Table 4 Mulliken population analysis for each of structures Au-A-Au and Au-B-Au in the presence/absence of electric fields of different intensities.

Au-A-Au

 C1

− 0.182035

− 0.169766

− 0.157938

− 0.146520

− 0.135510

− 0.124855

 C2

0.520506

0.505144

0.490869

0.477602

0.465484

0.454481

 C3

− 0.657876

− 0.660144

− 0.662929

− 0.666115

− 0.669786

− 0.673864

 C4

0.457172

0.467395

0.478484

0.490472

0.503378

0.517179

 C5

0.513862

0.524238

0.534760

0.545468

0.556407

0.567610

 C6

− 0.150958

− 0.147581

− 0.144514

− 0.141729

− 0.139206

− 0.136913

 H7

0.221281

0.226953

0.232626

0.238300

0.243973

0.249644

 H8

0.308903

0.303597

0.298335

0.293107

0.287910

0.282735

 H9

0.238079

0.247457

0.256758

0.265981

0.275121

0.284179

 C10

− 0.555333

− 0.564098

− 0.573760

− 0.584384

− 0.596073

− 0.608927

 C11

0.456743

0.459054

0.461691

0.464648

0.467955

0.471625

 C12

− 0.657328

− 0.666217

− 0.675842

− 0.686131

− 0.697082

− 0.708669

 C13

0.520351

0.500656

0.483078

0.467341

0.453227

0.440569

 C14

− 0.182393

− 0.165221

− 0.148836

− 0.133128

− 0.118016

− 0.103437

 C15

− 0.150851

− 0.147693

− 0.144632

− 0.141640

− 0.138684

− 0.135735

 C16

0.513411

0.525091

0.536815

0.548623

0.560581

0.572730

 H17

0.308902

0.305865

0.302945

0.300142

0.297461

0.294903

 H18

0.221279

0.231193

0.241049

0.250843

0.260569

0.270224

 H19

0.238079

0.246241

0.254360

0.262433

0.270457

0.278430

 O20

− 0.354937

− 0.367698

− 0.380312

− 0.392765

− 0.405043

− 0.417129

 S21

− 0.388678

− 0.378444

− 0.368372

− 0.358609

− 0.349288

− 0.340563

 S22

− 0.388576

− 0.359872

− 0.332015

− 0.305011

− 0.278872

− 0.253639

 Au23

− 0.424772

− 0.462410

− 0.500165

− 0.537985

− 0.575800

− 0.613508

 Au24

− 0.424834

− 0.453738

− 0.482454

− 0.510939

− 0.539161

− 0.567071

Au-B-Au

 C1

− 0.027755

− 0.015690

− 0.003890

0.007652

− 0.152166

0.030139

 C2

0.870011

0.851226

0.833398

0.816703

− 0.371896

0.786700

 C3

− 0.681581

− 0.682585

− 0.684093

− 0.686115

− 0.211616

− 0.691614

 C4

0.025089

0.033370

0.042009

0.050939

− 0.000370

0.069471

 C5

0.460244

0.467675

0.475115

0.482596

0.057658

0.497778

 C6

− 0.034856

− 0.031300

− 0.028024

− 0.024993

− 0.217953

− 0.019544

 H7

0.214512

0.220079

0.225666

0.231271

0.243729

0.242534

 H8

0.254370

0.248777

0.243249

0.237776

0.210001

0.226982

 H9

0.236240

0.245529

0.254759

0.263926

0.235058

0.282061

 C10

− 0.809553

− 0.815311

− 0.821162

− 0.827124

0.364166

− 0.839463

 C11

0.471697

0.478240

0.485101

0.492334

0.041874

0.508061

 C12

− 0.734138

− 0.743781

− 0.754250

− 0.765525

− 0.191876

− 0.790370

 C13

0.551541

0.530749

0.512043

0.495125

− 0.397514

0.465724

 C14

− 0.193333

− 0.176426

− 0.160376

− 0.145084

− 0.145370

− 0.116386

 C15

− 0.137676

− 0.134825

− 0.132056

− 0.129346

− 0.216575

− 0.124005

 C16

0.500000

0.510798

0.521619

0.532525

0.053584

0.554765

 H17

0.293406

0.290138

0.286978

0.283936

0.241913

0.278215

 H18

0.213480

0.223473

0.233403

0.243265

0.260688

0.262764

 H19

0.233812

0.242075

0.250288

0.258448

0.238815

0.274606

 O20

− 0.358370

− 0.363522

− 0.368466

− 0.373203

− 0.590935

− 0.382049

 S21

− 0.378959

− 0.368820

− 0.358959

− 0.349567

0.222303

− 0.332753

 S22

− 0.387375

− 0.358543

− 0.330647

− 0.303686

0.348580

− 0.252682

 Au23

− 0.466902

− 0.504609

− 0.542380

− 0.580155

− 0.371215

− 0.655393

 Au24

− 0.451997

− 0.480934

− 0.509665

− 0.538153

− 0.046524

− 0.594217

 H25

0.338092

0.334218

0.330339

0.326454

0.395644

0.318673