4023 3574 y Ft(a)p Fl(i)2042 3658 y Fu(from)27 b(Kl)r(\177)-44 b(uner)26 b(et)i(al.)36 b([27)o(])28 b(one)f(is)g(represen)n(ting)e(the)j (electronic)2042 3753 y(ground)c(state)i(and)f(the)h(other)f(a)h(c)n (harge)e(transfer)g(state)i(where)2042 3849 y(an)32 b(electron)f(from)h (the)g(substrate)f(is)h(transfered)f(in)n(to)h(an)g(ad-)2042 3944 y(sorbate)d(state.)44 b(These)29 b(p)r(oten)n(tials)h(w)n(ere)f (obtained)h(b)n(y)g(\014tting)2042 4039 y(analytical)d(expressions)g (to)i(energies)f(from)g(ab)g(initio)h(calcula-)2042 4135 y(tions.)36 b(The)27 b(t)n(w)n(o)f(degrees)f(of)i(freedom)f(used)h(are) e(the)i(molecule)2042 4230 y(surface)g(distance)g Fm(Z)33 b Fu(and)28 b(the)g(p)r(olar)e(angle)h Fm(\022)r Fu(.)2125 4334 y(In)i(order)f(to)h(come)f(to)h(a)g(complete)g(description)f(of)h (the)g(NO)2042 4430 y(molecule)h(w)n(e)f(extended)i(the)f Fn(ab)j(initio)e Fu(t)n(w)n(o)f(dimensional)g(p)r(o-)2042 4525 y(ten)n(tials)22 b(to)h(six)g(dimensions.)35 b(In)23 b(the)g(absence)f(of)h(an)n(y)f Fn(ab)k(initio)2042 4620 y Fu(results)f(w)n(e)h(w)n(ere)f(required)g(to)h(use)g(a)g(mo)r(del)g (p)r(oten)n(tial)g(for)g(the)2042 4716 y(additional)21 b(degrees)f(of)h(freedom.)34 b(Th)n(us)21 b(the)h(particular)e(c)n (hoice)2042 4811 y(of)35 b(the)g(parameters)e(has)h(to)h(b)r(e)h (considered)d(as)i(an)f(educated)2042 4907 y(guess.)53 b(W)-7 b(e)33 b(lik)n(e)g(to)g(p)r(oin)n(t)h(out,)g(ho)n(w)n(ev)n(er,)f (that)g(the)h(qualita-)2042 5002 y(tiv)n(e)c(results)f(w)n(e)h (obtained)g(did)g(not)g(dep)r(end)h(v)n(ery)e(sensitiv)n(ely)2042 5098 y(on)e(the)h(particular)e(c)n(hoice)h(of)h(parameters.)2167 5293 y Fm(V)2234 5258 y Fl(s)2215 5313 y Ft(6)p Fl(D)2309 5293 y Fu(\()p Fm(X)r(;)14 b(Y)5 b(;)14 b(Z)q(;)g(r)n(;)g(\022)r(;)g (\036)p Fu(\))23 b(=)g Fm(V)3043 5258 y Fl(s)3024 5313 y Ft(a)p Fl(i)3085 5293 y Fu(\()p Fm(Z)q(;)14 b(\022)r Fu(\))19 b(+)f Fm(V)3435 5305 y Fl(cor)3535 5293 y Fu(\()p Fm(X)r(;)c(Y)5 b(;)14 b(Z)6 b Fu(\))2896 5413 y(+)p Fm(V)3009 5425 y Fl(az)3084 5413 y Fu(\()p Fm(X)r(;)14 b(Y)5 b(;)14 b(Z)q(;)g(\036)p Fu(\))k(+)g Fm(V)3658 5379 y Fl(s)3639 5434 y(N)6 b(O)3755 5413 y Fu(\()p Fm(r)r Fu(\))79 b(\(11\))p eop %%Page: 4 4 4 3 bop 4043 -299 a Fu(4)-150 -83 y(The)30 b(upp)r(er)g(index)g Fm(s)g Fu(is)f(either)h Fm(g)j Fu(or)28 b Fm(e)p Fu(,)j(denoting)e(the) h(ground)-150 12 y(or)j(the)g(excited)h(state.)54 b(F)-7 b(or)33 b(p)r(oten)n(tials)g(where)g(this)h(index)g(is)-150 108 y(absen)n(t)20 b(w)n(e)h(do)f(not)h(distinguish)g(b)r(et)n(w)n(een) g(the)g(t)n(w)n(o)f(states.)34 b(The)-150 203 y Fm(X)f Fu(and)26 b Fm(Y)46 b Fu(co)r(ordinate)25 b(giv)n(e)g(the)i(lateral)f (p)r(osition)g(on)g(the)h(sur-)-150 299 y(face,)g Fm(\036)h Fu(is)g(the)f(azim)n(uthal)g(angle)g(and)g Fm(r)k Fu(is)c(the)h(N{O)f (distance)-150 394 y(in)36 b(the)g(NO)f(molecule.)60 b(The)36 b(corrugation)d(p)r(oten)n(tial)i Fm(V)1701 406 y Fl(cor)1837 394 y Fu(is)-150 490 y(giv)n(en)27 b(b)n(y)214 714 y Fm(V)262 726 y Fl(cor)361 714 y Fu(\()p Fm(X)r(;)14 b(Y)5 b(;)14 b(Z)6 b Fu(\))23 b(=)806 658 y Fm(C)865 670 y Fl(cor)p 806 695 159 4 v 865 771 a Fu(4)975 714 y Fm(e)1014 679 y Ff(\000)p Fl(\025)1105 687 y Fe(cor)1194 679 y Ft(\()p Fl(Z)t Ff(\000)p Fl(Z)1366 687 y Fd(0)1399 679 y Ft(\))339 866 y Fu(\(2)18 b Fi(\000)g Fu(cos)o(\()p Fm(G)722 878 y Fl(X)786 866 y Fm(X)7 b Fu(\))18 b Fi(\000)g Fu(cos)o(\()p Fm(G)1203 878 y Fl(Y)1261 866 y Fm(Y)h Fu(\)\))14 b Fm(;)316 b Fu(\(12\))-150 1048 y(and)27 b(the)h(azim)n(uthal)g(dep)r(endence)g(is)244 1272 y Fm(V)292 