Introduction

Overview

PSI4 provides a wide variety of quantum chemical methods using state-of-the-art numerical methods and algorithms. Several parts of the code feature shared-memory parallelization to run efficiently on multi-core machines (see Sec. Threading). An advanced parser written in Python allows the user input to have a very simple style for routine computations, but it can also automate very complex tasks with ease.

PSI4 is, in many ways, a whole new package compared to Psi3. While some libraries and modules remain the same, the majority of the code has been rewritten from scratch based on a powerful set of new libraries written in C++. A totally new Python front-end makes PSI4 incredibly user-friendly and automates many common tasks such as basis set extrapolation, composite methods, running the same computation on every molecule in a test set, etc. Density-functional theory, absent in Psi3, is quite efficient in PSI4, with many functionals available. Density fitting is ubiquitous in PSI4, leading to some of the most efficient MP2 and CCSD(T) code available. PSI4 also introduces extensive, powerful features for energy component analysis of non-covalent interactions via symmetry-adapted perturbation theory. Orbital-optimized versions of perturbation theory and coupled-cluster methods, and their analytic gradients, have also been added. Through external libraries, PSI4 gains access to implicit solvent (PCM) capabilities, density-matrix renormalization group CI, effective fragment potentials, Grimme dispersion corrections, and high-order coupled-cluster theory.

In this section, we provide an overview of some of the features of PSI4 along with the prerequisite steps for running calculations. Sec. Tutorial provides a brief tutorial to help new users get started. Section Psithon offers further details into the structure of PSI4 input files and how Python can be mixed with quantum chemistry directives in PSI4. Section Psithon Functions provides more detail on the Python functions provided by PSI4 and discusses some of the higher-level functions such as counterpoise correction, complete-basis-set extrapolation, and running computations on an entire database of molecules at a time. Later sections deal with the different types of computations which can be done using PSI4 (e.g., Hartree–Fock, MP2, coupled-cluster) and general procedures such as geometry optimization and vibrational frequency analysis. The Appendices include a complete description of all possible input keywords for each module, as well as tables of available basis sets and a listing of the sample input files available under psi4/samples. The user is urged to examine this directory of sample inputs, as most common types of computations are represented there. For the latest PSI4 documentation, check www.psicode.org.

Citing PSI4

Overall PSI4 Package

The following citation should be used in any publication utilizing the PSI4 program package:

• “Psi4 1.4: Open-Source Software for High-Throughput Quantum Chemistry”, D. G. A. Smith, L. A. Burns, A. C. Simmonett, R. M. Parrish, M. C. Schieber, R. Galvelis, P. Kraus, H. Kruse, R. Di Remigio, A. Alenaizan, A. M. James, S. Lehtola, J. P. Misiewicz, M. Scheurer, R. A. Shaw, J. B. Schriber, Y. Xie, Z. L. Glick, D. A. Sirianni, J. S. O’Brien, J. M. Waldrop, A. Kumar, E. G. Hohenstein, B. P. Pritchard, B. R. Brooks, H. F. Schaefer III, A. Yu. Sokolov, K. Patkowski, A. E. DePrince III, U. Bozkaya, R. A. King, F. A. Evangelista, J. M. Turney, T. D. Crawford, C. D. Sherrill, J. Chem. Phys. (2020). (doi: 10.1063/5.0006002).

The following citation covers PSI4 early stable releases:

• “Psi4 1.1: An Open-Source Electronic Structure Program Emphasizing Automation, Advanced Libraries, and Interoperability”, R. M. Parrish, L. A. Burns, D. G. A. Smith, A. C. Simmonett, A. E. DePrince III, E. G. Hohenstein, U. Bozkaya, A. Yu. Sokolov, R. Di Remigio, R. M. Richard, J. F. Gonthier, A. M. James, H. R. McAlexander, A. Kumar, M. Saitow, X. Wang, B. P. Pritchard, P. Verma, H. F. Schaefer III, K. Patkowski, R. A. King, E. F. Valeev, F. A. Evangelista, J. M. Turney, T. D. Crawford, and C. D. Sherrill, J. Chem. Theory Comput., 13(7) 3185–3197 (2017). (doi: 10.1021/acs.jctc.7b00174).

