Data set for Manuscript jz-2019-01349t Figure 2

The transition strengths for producing heat maps for a optical and vibrational processes in ||-SA and GS-SA in a quadmer. For each transition we label an initial state, a final state, a weight, and a transition frequency in eV. The eigenstate labels index from the highest energy eigenstate to the lowest. The number of eigenstates in each eigenstate rung can be determined with the binomial distribution: eC4, where e is the number of excitations in the system, which can be 0,1,2,3,4. Optical weights only consider the dipole contribution that is normal to plane of the ring, (in calculations we use all 3 components). The optical transition strengths for heat maps, with a flat spectral density assumed, are given by (weight)^2*(transition frequency)^3. The vibrational transition strengths for heat maps, with a flat spectral density assumed, are given by (weight)^2*(transition frequency). The vibrational lists each containt 4 lists (one for each local bath). The transition strengths from each of the 4 vibrational interaction lists are combined additively for total process strength combining eigenstates.

||-SA Optical:
{{1, 2, -0.0632456, 1.18772}, {2, 6, 2.43529, 1.57876}, {2, 11, -0.2634, 3.06186}, {3, 7, -0.87182, 1.70802}, {3, 8, -0.63068, 1.70802}, {3, 9, 0.917699, 1.70802}, {4, 7, 1.11352, 1.70802}, {4, 8, -0.493785, 1.70802}, {4, 9, 0.718503, 1.70802}, {5, 8, -0.0368567, 1.37167}, {5, 9, -0.0253295, 1.37167}, {6, 12, 2.43529, 2.02124}, {7, 13, -1., 1.89198}, {7, 14, 1., 1.89198}, {8, 13, -0.566384, 1.89198}, {8, 14, -0.566384, 1.89198}, {8, 15, 1.16551, 2.22833}, {9, 13, 0.824142, 1.89198}, {9, 14, 0.824142, 1.89198}, {9, 15, 0.800988, 2.22833}, {11, 12, -0.00832944, 0.538144}, {12, 16, -2., 2.41228}}

GS-SA Optical:
{{1, 5, -1.41421, 1.93008}, {2, 7, 0.00895444, 1.93008}, {2, 8, -0.0447079, 1.93008}, {2, 10, 0.99896, 1.93008}, {3, 7, -0.728926, 1.8}, {3, 8, -0.398769, 1.8}, {3, 9, 0.556347, 1.8}, {3, 10, -0.0113128, 1.8}, {4, 7, 0.0174844, 1.8}, {4, 8, 0.800797, 1.8}, {4, 9, 0.597616, 1.8}, {4, 10, 0.0356826, 1.8}, {5, 6, -0.0092621, 1.48597}, {5, 11, 1.70711, 1.85388}, {6, 15, -0.292893, 2.11403}, {7, 12, 0.000283164, 1.66992}, {7, 13, -0.0435247, 1.8}, {7, 14, -0.727835, 1.8}, {8, 12, -0.00141379, 1.66992}, {8, 13, -0.814538, 1.8}, {8, 14, -0.369894, 1.8}, {9, 13, -0.57735, 1.8}, {9, 14, 0.57735, 1.8}, {10, 12, 0.0315899, 1.66992}, {10, 13, -0.0360641, 1.8}, {10, 14, -0.0100303, 1.8}, {11, 15, 1.70711, 1.74612}, {15, 16, -0.0447214, 1.66992}}