1284 y Fl(az)366 1272 y Fu(\()p Fm(X)r(;)14 b(Y)5 b(;)14 b(Z)q(;)g(\022)r(;)g(\036)p Fu(\))24 b(=)971 1216 y Fm(C)1030 1228 y Fl(az)p 971 1253 134 4 v 1017 1329 a Fu(2)1115 1272 y Fm(e)1154 1238 y Ff(\000)p Fl(\025)1245 1246 y Fe(az)1311 1238 y Ft(\()p Fl(Z)t Ff(\000)p Fl(Z)1483 1246 y Fd(0)1516 1238 y Ft(\))97 1425 y Fu(cos)o(\(2)p Fm(\036)p Fu(\))14 b(sin\()p Fm(\022)r Fu(\))g(\()q(cos)o(\()p Fm(G)839 1437 y Fl(X)903 1425 y Fm(X)7 b Fu(\))18 b Fi(\000)g Fu(cos)o(\()p Fm(G)1320 1437 y Fl(Y)1378 1425 y Fm(Y)h Fu(\)\))14 b Fm(:)199 b Fu(\(13\))-150 1607 y(This)19 b(corresp)r(onds)f(to)h(a)g(molecule)g(with)h(t)n(w)n(o)f(equal)f (atoms,)j(but)-150 1702 y(as)28 b(an)h(\014rst)f(appro)n(ximation)f(it) i(will)g(su\016ce.)40 b(The)29 b(strength)f(of)-150 1798 y(the)39 b(corrugation)d(w)n(as)h(set)h(to)g Fm(C)939 1810 y Fl(cor)1080 1798 y Fu(=)i(1)p Fm(:)p Fu(0)e(eV)g(and)g(for)g (the)-150 1893 y(azim)n(uthal)29 b(dep)r(endence)i Fm(C)744 1905 y Fl(az)845 1893 y Fu(=)26 b(0)p Fm(:)p Fu(25)i(eV)i(with)h(deca)n (y)d(length)-150 1989 y(of)33 b Fm(\025)-2 2001 y Fl(cor)129 1989 y Fu(=)f Fm(\025)274 2001 y Fl(az)380 1989 y Fu(=)486 1956 y Ft(1)p 486 1970 34 4 v 486 2017 a(2)562 1974 y Fu(\027)562 1989 y(A)624 1959 y Ff(\000)p Ft(1)714 1989 y Fu(.)53 b(The)32 b(lattice)h(constan)n(ts)f Fm(G)1662 2001 y Fl(X)1759 1989 y Fu(and)-150 2084 y Fm(G)-85 2096 y Fl(Y)-4 2084 y Fu(are)23 b(set)h(to)f(the)h(Ni{Ni)g(distance)f(of)h (the)g(NiO\(100\))e(surface)-150 2180 y Fm(G)-85 2192 y Fl(X)5 2180 y Fu(=)27 b Fm(G)162 2192 y Fl(Y)247 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Fu(\()p Fm(s;)14 b(Z)q(;)g(R)q Fu(\))23 b(=)f Fm(V)805 3835 y Fl(s)786 3890 y Ft(N)841 3869 y Fu(\()p Fm(Z)i Fi(\000)18 b Fm(s;)c(R)q Fu(\))k(+)g Fm(V)1358 3881 y Ft(o)p Fl(sc)1457 3869 y Fu(\()p Fm(s)p Fu(\))1745 3990 y(\(15\))-150 4172 y(where)29 b Fm(R)h Fu(denotes)f(all)g(other)g (co)r(ordinates.)41 b(The)30 b(mass)f(of)g(the)-150 4267 y(oscillator)17 b(is)h(tak)n(en)g(equal)g(to)g(the)h(mass)f(of)h(a)f (Ni)h(atom)f(\(58)g(am)n(u\))-150 4363 y(since)24 b(NO)g(is)g(adsorb)r (ed)f(on)h(top)g(of)g(a)g(Ni)h(atom.)35 b(The)24 b(oscillator)-150 4458 y(frequency)29 b(has)h(b)r(een)g(c)n(hosen)f(to)g(corresp)r(ond)f (to)i(the)g(a)n(v)n(erage)-150 4554 y(v)-5 b(alue)20 b(of)g(a)g(Deb)n(y)n(e)g(sp)r(ectrum,)h(as)f(it)g(is)g(usually)g(done)g (in)g(sim)n(ula-)-150 4649 y(tions)29 b(using)f(the)i(surface)e (oscillator)f(mo)r(del)i([29)o(].)42 b(The)29 b(Deb)n(y)n(e)-150 4745 y(temp)r(erature)36 b(of)g(NiO)f(has)h(b)r(een)g(estimated)g(to)g (b)r(e)g(b)r(et)n(w)n(een)-150 4840 y(500)24 b(and)i(600)e(K)h([30)o (].)37 b(Accordingly)-7 b(,)25 b(w)n(e)g(ha)n(v)n(e)f(set)i(the)g (oscilla-)-150 4936 y(tor)f(frequency)h(to)f Fh(~)p Fm(!)h Fu(=)c(27)j(meV.)i(An)n(yw)n(a)n(y)-7 b(,)25 b(the)h(e\013ect)g(of)g (the)-150 5031 y(surface)f(oscillator)g(on)h(the)g(desorption)g (dynamics)f(is)h(not)h(v)n(ery)-150 5127 y(sensitiv)n(e)d(to)h(the)g (particular)f(c)n(hoice)g(of)g(the)h(frequency)-7 b(.)36 b(In)25 b(the)-150 5222 y(follo)n(wing)e(w)n(e)g(will)h(rep)r(ort)g (results)f(of)h(2D)g(and)f(6D)h(sim)n(ulations)-150 5318 y(without)31 b(and)f(with)h(the)g(surface)f(oscillator,)g(denoted)g(b)n (y)g(2D,)-150 5413 y(3D,)e(6D,)f(or)g(7D)h(calculations,)e(resp)r (ectiv)n(ely)-7 b(.)2354 826 y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 1700 @rwi @setspecial %%BeginDocument: graphs/COMP2_Des.ps %!PS-Adobe-2.0 EPSF-2.0 %%Title: COMP2_Des.ps %%Creator: gnuplot 3.7 