The following citation covers PSI4 alpha and beta versions:

• “Psi4: An open-source ab initio electronic structure program,” J. M. Turney, A. C. Simmonett, R. M. Parrish, E. G. Hohenstein, F. Evangelista, J. T. Fermann, B. J. Mintz, L. A. Burns, J. J. Wilke, M. L. Abrams, N. J. Russ, M. L. Leininger, C. L. Janssen, E. T. Seidl, W. D. Allen, H. F. Schaefer, R. A. King, E. F. Valeev, C. D. Sherrill, and T. D. Crawford, WIREs Comput. Mol. Sci. 2, 556 (2012). (doi: 10.1002/wcms.93).

Depending on the particular modules used, the user may also wish to cite some of the following references for theoretical, algorithmic, or implementation contributions specific to PSI4 (in addition to appropriate references for the underlying theory, which are not necessarily included in the list below).

Most PSI4 calculations employ density functional theory. PSI4 does not implement any density functionals; instead, all the density functionals come from LIBXC, which should be cited in addition to PSI4

• “Recent developments in LIBXC — a comprehensive library of functionals for density functional theory,” S. Lehtola, C. Steigemann, M. J. T. Oliveira, and M. A. L. Marques, SoftwareX 7, 1 (2018). (doi: 10.1016/j.softx.2017.11.002)

Regardless of the type of the calculation, an initial guess is necessary. PSI4 features several initial guesses for the molecular orbitals. The default guess is the superposition of atomic densities (SAD), discussed in

• “Principles for a direct SCF approach to LCAO-MO ab-initio calculations”, J. Almlöf, K. Faegri, and K. Korsell, J. Comput. Chem. 3, 385 (1982). (doi: 10.1002/jcc.540030314).

• “Starting SCF calculations by superposition of atomic densities”, J. H. Van Lenthe, R. Zwaans, H. J. J. Van Dam, and M. F. Guest, J. Comput. Chem. 27, 926 (2006). (doi: 10.1002/jcc.20393).

PSI4 also features a SAD natural orbital guess, an extended Hückel guess that employs on-the-fly atomic calculations alike the SAD guess, as well as a superposition of atomic potentials (SAP) guess that is based on screening of atomic nuclei. The SAD natural orbitals, Hückel and SAP guesses have been described in

• “An assessment of initial guesses for self-consistent field calculations. Superposition of Atomic Potentials: simple yet efficient”, S. Lehtola, J. Chem. Theory Comput. 15, 1593 (2019) (doi: 10.1021/acs.jctc.8b01089).

Density Cumulant Theory (DCT)

PSI4 features several formulations of newly-developed density cumulant theory (DCT), also known as density cumulant functional theory (DCFT). The theory and benchmark of this theory are discussed in the following papers:

DC-06 (also known as DCT-06):

• “Density Cumulant Functional Theory: First Implementation and Benchmark Results for the DCFT-06 Model,” A. C. Simmonett, J. J. Wilke, H. F. Schaefer, and W. Kutzelnigg, J. Chem. Phys. 133, 174122 (2010). (doi: 10.1063/1.3503657).

• “Analytic gradients for density cumulant functional theory: The DCFT-06 model,” A. Yu. Sokolov, J. J. Wilke, A. C. Simmonett, and H. F. Schaefer, J. Chem. Phys. 137, 054105 (2012). (doi: 10.1063/1.4739423).

DC-12:

• “Density cumulant functional theory: The DC-12 method, an improved description of the one-particle density matrix,” A. Yu. Sokolov, A. C. Simmonett, and H. F. Schaefer, J. Chem. Phys. 138, 024107 (2013). (doi: 10.1063/1.4773580).

ODC-06 and ODC-12:

• “Orbital-optimized density cumulant functional theory,” A. Yu. Sokolov, and H. F. Schaefer, J. Chem. Phys. 139, 204110 (2013). (doi: 10.1063/1.4833138).

ODC-13:

• “Density cumulant functional theory from a unitary transformation: N-representability, three-particle correlation effects, and application to O4+,” A. Yu. Sokolov, H. F. Schaefer, and W. Kutzelnigg, J. Chem. Phys. 141, 074111 (2014). (doi: 10.1063/1.4892946).

Configuration Interaction (CI)

PSI has a highly optimized code for full configuration interaction and highly correlated configuration interaction, as described in

• “The Configuration Interaction Method: Advances in Highly Correlated Approaches,” C. D. Sherrill and H. F. Schaefer, in Adv. Quantum Chem., vol. 34, P.-O. Löwdin, Ed. (Academic Press, New York, 1999), pp. 143-269. (doi: 10.1016/S0065-3276(08)60532-8).