||-SA Vibrational:
{{{1, 1, 0.5, 0}, {2, 2, 0.25, 0}, {2, 3, 0.701924, 0.704262}, {2,  4, -0.0854541, 0.704262}, {2, 5, -0.5, 1.04061}, {3, 3, 0.00730241,  0}, {3, 4, 0.0599823, 0}, {3, 5, 0.701924, 0.33635}, {4, 4,  0.492698, 0}, {4, 5, -0.0854541, 0.33635}, {5, 5, 0.25, 0}, {6,  7, -0.530103, 0.833528}, {6, 8, 0.245178, 0.833528}, {6, 9,  0.811714, 0.833528}, {7, 10, -0.707107, 0.183956}, {7, 11,  0.467965, 0.649572}, {8, 10, 0.400494, 0.183956}, {8, 11, 0.882889,  0.649572}, {9, 10, -0.582756, 0.183956}, {9, 11, 0.0389361,  0.649572}, {12, 12, -0.25, 0}, {12, 13, 0.707107, 0.704262}, {12,  15, 0.5, 1.04061}, {13, 15, 0.707107, 0.33635}, {14, 14, -0.5,  0}, {15, 15, -0.25, 0}, {16, 16, -0.5, 0}}, {{1, 1, 0.5, 0}, {2, 2,  0.25, 0}, {2, 3, -0.0854541, 0.704262}, {2, 4, -0.701924,  0.704262}, {2, 5, 0.5, 1.04061}, {3, 3, 0.492698, 0}, {3,  4, -0.0599823, 0}, {3, 5, 0.0854541, 0.33635}, {4, 4, 0.00730241,  0}, {4, 5, 0.701924, 0.33635}, {5, 5, 0.25, 0}, {6, 7, -0.530103,  0.833528}, {6, 8, -0.245178, 0.833528}, {6, 9, -0.811714,  0.833528}, {7, 10, -0.707107, 0.183956}, {7, 11, 0.467965,  0.649572}, {8, 10, -0.400494, 0.183956}, {8, 11, -0.882889,  0.649572}, {9, 10, 0.582756, 0.183956}, {9, 11, -0.0389361,  0.649572}, {12, 12, -0.25, 0}, {12, 14, -0.707107, 0.704262}, {12,  15, -0.5, 1.04061}, {13, 13, -0.5, 0}, {14, 15, 0.707107,  0.33635}, {15, 15, -0.25, 0}, {16, 16, -0.5, 0}}, {{1, 1, 0.5,  0}, {2, 2, 0.25, 0}, {2, 3, -0.701924, 0.704262}, {2, 4, 0.0854541,  0.704262}, {2, 5, -0.5, 1.04061}, {3, 3, 0.00730241, 0}, {3, 4,  0.0599823, 0}, {3, 5, -0.701924, 0.33635}, {4, 4, 0.492698, 0}, {4,  5, 0.0854541, 0.33635}, {5, 5, 0.25, 0}, {6, 7, 0.530103,  0.833528}, {6, 8, 0.845661, 0.833528}, {6, 9, -0.0620453,  0.833528}, {7, 10, 0.707107, 0.183956}, {7, 11, -0.467965,  0.649572}, {8, 10, -0.400494, 0.183956}, {8, 11, 0.352793,  0.649572}, {9, 10, 0.582756, 0.183956}, {9, 11, 0.810275,  0.649572}, {12, 12, -0.25, 0}, {12, 13, -0.707107, 0.704262}, {12,  15, 0.5, 1.04061}, {13, 15, -0.707107, 0.33635}, {14, 14, -0.5,  0}, {15, 15, -0.25, 0}, {16, 16, -0.5, 0}}, {{1, 1, 0.5, 0}, {2, 2,  0.25, 0}, {2, 3, 0.0854541, 0.704262}, {2, 4, 0.701924,  0.704262}, {2, 5, 0.5, 1.04061}, {3, 3, 0.492698, 0}, {3,  4, -0.0599823, 0}, {3, 5, -0.0854541, 0.33635}, {4, 4, 0.00730241,  0}, {4, 5, -0.701924, 0.33635}, {5, 5, 0.25, 0}, {6, 7, 0.530103,  0.833528}, {6, 8, -0.845661, 0.833528}, {6, 9, 0.0620453,  0.833528}, {7, 10, 0.707107, 0.183956}, {7, 11, -0.467965,  0.649572}, {8, 10, 0.400494, 0.183956}, {8, 11, -0.352793,  0.649572}, {9, 10, -0.582756, 0.183956}, {9, 11, -0.810275,  0.649572}, {12, 12, -0.25, 0}, {12, 14, 0.707107, 0.704262}, {12,  15, -0.5, 1.04061}, {13, 13, -0.5, 0}, {14, 15, -0.707107,  0.33635}, {15, 15, -0.25, 0}, {16, 16, -0.5, 0}}}

