ADC

Official Resources

• Homepage: https://manual.q-chem.com/latest/sec_adc_pp_scheme.html (Q-Chem implementation)
• Documentation: https://pyscf.org/user/adc.html (PySCF implementation)
• License: Varies by implementation (Q-Chem: commercial; PySCF: Apache 2.0)

Overview

The Algebraic Diagrammatic Construction (ADC) scheme for the polarization propagator is a family of ab initio methods for the calculation of excited electronic states, ionization potentials, and electron affinities. First derived by Schirmer in 1982 using the diagrammatic perturbation expansion of the polarization propagator, ADC methods provide a size-consistent, Hermitian approach to computing excited-state properties with perturbation-theory-based accuracy at each order.

ADC methods originate from Green's function (propagator) theory and are derived via the intermediate state representation (ISR). The nth-order ADC scheme (ADC(n)) uses the nth-order Møller-Plesset ground state as its starting point, yielding excitation energies and transition probabilities through a one-shot calculation. The second-order ADC(2) scheme has attracted significant attention for its reliable accuracy and reasonable computational cost, while ADC(3) offers high accuracy for typical valence excited states of organic chromophores.

Scientific domain: Quantum chemistry, excited-state methods
Target user community: Computational chemists studying molecular excited states

Theoretical Methods

• Polarization propagator theory
• Diagrammatic perturbation expansion (Møller-Plesset partition)
• Intermediate state representation (ISR) for derivation
• ADC(2), ADC(2)-X (extended), and ADC(3) approximation schemes
• Hermitian eigenvalue problem in limited configuration space
• One-particle Green's function for ionization potentials and electron affinities
• Size-consistent excited-state methods

Capabilities (CRITICAL)

• Excitation energies (EE-ADC) for neutral electronic excitations
• Ionization potentials (IP-ADC) via one-particle Green's function
• Electron affinities (EA-ADC)
• ADC(2), ADC(2)-X, and ADC(3) variants
• Excited-state properties via intermediate state representation
• Transition intensities and oscillator strengths
• Photoelectron and absorption spectra
• Hermitian matrix structure for stable eigenvalue solutions
• Size-consistency for large molecule applications

Inputs & Outputs

Input formats:

• Q-Chem input files (for Q-Chem ADC implementation)
• PySCF Python scripts (for PySCF ADC module)
• Hartree-Fock or MP ground state as starting point

Output data types:

• Excitation energies
• Transition moments and oscillator strengths
• Excited-state properties (dipole moments, etc.)
• Photoelectron spectra
• Electron attachment spectra

Interfaces & Ecosystem

• Q-Chem: Most complete ADC suite of methods (commercial)
• PySCF: ADC module for EE, IP, and EA calculations (open-source, Apache 2.0)
• Programming language: Python (PySCF), C++ (Q-Chem)
• Related methods: ADC available in several quantum chemistry packages

Limitations & Known Constraints

• Single-reference methods; may fail for strong correlation
• ADC(3) is computationally expensive (scaling ~O(N^6))
• Accuracy depends on quality of MPn ground state
• Predominantly singly excited states well-described; double excitations limited

Performance Characteristics

• ADC(2): O(N^5) scaling, suitable for medium molecules
• ADC(3): O(N^6) scaling, more expensive but higher accuracy
• One-shot calculation (no iteration beyond matrix diagonalization)
• Size-consistent, enabling study of large molecules
• Hermitian structure ensures stable and efficient diagonalization

Comparison with Other Codes

• vs TD-DFT: ADC does not require XC functional tuning; more systematic but more expensive
• vs EOM-CCSD: ADC(2) is less expensive than EOM-CCSD; ADC(3) comparable in accuracy
• vs CIS: ADC(2) includes electron correlation effects missing in CIS
• vs CASPT2: ADC is single-reference; CASPT2 handles multi-reference cases

Best Practices

• Use ADC(2) for balanced accuracy and cost on medium molecules
• Use ADC(3) for high-accuracy valence excitations of organic chromophores
• Verify results are not dominated by double excitations
• Check MPn ground state convergence before ADC calculation
• Use PySCF for open-source access; Q-Chem for most complete feature set

Verification & Sources

Primary sources:

1. Schirmer, Phys. Rev. A 26, 2395 (1982) - original ADC derivation
2. A. Dreuw and M. Wormit, WIREs Comput. Mol. Sci. 5, 82-95 (2015)
3. PySCF ADC documentation: https://pyscf.org/user/adc.html
4. Q-Chem ADC manual: https://manual.q-chem.com/latest/sec_adc_pp_scheme.html

Confidence: VERIFIED - Method well-documented in multiple implementations and literature