Coupled Cluster (CC)

A general discussion of coupled cluster theory is given in

• “An Introduction to Coupled Cluster Theory for Computational Chemists,” T. D. Crawford and H. F. Schaefer, Rev. Comp. Chem. 14, 33-136 (2000). (doi: 10.1002/9780470125915.ch2).

Implementation of frozen natural orbital (FNO) coupled cluster theory in PSI and its performance for non-covalent interactions is discussed in

• “Accurate Noncovalent Interaction Energies Using Truncated Basis Sets Based on Frozen Natural Orbitals,” A. E. DePrince and C. D. Sherrill, J. Chem. Theory Comput. 9, 293-299 (2013). (doi: 10.1021/ct300780u).

Implementation of density-fitted (DF) and Cholesky decomposition (CD) coupled cluster in PSI, and its performance for non-covalent interactions and reaction energies, is discussed in

• “Accuracy and Efficiency of Coupled-Cluster Theory Using Density Fitting / Cholesky Decomposition, Frozen Natural Orbitals, and a T1-Transformed Hamiltonian,” A. E. DePrince and C. D. Sherrill, J. Chem. Theory Comput. 9, 2687-2696 (2013). (doi: 10.1021/ct400250u).

Implementation of the asymmetric triples correction for the density-fitted and cholesky-decomposed coupled-cluster singles and doubles method

• “A noniterative asymmetric triple excitation correction for the density-fitted coupled-cluster singles and doubles method: Preliminary applications,” U. Bozkaya, J. Chem. Phys. 144, 144108 (2016). (doi: 10.1063/1.4945706).

Implementation of analytic gradients for the density-fitted coupled-cluster singles and doubles method

• “Analytic energy gradients for the coupled-cluster singles and doubles method with the density-fitting approximation,” U. Bozkaya and C. D. Sherrill, J. Chem. Phys. 144, 174103 (2016). (doi: 10.1063/1.4948318).

Implementation of analytic gradients for the density-fitted coupled-cluster singles and doubles with perturbative triples method

• “Analytic energy gradients for the coupled-cluster singles and doubles with perturbative triples method with the density-fitting approximation,” U. Bozkaya and C. D. Sherrill, J. Chem. Phys. 147, 044104 (2017). (doi: 10.1063/1.4994918).

Mukherjee State-Specific Multi-Reference Coupled Cluster (Mk-MRCC)

PSI4 features production-level Mukherjee-style state-specific coupled-cluster theory, including perturbative triples and also associated multi-reference perturbation theories. The theory and PSI4 implementation of these methods is discussed in the following papers.

General Mk-MRCC

• “Coupling Term Derivation and General Implementation of State-Specific Multireference Coupled-Cluster Theories,” F. A. Evangelista, W. D. Allen, and H. F. Schaefer, J. Chem. Phys. 127, 024102 (2007). (doi: 10.1063/1.2743014).

Mk-MRCCSD(T)

• “Perturbative Triples Corrections in State-Specific Multireference Coupled Cluster Theory,” F. A. Evangelista, E. Prochnow, J. Gauss, and H. F. Schaefer, J. Chem. Phys. 132, 074107 (2010). (doi: 10.1063/1.3305335).

Mk-MRCCSDT(-n)

• “Triple Excitations in State-Specific Multireference Coupled Cluster Theory: Application of Mk-MRCCSDT and Mk-MRCCSDT-n Methods to Model Systems,” F. A. Evangelista, A. C. Simmonett, W. D. Allen, H. F. Schaefer, and J. Gauss, J. Chem. Phys. 128, 124104 (2008). (doi: 10.1063/1.2834927).

Mk-MRPT2

• “A Companion Perturbation Theory for State-specific Multireference Coupled Cluster Methods,” F. A. Evangelista, A. C. Simmonett, H. F. Schaefer, D. Mukherjee, and W. D. Allen, Phys. Chem. Chem. Phys. 11, 4728-4741 (2009). (doi: 10.1039/b822910d).

Symmetry-Adapted Perturbation Theory (SAPT)

PSI4 features an extremely efficient code to perform wavefunction-based Symmetry Adapted Perturbation Theory (SAPT). A good review article for this method is as follows:

• “Perturbation Theory Approach to Intermolecular Potential Energy Surfaces of van der Waals Complexes,” B. Jeziorski, R. Moszynski, and K. Szalewicz, Chem. Rev. 94, 1887-1930 (1994). (doi: 10.1021/cr00031a008).