patchlevel 1 %%CreationDate: Tue Apr 15 17:29:12 2003 %%DocumentFonts: (atend) %%BoundingBox: 50 50 410 302 %%Orientation: 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mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke Pnt } def /Star { 2 copy Pls Crs } def /BoxF { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath fill } def /TriUF { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath fill } def /TriD { stroke [] 0 setdash 2 copy vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke Pnt } def /TriDF { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath fill} def /DiaF { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath fill } def /Pent { stroke [] 0 setdash 2 copy gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore Pnt } def /PentF { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath fill grestore } def /Circle { stroke [] 0 setdash 2 copy hpt 0 360 arc stroke Pnt } def /CircleF { stroke [] 0 setdash hpt 0 360 arc fill } def /C0 { BL [] 0 setdash 2 copy moveto vpt 90 450 arc } bind def /C1 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc closepath fill vpt 0 360 arc closepath } bind def /C2 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 180 arc closepath fill vpt 0 360 arc closepath } bind def /C3 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 180 arc closepath fill vpt 0 360 arc closepath } bind def /C4 { BL [] 0 setdash 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc closepath } bind def /C5 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 90 arc 2 copy moveto 2 copy vpt 180 270 arc closepath fill vpt 0 360 arc } bind def /C6 { BL [] 0 setdash 2 copy moveto 2 copy vpt 90 270 arc closepath fill vpt 0 360 arc closepath } bind def /C7 { BL [] 0 setdash 2 copy moveto 2 copy vpt 0 270 arc closepath fill vpt 0 360 arc closepath } bind def /C8 { BL [] 0 setdash 2 copy moveto 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translate 45 rotate 0 0 S5 stroke grestore } bind def /D6 { gsave translate 45 rotate 0 0 S6 stroke grestore } bind def /D7 { gsave translate 45 rotate 0 0 S7 stroke grestore } bind def /D8 { gsave translate 45 rotate 0 0 S8 stroke grestore } bind def /D9 { gsave translate 45 rotate 0 0 S9 stroke grestore } bind def /D10 { gsave translate 45 rotate 0 0 S10 stroke grestore } bind def /D11 { gsave translate 45 rotate 0 0 S11 stroke grestore } bind def /D12 { gsave translate 45 rotate 0 0 S12 stroke grestore } bind def /D13 { gsave translate 45 rotate 0 0 S13 stroke grestore } bind def /D14 { gsave translate 45 rotate 0 0 S14 stroke grestore } bind def /D15 { gsave translate 45 rotate 0 0 S15 stroke grestore } bind def /DiaE { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V closepath stroke } def /BoxE { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V closepath stroke } def /TriUE { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V closepath stroke } def /TriDE { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V closepath stroke } def /PentE { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat closepath stroke grestore } def /CircE { stroke [] 0 setdash hpt 0 360 arc stroke } def /Opaque { gsave closepath 1 setgray fill grestore 0 setgray closepath } def /DiaW { stroke [] 0 setdash vpt add M hpt neg vpt neg V hpt vpt neg V hpt vpt V hpt neg vpt V Opaque stroke } def /BoxW { stroke [] 0 setdash exch hpt sub exch vpt add M 0 vpt2 neg V hpt2 0 V 0 vpt2 V hpt2 neg 0 V Opaque stroke } def /TriUW { stroke [] 0 setdash vpt 1.12 mul add M hpt neg vpt -1.62 mul V hpt 2 mul 0 V hpt neg vpt 1.62 mul V Opaque stroke } def /TriDW { stroke [] 0 setdash vpt 1.12 mul sub M hpt neg vpt 1.62 mul V hpt 2 mul 0 V hpt neg vpt -1.62 mul V Opaque stroke } def /PentW { stroke [] 0 setdash gsave translate 0 hpt M 4 {72 rotate 0 hpt L} repeat Opaque stroke grestore } def /CircW { stroke [] 0 setdash hpt 0 360 arc Opaque stroke } def /BoxFill { gsave Rec 1 setgray fill grestore } def /Symbol-Oblique /Symbol findfont [1 0 .167 1 0 0] makefont dup length dict begin {1 index /FID eq {pop pop} {def} ifelse} forall currentdict end definefont /Helvetica reencodeISO def /MFshow {{dup dup 0 get findfont exch 1 get scalefont setfont [ currentpoint ] exch dup 2 get 0 exch rmoveto dup dup 5 get exch 4 get {show} {stringwidth pop 0 rmoveto}ifelse dup 3 get {2 get neg 0 exch rmoveto pop} {pop aload pop moveto}ifelse} forall} bind def /MFwidth {0 exch {dup 3 get{dup dup 0 get findfont exch 1 get scalefont setfont 5 get stringwidth pop add} {pop} ifelse} forall} bind def /MLshow { currentpoint stroke M 0 exch R MFshow } bind def /MRshow { currentpoint stroke M exch dup MFwidth neg 3 -1 roll R MFshow } def /MCshow { currentpoint stroke M exch dup MFwidth -2 div 3 -1 roll R MFshow } def 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V 211 374 V 210 282 V 211 27 V 211 -16 V 211 -97 V 211 -152 V 211 -66 V 211 -33 V 211 -24 V 211 -14 V 211 -1 V 211 7 V 211 17 V 211 20 V 211 22 V 211 22 V 3.000 UL LT0 1765 1563 M 211 28 V 211 352 V 211 275 V 211 50 V 211 -32 V 211 -89 V 211 -123 V 211 -74 V 211 -33 V 211 -22 V 211 -23 V 211 0 V 211 7 V 210 16 V 211 18 V 211 22 V 211 22 V 1 0 V 3.000 UL LT0 1793 1521 M 210 29 V 211 348 V 211 291 V 211 32 V 211 -15 V 211 -119 V 211 -109 V 211 -65 V 211 -23 V 211 -30 V 211 -21 V 211 -8 V 211 7 V 211 12 V 211 21 V 211 21 V 211 23 V 3.000 UL LT0 1820 1479 M 211 25 V 211 353 V 211 293 V 211 17 V 211 -24 V 211 -105 V 211 -92 V 211 -38 V 211 -45 V 211 -31 V 211 -24 V 210 -16 V 211 3 V 211 14 V 211 19 V 211 23 V 211 22 V 3.000 UL LT0 1847 1438 M 211 25 V 211 388 V 211 263 V 211 0 V 211 -44 V 211 -78 V 211 -57 V 211 -48 V 211 -40 V 211 -49 V 211 -28 V 211 -18 V 211 1 V 211 14 V 211 20 V 211 21 V 211 23 V 3.000 UL LT0 1875 1396 M 211 25 V 211 375 V 211 299 V 211 6 V 211 -48 V 211 -102 V 211 -29 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-11 V 211 12 V 211 20 V 211 21 V 210 23 V 1 0 V 3.000 UL LT0 2040 1144 M 211 23 V 211 234 V 211 234 V 210 145 V 211 106 V 211 81 V 211 -46 V 211 -121 V 211 -100 V 211 -97 V 211 -88 V 211 -44 V 211 -8 V 211 10 V 211 20 V 211 21 V 211 23 V 3.000 UL LT0 2067 1102 M 211 23 V 211 155 V 211 143 V 211 136 V 211 94 V 211 119 V 211 42 V 211 -68 V 211 -107 V 211 -71 V 211 -96 V 211 -42 V 211 -10 V 211 12 V 210 18 V 211 23 V 211 22 V 1 0 V 3.000 UL LT0 2095 1060 M 211 23 V 210 83 V 211 93 V 211 85 V 211 96 V 211 95 V 211 88 V 211 10 V 211 -66 V 211 -68 V 211 -67 V 211 -41 V 211 -12 V 211 10 V 211 20 V 211 22 V 211 23 V 3.000 UL LT0 2122 1018 M 211 23 V 211 48 V 211 51 V 211 44 V 211 71 V 211 69 V 211 89 V 211 51 V 211 -1 V 211 -31 V 211 -38 V 211 -47 V 210 -12 V 211 13 V 211 18 V 211 22 V 211 24 V 3.000 UL LT0 2149 976 M 211 24 V 211 32 V 211 37 V 211 33 V 211 41 V 211 51 V 211 58 V 211 56 V 211 22 V 211 10 V 211 -12 V 211 -21 V 211 -12 V 211 10 V 211 19 V 211 23 V 211 23 V 3.000 UL LT0 2177 934 M 211 24 V 211 25 V 211 27 V 211 30 V 211 30 V 211 33 V 211 41 V 211 47 V 211 