GS-SA Vibrational:
{{{1, 1, 0.5, 0}, {2, 2, 0.25, 0}, {2, 3, 0.0252717, 0.130077}, {2,  4, -0.706655, 0.130077}, {2, 5, 0.5, 0.260153}, {3, 3, 0.499361,  0}, {3, 4, 0.0178583, 0}, {3, 5, -0.0252717, 0.130077}, {4, 4,  0.000638657, 0}, {4, 5, 0.706655, 0.130077}, {5, 5, 0.25, 0}, {6,  7, -0.0244449, 0.183956}, {6, 8, -0.607578, 0.183956}, {6,  9, -0.408248, 0.183956}, {6, 10, 0.68087, 0.183956}, {7, 7,  0.498066, 0}, {7, 8, -0.0352524, 0}, {7, 9, 0.0125645, 0}, {7,  10, -0.00604224, 0}, {7, 11, 0.0371084, 0.183956}, {8,  8, -0.164471, 0}, {8, 9, 0.235137, 0}, {8, 10, -0.00704482, 0}, {8,  11, 0.544352, 0.183956}, {9, 9, -0.333333, 0}, {9, 10, 0.0104108,  0}, {9, 11, 0.408248, 0.183956}, {10, 10, -0.000261126, 0}, {10,  11, 0.731873, 0.183956}, {12, 12, -0.25, 0}, {12, 13, -0.707107,  0.130077}, {12, 15, 0.5, 0.260153}, {13, 15, -0.707107,  0.130077}, {14, 14, -0.5, 0}, {15, 15, -0.25, 0}, {16, 16, -0.5,  0}}, {{1, 1, 0.5, 0}, {2, 2, 0.25, 0}, {2, 3, 0.706655,  0.130077}, {2, 4, 0.0252717, 0.130077}, {2, 5, -0.5, 0.260153}, {3,  3, 0.000638657, 0}, {3, 4, -0.0178583, 0}, {3, 5, 0.706655,  0.130077}, {4, 4, 0.499361, 0}, {4, 5, 0.0252717, 0.130077}, {5, 5,  0.25, 0}, {6, 7, 0.508326, 0.183956}, {6, 8, 0.293168,  0.183956}, {6, 9, -0.408248, 0.183956}, {6, 10, -0.699279,  0.183956}, {7, 7, -0.0297844, 0}, {7, 8, -0.269022, 0}, {7,  9, -0.210108, 0}, {7, 10, -0.011773, 0}, {7, 11, -0.520989,  0.183956}, {8, 8, 0.362179, 0}, {8, 9, -0.106779, 0}, {8, 10,  0.0186206, 0}, {8, 11, -0.229941, 0.183956}, {9, 9, -0.333333,  0}, {9, 10, -0.00289549, 0}, {9, 11, 0.408248, 0.183956}, {10, 10,  0.000938884, 0}, {10, 11, -0.713464, 0.183956}, {12, 12, -0.25,  0}, {12, 14, -0.707107, 0.130077}, {12, 15, -0.5, 0.260153}, {13,  13, -0.5, 0}, {14, 15, 0.707107, 0.130077}, {15, 15, -0.25,  0}, {16, 16, -0.5, 0}}, {{1, 1, 0.5, 0}, {2, 2, 0.25, 0}, {2,  3, -0.0252717, 0.130077}, {2, 4, 0.706655, 0.130077}, {2, 5, 0.5,  0.260153}, {3, 3, 0.499361, 0}, {3, 4, 0.0178583, 0}, {3, 5,  0.0252717, 0.130077}, {4, 4, 0.000638657, 0}, {4, 5, -0.706655,  0.130077}, {5, 5, 0.25, 0}, {6, 7, 0.0371084, 0.183956}, {6, 8,  0.544352, 0.183956}, {6, 9, 0.408248, 0.183956}, {6, 10, 0.731873,  0.183956}, {7, 7, -0.498066, 0}, {7, 8, 0.0352524, 0}, {7,  9, -0.0125645, 0}, {7, 10, 0.00604224, 0}, {7, 11, -0.0244449,  0.183956}, {8, 8, 0.164471, 0}, {8, 9, -0.235137, 0}, {8, 10,  0.00704482, 0}, {8, 11, -0.607578, 0.183956}, {9, 9, 0.333333,  0}, {9, 10, -0.0104108, 0}, {9, 11, -0.408248, 0.183956}, {10, 10,  0.000261126, 0}, {10, 11, 0.68087, 0.183956}, {12, 12, -0.25,  0}, {12, 13, 0.707107, 0.130077}, {12, 15, 0.5, 0.260153}, {13, 15,  0.707107, 0.130077}, {14, 14, -0.5, 0}, {15, 15, -0.25, 0}, {16,  16, -0.5, 0}}, {{1, 1, 0.5, 0}, {2, 2, 0.25, 0}, {2, 3, -0.706655,  0.130077}, {2, 4, -0.0252717, 0.130077}, {2, 5, -0.5,  0.260153}, {3, 3, 0.000638657, 0}, {3, 4, -0.0178583, 0}, {3,  5, -0.706655, 0.130077}, {4, 4, 0.499361, 0}, {4, 5, -0.0252717,  0.130077}, {5, 5, 0.25, 0}, {6, 7, -0.520989, 0.183956}, {6,  8, -0.229941, 0.183956}, {6, 9, 0.408248, 0.183956}, {6,  10, -0.713464, 0.183956}, {7, 7, 0.0297844, 0}, {7, 8, 0.269022,  0}, {7, 9, 0.210108, 0}, {7, 10, 0.011773, 0}, {7, 11, 0.508326,  0.183956}, {8, 8, -0.362179, 0}, {8, 9, 0.106779, 0}, {8,  10, -0.0186206, 0}, {8, 11, 0.293168, 0.183956}, {9, 9, 0.333333,  0}, {9, 10, 0.00289549, 0}, {9, 11, -0.408248, 0.183956}, {10,  10, -0.000938884, 0}, {10, 11, -0.699279, 0.183956}, {12,  12, -0.25, 0}, {12, 14, 0.707107, 0.130077}, {12, 15, -0.5,  0.260153}, {13, 13, -0.5, 0}, {14, 15, -0.707107, 0.130077}, {15,  15, -0.25, 0}, {16, 16, -0.5, 0}}}