PSI4 benefits enormously from the introduction of density fitting (DF) into SAPT. There are several SAPT truncations available in PSI4. For guidance on which one to choose, see the SAPT section of the manual and refer to the following systematic study:

• “Levels of Symmetry Adapted Perturbation Theory (SAPT). I. Efficiency and Performance for Interaction Energies,’’ T. M. Parker, L. A. Burns, R. M. Parrish, A. G. Ryno, and C. D. Sherrill, J. Chem. Phys. 140, 094106 (2014). (doi: 10.1063/1.4867135).

The theory and implementation of DF-SAPT is discussed in the following papers for various levels of SAPT.

DF-SAPT0

• “Large-scale Symmetry-adapted Perturbation Theory Computations via Density Fitting and Laplace Transformation Techniques: Investigating the Fundamental Forces of DNA-Intercalator Interactions,” E. G. Hohenstein, R. M. Parrish, C. D. Sherrill, J. M. Turney, and H. F. Schaefer, J. Chem. Phys. 135, 174017 (2011). (doi: 10.1063/1.3656681).

• “Density Fitting and Cholesky Decomposition Approximations in Symmetry-Adapted Perturbation Theory: Implementation and Application to Probe the Nature of \(\pi - \pi\) Interactions in Linear Acenes,” E. G. Hohenstein and C. D. Sherrill, J. Chem. Phys. 132, 184111 (2010). (doi: 10.1063/1.3426316).

SAPT2

• “Density Fitting of Intramonomer Correlation Effects in Symmetry-Adapted Perturbation Theory,” E. G. Hohenstein and C. D. Sherrill, J. Chem. Phys. 133, 014101 (2010). (doi: 10.1063/1.3451077).

SAPT2+, SAPT2+(3), SAPT2+3

• “Wavefunction Methods for Noncovalent Interactions,” E. G. Hohenstein and C. D. Sherrill, WIREs: Comput. Mol. Sci. 2, 304-326 (2012). (doi: 10.1002/wcms.84).

• “Density Fitting of Intramonomer Correlation Effects in Symmetry-Adapted Perturbation Theory,” E. G. Hohenstein and C. D. Sherrill, J. Chem. Phys. 133, 014101 (2010). (doi: 10.1063/1.3451077).

• “Efficient Evaluation of Triple Excitations in Symmetry-Adapted Perturbation Theory via MP2 Natural Orbitals,” E. G. Hohenstein and C. D. Sherrill, J. Chem. Phys. 133, 104107 (2010). (doi: 10.1063/1.3479400).

SAPT2+(CCD), SAPT2+(3)(CCD), and SAPT2+3(CCD)

• “Tractability Gains in Symmetry-Adapted Perturbation Theory Including Coupled Double Excitations: CCD+ST(CCD) Dispersion with Natural Orbital Truncations,’’ R. M. Parrish, E. G. Hohenstein, and C. D. Sherrill, J. Chem. Phys. 139, 174102 (2013). (doi: 10.1063/1.4826520).

• “Wavefunction Methods for Noncovalent Interactions,” E. G. Hohenstein and C. D. Sherrill, WIREs: Comput. Mol. Sci. 2, 304-326 (2012). (doi: 10.1002/wcms.84).

• “Density Fitting of Intramonomer Correlation Effects in Symmetry-Adapted Perturbation Theory,” E. G. Hohenstein and C. D. Sherrill, J. Chem. Phys. 133, 014101 (2010). (doi: 10.1063/1.3451077).

F/I-SAPT

• “Chemical Assignment of Symmetry-Adapted Perturbation Theory Interaction Energy Components: The Functional-Group SAPT Partition,” R. M. Parrish, T. M. Parker, and C. D. Sherrill, J. Chem. Theory Comput. 10, 4417 (2014). (doi: 10.1021/ct500724p).

• “Communication: Practical Intramolecular Symmetry Adapted Perturbation Theory via Hartree-Fock Embedding,” R. M. Parrish, J. F. Gonthier, C. Corminboeuf, and C. D. Sherrill, J. Chem. Phys. 143, 051103 (2015). (doi: 10.1063/1.4927575)

The derivation of the second-order exchange terms without the single-exchange approximation are found in the following two works:

• “Intermolecular exchange-induction energies without the overlap expansion,” R. Schäffer and G. Jansen, Theor. Chem. Acc. 131, 1235 (2012). (doi: 10.1007/s00214-012-1235-6)

• “Single-determinant-based symmetry-adapted perturbation theory without single-exchange approximation,” R. Schäffer and G. Jansen, Mol. Phys. 111, 2570 (2013). (doi: 10.1080/00268976.2013.827253)

Orbital-Optimized Post-Hartree–Fock Methods

Orbital-optimized second-order perturbation theory (OMP2)

• “Quadratically convergent algorithm for orbital optimization in the orbital-optimized coupled-cluster doubles method and in orbital-optimized second-order Møller–Plesset perturbation theory,” U. Bozkaya, J. M. Turney, Y. Yamaguchi, H. F. Schaefer, and C. D. Sherrill, J. Chem. Phys. 135, 104103 (2011). (doi: 10.1063/1.3631129).