33 V 211 21 V 210 16 V 211 -1 V 211 -8 V 211 13 V 211 18 V 211 22 V 211 23 V 3.000 UL LT0 2204 893 M 211 23 V 211 24 V 211 23 V 211 26 V 211 25 V 211 30 V 211 24 V 211 33 V 211 30 V 211 32 V 211 21 V 211 14 V 211 10 V 211 14 V 211 19 V 211 22 V 211 23 V 3.000 UL LT0 2232 851 M 211 23 V 211 23 V 211 23 V 211 24 V 211 23 V 211 26 V 211 23 V 211 26 V 210 31 V 211 26 V 211 24 V 211 19 V 211 20 V 211 17 V 211 19 V 211 23 V 211 23 V 3.000 UL LT0 2259 809 M 211 23 V 211 23 V 211 24 V 211 22 V 211 24 V 211 23 V 211 23 V 211 24 V 211 26 V 211 25 V 211 23 V 211 24 V 211 22 V 211 20 V 211 21 V 211 23 V 211 23 V 3.000 UL LT0 2287 767 M 211 23 V 211 23 V 211 23 V 211 23 V 211 23 V 211 24 V 210 23 V 211 23 V 211 24 V 211 24 V 211 24 V 211 23 V 211 23 V 211 23 V 211 21 V 211 23 V 211 23 V 1.000 UL LTb 5873 1160 M 2287 767 L 1326 2234 M 2287 767 L 1326 2234 M 3586 393 V 5873 1160 M 4912 2627 L 1326 2234 M 0 877 V 0 -877 R 62 6 V stroke 1182 2207 M [ [(Helvetica) 240.0 0.0 true true (0)] ] -80.0 MRshow 4912 2627 M -63 -7 V 1353 2192 M 31 3 V 3556 390 R -32 -4 V 1381 2150 M 31 3 V 3555 390 R -32 -4 V 1408 2108 M 31 3 V 3556 390 R -32 -4 V 1436 2066 M 31 3 V 3555 391 R -32 -4 V 1463 2024 M 62 6 V stroke 1319 1997 M [ [(Helvetica) 240.0 0.0 true true (5)] ] -80.0 MRshow 5050 2418 M -63 -7 V 1491 1983 M 31 3 V 3555 390 R -32 -4 V 1518 1941 M 31 3 V 3555 390 R -32 -4 V 1545 1899 M 31 3 V 3556 390 R -32 -4 V 1573 1857 M 31 3 V 3555 390 R -32 -4 V 1600 1815 M 62 6 V stroke 1456 1788 M [ [(Helvetica) 240.0 0.0 true true (10)] ] -80.0 MRshow 5187 2208 M -63 -7 V 1628 1773 M 31 3 V 3555 390 R -32 -4 V 1655 1731 M 31 3 V 3556 390 R -32 -4 V 1683 1689 M 31 3 V 3555 390 R -32 -4 V 1710 1647 M 31 3 V 3556 390 R -32 -4 V 1738 1605 M 62 6 V stroke 1594 1578 M [ [(Helvetica) 240.0 0.0 true true (15)] ] -80.0 MRshow 5324 1998 M -63 -7 V 1765 1563 M 31 3 V 3556 390 R -32 -4 V 1793 1521 M 31 3 V 3555 391 R -32 -4 V 1820 1479 M 31 3 V 3555 391 R -32 -4 V 1847 1438 M 31 3 V 3556 390 R -32 -4 V 1875 1396 M 62 6 V stroke 1731 1369 M [ [(Helvetica) 240.0 0.0 true true (20)] ] -80.0 MRshow 5461 1789 M -63 -7 V 1902 1354 M 31 3 V 3556 390 R -32 -4 V 1930 1312 M 31 3 V 3555 390 R -32 -4 V 1957 1270 M 31 3 V 3556 390 R -32 -4 V 1985 1228 M 31 3 V 3555 390 R -32 -4 V 2012 1186 M 62 6 V stroke 1868 1159 M [ [(Helvetica) 240.0 0.0 true true (25)] ] -80.0 MRshow 5599 1579 M -63 -7 V 2040 1144 M 31 3 V 3555 390 R -32 -4 V 2067 1102 M 31 3 V 3556 390 R -32 -4 V 2095 1060 M 31 3 V 3555 390 R -32 -4 V 2122 1018 M 31 3 V 3555 390 R -32 -4 V 2149 976 M 62 6 V stroke 2005 949 M [ [(Helvetica) 240.0 0.0 true true (30)] ] -80.0 MRshow 5736 1370 M -63 -7 V 2177 934 M 31 3 V 3555 391 R -32 -4 V 2204 893 M 31 3 V 3556 390 R -32 -4 V 2232 851 M 31 3 V 3555 390 R -32 -4 V 2259 809 M 31 3 V 3556 390 R -32 -4 V 2287 767 M 62 6 V stroke 2143 740 M [ [(Helvetica) 240.0 0.0 true true (35)] ] -80.0 MRshow 5873 1160 M -63 -7 V 3131 859 M -35 52 V stroke 3209 658 M [ [(Helvetica) 240.0 0.0 true true (500.0)] ] -80.0 MCshow 2170 2327 M 34 -53 V 4185 975 M -35 52 V stroke 4263 774 M [ [(Helvetica) 240.0 0.0 true true (1000.0)] ] -80.0 MCshow 3224 2442 M 34 -53 V 5240 1091 M -35 52 V stroke 5318 890 M [ [(Helvetica) 240.0 0.0 true true (1500.0)] ] -80.0 MCshow 4279 2558 M 34 -53 V stroke grestore end showpage %%Trailer %%DocumentFonts: Helvetica cleartomark countdictstack exch sub { end } repeat restore grestore % % End Imported PIC File: 2D_CO125_VDist_3D.eps %%EndDocument % /Helvetica ff 225.00 scf sf 2475 3015 m gs 1 -1 sc 3.0 rot (Velocity\(m/s\)) col0 sh gr /Helvetica ff 225.00 scf sf 353 1755 m gs 1 -1 sc 295.0 rot (number) col0 sh gr /Helvetica ff 225.00 scf sf 535 1672 m gs 1 -1 sc 295.0 rot (Rot. quantum) col0 sh gr /Helvetica ff 225.00 scf sf 720 765 m gs 1 -1 sc (Intensity) col0 sh gr $F2psEnd rs %%EndDocument @endspecial 2042 1863 a Fq(FIG.)37 b(4:)56 b(Complete)37 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Fu(p)r(o-)2042 4076 y(ten)n(tial)29 b(to)g(six)g(dimensions)g(w)n(e)g(used)g(the)h (gas)e(phase)h(v)-5 b(alue)29 b(of)2042 4172 y Fm(r)2079 4184 y Fl(N)6 b(O)2218 4172 y Fu(=)22 b(2)p Fm(:)p Fu(377a)2538 4184 y Ft(0)2596 4172 y Fu(for)h(the)h(NO)2985 4142 y Ff(\000)3064 4172 y Fu(ion)f(equilibrium)h(distance.)35 b(As)2042 4267 y(is)29 b(long)g(kno)n(wn)g([1)o(])h(and)f(can)g(b)r(e)h (seen)g(in)f(\014gure)g(5)g(\(thin)i(solid)2042 4363 y(line\))24 b(this)g(is)g(leading)f(to)h(unrealistic)f(high)h (vibrational)e(excita-)2042 4458 y(tions.)34 b(Ho)n(w)n(ev)n(er)19 b(when)i(using)g(a)f(separation)f(of)i(0)p Fm(:)p Fu(05a)3760 4470 y Ft(0)3796 4458 y Fu(,)h(as)e(sug-)2042 4554 y(gested)30 b(in)h([28)o(])g(b)r(et)n(w)n(een)g(the)g(atomic)g(and)f(ionic)h (equilibrium)2042 4649 y(distance,)i(w)n(e)f(get)f(go)r(o)r(d)h (agreemen)n(t)f(with)h(the)h(exp)r(erimen)n(tal)2042 4745 y(v)-5 b(alues.)2125 4840 y(Another)40 b(observ)-5 b(ation)39 b(from)h(v)-5 b(arying)40 b(the)h(NO)3718 4810 y Ff(\000)3814 4840 y Fu(equilib-)2042 4936 y(rium)f(distance)f (is,)k(that)d(the)h(total)e(desorption)g(probabilit)n(y)2042 5031 y(did)e(not)g(c)n(hange)e(within)i(the)g(lev)n(el)g(of)f(the)h (accuracy)e(of)i(our)2042 5127 y(sim)n(ulations.)d(This)24 b(indicates)f(that)g(energy)g(transfer)f(from)h(the)2042 5222 y(vibrational)36 b(co)r(ordinate)g(in)n(to)h(other)g(degrees)f(of) h(freedom)g(is)2042 5318 y(v)n(ery)d(lo)n(w,)i(since)e(when)i(using)e (the)h(gas)f(phase)h(v)-5 b(alue)34 b(for)h(the)2042 5413 y(N{O)23 b(distance)h(half)g(of)f(the)i(tra)5 b(jectories)22 b(ha)n(v)n(e)g(enough)h(energy)p eop %%Page: 6 6 6 5 bop 4043 -299 a Fu(6)163 826 y @beginspecial 50 @llx 50 @lly 410 @urx 302 @ury 1700 @rwi @setspecial %%BeginDocument: graphs/Vib.eps %!PS-Adobe-2.0 EPSF-2.0 %%Title: Vib.eps %%Creator: gnuplot 3.7 patchlevel 1 %%CreationDate: Fri Apr 25 16:16:15 2003 %%DocumentFonts: (atend) %%BoundingBox: 50 50 410 302 %%Orientation: Portrait %%EndComments /gnudict 256 dict def gnudict begin 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V 211 29 V 211 16 V 211 25 V 211 28 V 211 15 V 211 23 V 211 23 V 211 23 V 211 24 V 211 24 V 211 25 V 211 24 V 1.000 UL LTb 5873 1203 M 2287 791 L 1326 2327 M 2287 791 L 1326 2327 M 3586 411 V 5873 1203 M 4912 2738 L 1326 2327 M 0 741 V 0 -741 R 62 7 V stroke 1182 2299 M [ [(Helvetica) 240.0 0.0 true true (0)] ] -80.0 MRshow 4912 2738 M -63 -8 V 1353 2283 M 31 3 V 3556 408 R -32 -4 V 1381 2239 M 31 3 V 3555 409 R -32 -4 V 1408 2195 M 31 3 V 3556 409 R -32 -4 V 1436 2151 M 31 3 V 3555 409 R -32 -4 V 1463 2108 M 62 7 V stroke 1319 2080 M [ [(Helvetica) 240.0 0.0 true true (5)] ] -80.0 MRshow 5050 2519 M -63 -8 V 1491 2064 M 31 3 V 3555 408 R -32 -4 V 1518 2020 M 31 3 V 3555 408 R -32 -4 V 1545 1976 M 31 3 V 3556 408 R -32 -4 V 1573 1932 M 31 3 V 3555 408 R -32 -4 V 1600 1888 M 62 7 V stroke 1456 1860 M [ [(Helvetica) 240.0 0.0 true true (10)] ] -80.0 MRshow 5187 2300 M -63 -8 V 1628 1844 M 31 3 V 3555 409 R -32 -4 V 1655 1800 M 31 3 V 3556 409 R -32 -4 V 1683 1757 M 31 3 V 3555 408 R -32 -4 V 1710 1713 M 31 3 V 3556 408 R -32 -4 V 1738 1669 M 62 7 V stroke 1594 1641 M [ [(Helvetica) 240.0 0.0 true true (15)] ] -80.0 MRshow 5324 2080 M -63 -8 V 1765 1625 M 31 3 V 3556 408 R -32 -4 V 1793 1581 M 31 3 V 3555 409 R -32 -4 V 1820 1537 M 31 3 V 3555 409 R -32 -4 V 1847 1493 M 31 3 V 3556 409 R -32 -4 V 1875 1449 M 62 7 V stroke 1731 1421 M [ [(Helvetica) 240.0 0.0 true true (20)] ] -80.0 MRshow 5461 1861 M -63 -8 V 1902 1406 M 31 3 V 3556 408 R -32 -4 V 1930 1362 M 31 3 V 3555 408 R -32 -4 V 1957 1318 M 31 3 V 3556 408 R -32 -4 V 1985 1274 M 31 3 V 3555 408 R -32 -4 V 2012 1230 M 62 7 V stroke 1868 1202 M [ [(Helvetica) 240.0 0.0 true true (25)] ] -80.0 MRshow 5599 1642 M -63 -8 V 2040 1186 M 31 3 V 3555 409 R -32 -4 V 2067 1142 M 31 3 V 3556 409 R -32 -4 V 2095 1098 M 31 3 V 3555 409 R -32 -4 V 2122 1055 M 31 3 V 3555 408 R -32 -4 V 2149 1011 M 62 7 V stroke 2005 983 M [ [(Helvetica) 240.0 0.0 true true (30)] ] -80.0 MRshow 5736 1422 M -63 -8 V 2177 967 M 31 3 V 3555 408 R -32 -4 V 2204 923 M 31 3 V 3556 408 R -32 -4 V 2232 879 M 31 3 V 3555 409 R -32 -4 V 2259 835 M 31 3 V 3556 409 R -32 -4 V 2287 791 M 62 7 V stroke 2143 763 M [ [(Helvetica) 240.0 0.0 true true (35)] ] -80.0 MRshow 5873 1203 M -63 -8 V 3131 888 M -34 53 V stroke 3207 684 M [ [(Helvetica) 240.0 0.0 true true (5.0)] ] -80.0 MCshow 2170 2424 M 33 -54 V 4185 1009 M -34 53 V stroke 4261 805 M [ [(Helvetica) 240.0 0.0 true true (10.0)] ] -80.0 MCshow 3224 2545 M 33 -54 V 5240 1130 M -34 53 V stroke 5316 926 M [ [(Helvetica) 240.0 0.0 true true (15.0)] ] -80.0 MCshow 4279 2666 M 33 -54 V stroke grestore end showpage %%Trailer %%DocumentFonts: Helvetica cleartomark countdictstack exch sub { end } repeat restore grestore % % End Imported PIC File: 7D_VDist_3D.eps %%EndDocument % /Helvetica ff 225.00 scf sf 2475 3015 m gs 1 -1 sc 3.0 rot (Velocity\(m/s\)) col0 sh gr /Helvetica ff 225.00 scf sf 353 1755 m gs 1 -1 sc 295.0 rot (number) col0 sh gr /Helvetica ff 225.00 scf sf 535 1672 m gs 1 -1 sc 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b(a)h(realistic,)g (spatially)f(v)-5 b(arying)25 b(tran-)2042 1743 y(sition)j(probabilit)n (y)g(could)g(impro)n(v)n(e)f(the)i(agreemen)n(t)f(with)h(the)2042 1839 y(exp)r(erimen)n(t.)34 b(F)-7 b(uture)21 b(researc)n(h)d(along)i (this)h(line)f(is)h(in)f(progress.)p 948 2041 2039 5 v 1203 2042 1529 7 v 1458 2043 1020 9 v 1712 2044 510 11 v -112 2289 a Fq([1])35 b(F.)28 b(M.)g(Zimmermann)d(and)i(W.)h(Ho,)h (Surf.)f(Sci.)g(Rep.)f Fo(22)p Fq(,)i(127)3 2376 y(\(1995\).)-112 2463 y([2])35 b(M.)26 b(Bonn,)g(A.)g(W.)g(Kleyn,)g(and)f(G.)i(J.)f(Kro) r(es,)h(Surf.)f(Sci.)g Fo(500)p Fq(,)3 2550 y(475)g(\(2002\).)-112 2637 y([3])35 b(M.)30 b(Bonn,)h(S.)e(F)-6 b(unk,)30 b(C.)g(Hess,)h(D.)f (N.)f(Denzler,)i(C.)g(Stamp\015,)3 2725 y(M.)k(Sc)n(he\017er,)h(M.)f(W) -6 b(olf,)38 b(and)c(G.)h(Ertl,)i(Science)d Fo(285)p Fq(,)k(1042)3 2812 y(\(1999\).)-112 2899 y([4])d(H.)17 b(P)n(etek,)j(M.)f(J.)f(W)-6 b(eida,)20 b(H.)e(Nagano,)j(and)c(S.)h (Oga)n(w)n(a,)j(Science)3 2986 y Fo(288)p Fq(,)26 b(1402)h(\(2000\).) -112 3073 y([5])35 b(A.)25 b(Gro\031,)i(Surf.)f(Sci.)g(Rep.)f Fo(32)p Fq(,)i(291)f(\(1998\).)-112 3160 y([6])35 b(G.-J.)26 b(Kro)r(es,)h(Prog.)g(Surf.)f(Sci.)g Fo(60)p Fq(,)g(1)g(\(1999\).)-112 3248 y([7])35 b(A.)25 b(Gro\031,)i(Surf.)f(Sci.)g Fo(500)p Fq(,)h(347)f(\(2002\).)-112 3335 y([8])35 b(H.)30 b(Guo,)i(P)-6 b(.)30 b(Saalfrank,)j(and)d(T.)h(Seidman,)g(Prog.)g(Surf.)g(Sci.)3 3422 y Fo(62)p Fq(,)26 b(239)h(\(1999\).)