• “Analytic energy gradients for the orbital-optimized second-order Møller–Plesset perturbation theory,” U. Bozkaya and C. D. Sherrill, J. Chem. Phys. 138, 184103 (2013). (doi: 10.1063/1.4803662).

• “Orbital-Optimized Second-Order Perturbation Theory with Density-Fitting and Cholesky Decomposition Approximations: An Efficient Implementation,” U. Bozkaya, J. Chem. Theory Comput. 10, 2371 (2014). (doi: 10.1021/ct500231c).

Orbital-optimized third-order perturbation theory (OMP3)

• “Orbital-Optimized Third-Order Møller–Plesset Perturbation Theory and Its Spin-Component and Spin-Opposite Scaled Variants: Application to Symmetry Breaking Problems,” U. Bozkaya, J. Chem. Phys. 135, 224103 (2011). (doi: 10.1063/1.3665134).

• “Assessment of Orbital-Optimized Third-Order Møller–Plesset Perturbation Theory and Its Spin-Component and Spin-Opposite Scaled Variants for Thermochemistry and Kinetics,” E. Soydas and U. Bozkaya, J. Chem. Theory Comput. 9, 1452 (2013). (doi: 10.1021/ct301078q).

• “Analytic energy gradients for the orbital-optimized third-order Møller–Plesset Perturbation Theory,” U. Bozkaya, J. Chem. Phys. 139, 104116 (2013). (doi: 10.1063/1.4820877).

Orbital-optimized linearized coupled-cluster doubles method (OLCCD)

• “Orbital-optimized coupled-electron pair theory and its analytic gradients: Accurate equilibrium geometries, harmonic vibrational frequencies, and hydrogen transfer reactions,” U. Bozkaya and C. D. Sherrill, J. Chem. Phys. 139, 054104 (2013). (doi: 10.1063/1.4816628).

Orbital-optimized MP2.5 (OMP2.5)

• “Orbital-optimized MP2.5 and its analytic gradients: Approaching CCSD(T) quality for noncovalent interactions,” U. Bozkaya and C. D. Sherrill, J. Chem. Phys. 141, 204105 (2014). (doi: 10.1063/1.4902226).

Extended Koopmans’ Theorem

• “The extended Koopmans’ theorem for orbital-optimized methods: Accurate computation of ionization potentials,” U. Bozkaya, J. Chem. Phys. 139, 154105 (2013). (doi: 10.1063/1.4825041).

• “Accurate Electron Affinities from the Extended Koopmans’ Theorem Based on Orbital-Optimized Methods,” U. Bozkaya, J. Chem. Theory Comput. 10, 2041 (2014). (doi: 10.1021/ct500186j).

Density-Fitted and Cholesky-Decomposed Orbital-optimized second-order perturbation theory (DF-OMP2)

• “Orbital-Optimized Second-Order Perturbation Theory with Density-Fitting and Cholesky Decomposition Approximations: An Efficient Implementation,” U. Bozkaya, J. Chem. Theory Comput. 10, 2371 (2014). (doi: 10.1021/ct500231c).

• “Analytic Energy Gradients and Spin Multiplicities for Orbital-Optimized Second-Order Perturbation Theory with Density-Fitting Approximation: An Efficient Implementation,” U. Bozkaya, J. Chem. Theory Comput. 10, 4389 (2014). (doi: 10.1021/ct500634s).

Density-Fitted and Cholesky-Decomposed Orbital-optimized MP3 and MP2.5 (DF-OMP3 and DF-OMP2.5)

• “Orbital-Optimized MP3 and MP2.5 with Density-Fitting and Cholesky Decomposition Approximations,” U. Bozkaya, J. Chem. Theory Comput. 12, 1179 (2016). (doi: 10.1021/acs.jctc.5b01128).

Density-Fitted and Cholesky-Decomposed Orbital-Optimized Linearized Coupled-Cluster Doubles Method (DF-OLCCD)

• “Orbital-optimized linearized coupled-cluster doubles with density-fitting and Cholesky decomposition approximations: an efficient implementation,” U. Bozkaya, Phys. Chem. Chem. Phys. 18, 11362 (2016). (doi: 10.1039/c6cp00164e).

Algebraic-Diagrammatic Construction methods (ADC)

General ADC theory

• “Intermediate state representation approach to physical properties of electronically excited molecules,” J. Schirmer, and A. B. Trofimov, J. Chem. Phys. 120, 11449-11464 (2004). (doi: 10.1063/1.1752875).

Implementation inside adcc, the ADC backend used for most ADC methods available in PSI4

• “adcc: A versatile toolkit for rapid development of algebraic-diagrammatic construction methods,” M. F. Herbst, M. Scheurer, T. Fransson, D. R. Rehn, and A. Dreuw. WIREs Comput. Mol. Sci., (2020). (DOI: 10.1002/wcms.1462, Preprint https://adc-connect.org/q/publications

Density Matrix Renormalization Group (DMRG)

• “CheMPS2: a free open-source spin-adapted implementation of the density matrix renormalization group for ab initio quantum chemistry,” S. Wouters, W. Poelmans, P. W. Ayers and D. Van Neck, Comput. Phys. Commun. 185 (6), 1501-1514 (2014). (doi: 10.1016/j.cpc.2014.01.019).

• “The density matrix renormalization group for ab initio quantum chemistry,” S. Wouters and D. Van Neck, Eur. Phys. J. D 68 (9), 272 (2014). (doi: 10.1140/epjd/e2014-50500-1).

Scalar Relativistic Corrections

General theory for the exact two-component approach (X2C)

• “Analytic energy gradients for the spin-free exact two-component theory using an exact block diagonalization for the one-electron Dirac Hamiltonian,” L. Cheng and J. Gauss, J. Chem. Phys. 135, 084114 (2011). (doi: 10.1063/1.3624397).

Implementation within Psi4

• “Predicting Near Edge X-ray Absorption Spectra with the Spin-Free Exact-Two-Component Hamiltonian and Orthogonality Constrained Density Functional Theory,” P. Verma, W. D. Derricotte and F. A. Evangelista, J. Chem. Theory Comput. (2015). (doi: 10.1021/acs.jctc.5b00817).

Supported Systems

Architectures

The majority of PSI4 was developed on Mac and Linux machines; in principle, it should work on any Unix system. The latest version of the PSI4 program package may be obtained at psicode.org. The package is available as a binary (Installing from Binary) for Linux, macOS (both Intel and Apple Silicon), or Windows (both native and via Windows Subsystem for Linux aka Bash on Ubuntu on Windows) or as source code (git repository or zipped archive from https://github.com/psi4/psi4.

Compilers

PSI4 has been successfully compiled using Intel, GCC, and Clang compilers. Compiler requirements are primarily C++20 compliance (now GCC version 10.0 or above). For some architectures, a precompiled binary is available. See Compiling and Installing for details.

Python

PSI4 1.1 and 1.2 are supported on Python 2.7, 3.5, and 3.6. After 1.2, only Python 3 will be supported in accordance with other scientific software projects). PSI4 1.3 supports Python 3.6 and 3.7. PSI4 1.4 supports Python 3.6, 3.7, 3.8, and 3.9. PSI4 1.5 supports Python 3.7, 3.8, and 3.9. PSI4 1.6 supports Python 3.8, 3.9, and 3.10. PSI4 1.7 supports Python 3.8, 3.9, 3.10, and 3.11 (no binary packages for 3.11). PSI4 1.8 supports Python 3.8, 3.9, 3.10, and 3.11. PSI4 1.9 supports Python 3.8, 3.9, 3.10, 3.11, and 3.12. PSI4 1.10 is anticipated to support Python 3.8, 3.9, 3.10, 3.11, and 3.12. The future plan is to (1) be compatible with 3.8 and above until there is a good reason to drop older versions but (2) only build and test for versions conda-forge supports. The current master supports 3.8, 3.9, 3.10, 3.11, and 3.12.

License

PSI4 is distributed under the GNU Lesser General Public License version 3, LGPL-3.0. Its required dependencies and add-ons have their own licenses, ranging from BSD-2-Clause to GPL-2.0+. It is possible to build PSI4 without any General GPL dependencies.