-112 3509 y([9])35 b(C.)26 b(Bac)n(h)g(and)f(A.)h(Gro\031,)h(F)-6 b(arada)n(y)26 b(Diss.)g Fo(117)p Fq(,)h(99)f(\(2000\).)-150 3596 y([10])35 b(C.)25 b(Bac)n(h)h(and)e(A.)h(Gro\031,)h(J.)g(Chem.)e(Ph)n(ys.)h Fo(114)p Fq(,)h(6396)h(\(2001\).)-150 3683 y([11])35 b(J.)26 b(C.)g(T)-6 b(ully)g(,)26 b(J.)g(Chem.)g(Ph)n(ys.)f Fo(93)p Fq(,)h(1061)i(\(1990\).)-150 3771 y([12])35 b(D.)d(S.)g(Sholl)h (and)e(J.)i(C.)g(T)-6 b(ully)g(,)34 b(J.)f(Chem.)f(Ph)n(ys.)g Fo(109)p Fq(,)j(7702)3 3858 y(\(1998\).)-150 3945 y([13])g(W.)26 b(Brenig,)g(Z.)g(Ph)n(ys.)g(B)g Fo(23)p Fq(,)g(361)h(\(1976\).)-150 4032 y([14])35 b(P)-6 b(.)25 b(Saalfrank,)i(Chem.)e(Ph)n(ys.)h Fo(193)p Fq(,)h(119)f(\(1995\).)-150 4119 y([15])35 b(T.)28 b(Kl)r(\177)-41 b(uner,)29 b(H.-J.)g(F)-6 b(reund,)27 b(V.)h(Staemmler,)f(and)g(R.)h(Koslo\013,)3 4206 y(Ph)n(ys.)d(Rev.)g (Lett.)h Fo(80)p Fq(,)h(5208)g(\(1998\).)-150 4294 y([16])35 b(T.)30 b(Kl)r(\177)-41 b(uner,)31 b(H.-J.)f(F)-6 b(reund,)29 b(J.)h(F)-6 b(reitag,)32 b(and)d(V.)g(Staemmler,)3 4381 y(J.)d(Mol.)h(Catal.)g(A)f Fo(119)p Fq(,)g(155)h(\(1997\).)-150 4468 y([17])35 b(T.)51 b(Mull,)58 b(B.)52 b(Baumeister,)57 b(M.)52 b(Menges,)58 b(H.-J.)51 b(F)-6 b(reund,)2194 2289 y(D.W)g(eide,)33 b(C.)f(Fisc)n(her,)i(and)d(P)-6 b(.)32 b(Andersen,)g(J.)g(Chem.)f(Ph)n(ys.)2194 2376 y Fo(96)p Fq(,)c(7108)g(\(1992\).)2042 2463 y([18])34 b(G.)80 b(Eic)n(hhorn,)92 b(M.)79 b(Ric)n(h)n(ter,)91 b(K.)79 b(Al-Shamery)-6 b(,)89 b(and)2194 2550 y(H.)26 b(Zac)n(harias,)h(Surf.)f(Sci.)g Fo(368)p Fq(,)h(67)f(\(1996\).)2042 2637 y([19])34 b(D.)44 b(Menzel)f(and)g(R.)g(Gomer,)48 b(J.)c(Chem.)e(Ph)n(ys.)h Fo(41)p Fq(,)49 b(3311)2194 2725 y(\(1964\).)2042 2812 y([20])34 b(P)-6 b(.)26 b(A.)g(Redhead,)f (Can.)h(J.)h(Ph)n(ys.)e Fo(42)p Fq(,)i(886)f(\(1964\).)2042 2899 y([21])34 b(P)-6 b(.)26 b(R.)g(An)n(toniewicz,)g(Ph)n(ys.)g(Rev.)f (B)h Fo(21)p Fq(,)g(3811)h(\(1980\).)2042 2986 y([22])34 b(H.)40 b(Zac)n(harias,)46 b(G.)40 b(Eic)n(hhorn,)k(R.)c(Sc)n (hliesing,)45 b(and)40 b(K.)g(Al-)2194 3073 y(Shamery)-6 b(,)24 b(Appl.)i(Ph)n(ys.)f(B)h Fo(68)p Fq(,)g(605)h(\(1999\).)2042 3160 y([23])34 b(G.)80 b(Eic)n(hhorn,)92 b(M.)79 b(Ric)n(h)n(ter,)91 b(K.)79 b(Al-Shamery)-6 b(,)89 b(and)2194 3248 y(H.)26 b(Zac)n(harias,)h(J.)g(Chem.)e(Ph)n(ys.)g Fo(111)p Fq(,)i(386)g (\(1999\).)2042 3335 y([24])34 b(R.)22 b(G.)h(Newton,)g Fr(Sc)l(attering)j(The)l(ory)f(of)f(Waves)g(and)h(Particles)2194 3422 y Fq(\(McGra)n(w-Hill,)j(1966\).)2042 3509 y([25])34 b(R.)f(Brak)n(o)g(and)g(D.)f(M.)i(Newns,)h(Rep.)d(Prog.)i(Ph)n(ys.)f Fo(52)p Fq(,)i(655)2194 3596 y(\(1989\).)2042 3683 y([26])f(J.)27 b(W.)f(Gadzuk,)f(Surf.)h(Sci.)g Fo(342)p Fq(,)h(345)f(\(1995\).)2042 3771 y([27])34 b(T.)d(Kl)r(\177)-41 b(uner,)31 b(H.-J.)f(F)-6 b(reund,)29 b(J.)h(F)-6 b(reitag,)32 b(and)d(V.)g(Staemmler,)2194 3858 y(J.)e(Chem.)e(Ph)n(ys.)h Fo(104)p Fq(,)g(10030)i(\(1996\).)2042 3945 y([28])34 b(T.)j(Kl)r(\177)-41 b(uner,)40 b(S.)c(Thiel,)k(H.-J.)c (F)-6 b(reund,)38 b(and)d(V.)h(Staemmler,)2194 4032 y(Chem.)26 b(Ph)n(ys.)f(Lett.)h Fo(294)p Fq(,)h(413)f(\(1998\).)2042 4119 y([29])34 b(A.)26 b(Gro\031)h(and)e(W.)h(Brenig,)h(Surf.)e(Sci.)i Fo(302)p Fq(,)f(403)h(\(1994\).)2042 4206 y([30])34 b(K.)28 b(S.)f(Upadh)n(y)n(a)n(y)n(a,)g(G.)h(K.)f(Upadh)n(y)n(a)n(y)n(a,)g(and) g(A.)g(N.)h(P)n(andey)-6 b(,)2194 4294 y(J.)27 b(Ph)n(ys.)e(Chem.)h (Solids)g Fo(63)p Fq(,)g(127)h(\(2002\).)p eop %%Trailer end userdict /end-hook known{end-hook}if %%EOF