Capabilities

PSI4 can perform ab initio computations employing basis sets of contracted Gaussian-type functions of virtually arbitrary orbital quantum number. Many parts of PSI4 can recognize and exploit the largest Abelian subgroup of the molecular point group. Table Methods displays the range of theoretical methods available in PSI4.

Geometry optimization can be performed using either analytic gradients or energy points. Likewise, vibrational frequencies can be computed by analytic second derivatives, by finite differences of analytic gradients, or by finite differences of energies. PSI4 can also compute an extensive list of one-electron properties.

For more tables with capabilities details:

• Full Capabilities (first below) lists all methods

• Capabilities Breakdown (second below) lists selected methods by reference, etc.

• Module Capabilities lists selected methods by implementation

• Energy, Energy (DFT), Energy (MRCC), Energy (CFOUR) fully list energy target methods

• Gradient, Gradient (CFOUR) fully list gradient target methods

• Frequency fully lists Hessian target methods

Summary of theoretical methods available in PSI4

Method [1]	Reference[2]	Type[2]	Variants[3]
			Canonical	OO	FNO [4]	DLPNO
HF	RHF/UHF/ROHF/CUHF	CONV/DF/CD	E/G/H
DFT	RKS/UKS	CONV/DF/CD	E/G
DFT-D2, DFT-NL	RKS/UKS	CONV/DF/CD	E/G
DCT	RHF/UHF	CONV/DF	E/G
MP2	RHF/UHF/ROHF	CONV/DF/CD	E/G	E/G		E
MP3	RHF/UHF	CONV/DF/CD	E/G	E/G	E
MP2.5	RHF/UHF	CONV/DF/CD	E/G	E/G
MP4, MP4(SDQ)	RHF	CONV	E		E
MPn	RHF	CONV	E
ZAPTn	ROHF	CONV	E
REMP2	RHF/UHF	CONV/DF/CD	E	E/G
LCCD	RHF/UHF	CONV/DF/CD	E/G	E/G	E
LCCSD, CEPA(0)	RHF	CONV	E		E
CEPA(n), n=0,1,3	RHF	CONV	E		E
CCD	RHF	DF/CD	E/G
BCCD	RHF/UHF/ROHF	CONV	E
CC2	RHF/UHF/ROHF	CONV	E/G
CCSD	RHF/UHF/ROHF	CONV/DF/CD	E/G		E [5]
CCSD(T)	RHF/UHF/ROHF	CONV/DF/CD	E/G		E [5]
A-CCSD(T)	RHF	CONV/DF/CD	E
BCCD(T)	RHF/UHF/ROHF	CONV	E
CC3	RHF/UHF/ROHF	CONV	E
ACPF/AQCC	RHF	CONV	E		E
CISD	RHF/ROHF	CONV	E		E
QCISD	RHF	CONV	E		E
QCISD(T)	RHF	CONV	E		E
CIn	RHF/ROHF	CONV	E
FCI	RHF/ROHF	CONV	E
Mk-MRPT2	RHF/ROHF/TCSCF	CONV	E
Mk-MRCCSD	RHF/ROHF/TCSCF	CONV	E
Mk-MRCCSD(T)	RHF/ROHF/TCSCF	CONV	E
CASCI, RASCI	RHF/ROHF	CONV	E
CASSCF, RASSCF	RHF/ROHF	CONV/DF	E
SAPT0, SF-SAPT0	RHF/UHF/ROHF	CONV/DF	E
SAPT(DFT)	RKS	DF	E
SAPT2, 2+, 2+(3), 2+3	RHF	DF	E
F/I-SAPT0	RHF	DF	E
TDDFT	RKS/UKS	CONV/DF	E
EP2	RHF	DF	E
EOM-CC2	RHF	CONV	E
EOM-CCSD	RHF/UHF/ROHF	CONV	E/G
EOM-CC3	RHF/UHF/ROHF	CONV	E
❖ with LibEFP
EFP/EFP	RHF		E/G
QM/EFP	RHF		E
❖ with DFTD3, DFTD4, and gCP
HF-3c, PBEh-3c, B97-3C, r2SCAN-3c, wB97X-3c	R/U/ROHF, R/UKS		E/G
DFT-D3, DFT-D4	RKS/UKS		E/G
❖ with ADCC
ADC(1), CVS-ADC(1)	RHF/UHF	CONV	E
ADC(2), CVS-ADC(2)	RHF/UHF	CONV	E
ADC(2)-x, CVS-ADC(2)-x	RHF/UHF	CONV	E
ADC(3), CVS-ADC(3)	RHF/UHF	CONV	E
❖ with CheMPS2
DMRG-CI	RHF	CONV	E
DMRG-SCF	RHF	CONV	E
DMRG-CASPT2	RHF	CONV	E

[1]

Many methods have a more detailed breakdown of capabilities here.

[2] (1,2)

Not all combinations of reference and algorithm type may be available for any variant and derivative. See detailed capabilities tables.

[3]

Shown are analytic implementations for energy (E), gradient, (G), and Hessian (H); finite difference derivatives are invoked automatically if analytic not available.

[4]

Frozen natural orbital variant available. In particular, RHF available as CONV.

[5] (1,2)

Frozen natural orbital variant available. In particular, RHF available as CONV/DF.

Summary capabilities of PSI4. “✓” runs analytically. “∷” runs derivative with internal finite difference. Double underline “✓̳” or “∷̳” is default algorithm type when type selector (e.g., CC_TYPE) unspecified.

◻ name ↓ → ◻ ◻		REFERENCE → ◻ type[6] ↓ → FREEZE_CORE[7]→	Restricted (RHF)												Unrestricted (UHF)												Restricted Open (ROHF)
			energy()						gradient()[8]						energy()						gradient()[8]						energy()						gradient()[8]
			CV		DF		CD		CV		DF		CD		CV		DF		CD		CV		DF		CD		CV		DF		CD		CV		DF		CD
			A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F	A	F
hf		SCF_TYPE	✓		✓̳		✓		✓		✓̳		∷		✓		✓̳		✓		✓		✓̳		∷		✓		✓̳		✓		✓		✓̳		∷
mp2		MP2_TYPE	✓	✓	✓̳	✓̳	✓	✓	✓	∷	✓̳	✓̳	∷	∷	✓	✓	✓̳	✓̳	✓	✓	✓	∷	✓̳	✓̳	∷	∷	✓	✓	✓̳	✓̳	✓	✓	∷	∷	∷̳	∷̳	∷	∷
mp2.5		MP_TYPE	✓	✓	✓̳	✓̳	✓	✓	✓	∷	✓̳	✓̳	∷	∷	✓	✓	✓̳	✓̳	✓	✓	✓	∷	✓̳	✓̳	∷	∷
mp3		MP_TYPE	✓	✓	✓̳	✓̳	✓	✓	✓	∷	✓̳	✓̳	∷	∷	✓	✓	✓̳	✓̳	✓	✓	✓	∷	✓̳	✓̳	∷	∷
mp4(sdq)		MP_TYPE	✓̳	✓̳
mp4, mpn[9]		MP_TYPE	✓̳	✓̳
zapt2, zaptn[9]		MP_TYPE																									✓̳	✓̳
cisd, cin[9]		CI_TYPE	✓̳	✓̳																							✓̳	✓̳
qcisd		CI_TYPE	✓̳	✓̳
qcisd(t)		CI_TYPE	✓̳	✓̳
fci		CI_TYPE	✓̳	✓̳																							✓̳	✓̳
remp2		CC_TYPE	✓̳	✓̳	✓	✓	✓	✓							✓̳	✓̳	✓	✓	✓	✓
lccd		CC_TYPE	✓̳	✓̳	✓	✓	✓	✓	✓̳	∷̳	✓	✓	∷	∷	✓̳	✓̳	✓	✓	✓	✓	✓̳	∷̳	✓	✓	∷	∷
lccsd, cepa(0)		CC_TYPE	✓̳	✓̳
cepa(1)		CC_TYPE	✓̳	✓̳
cepa(3)		CC_TYPE	✓̳	✓̳
acpf		CC_TYPE	✓̳	✓̳
aqcc		CC_TYPE	✓̳	✓̳
ccd		CC_TYPE			✓	✓	✓	✓			✓	✓	∷	∷			✓	✓	✓	✓			✓	✓	∷	∷
bccd		CC_TYPE	✓̳	✓̳											✓̳	✓̳											✓̳	✓̳
cc2		CC_TYPE	✓̳	✓̳					✓̳	∷̳					✓̳	✓̳					∷̳	∷̳					✓̳	✓̳					∷̳	∷̳
ccsd		CC_TYPE	✓̳	✓̳	✓	✓	✓	✓	✓̳	∷̳	✓	✓	∷	∷	✓̳	✓̳	✓	✓	✓	✓	✓̳	∷̳	✓	✓	∷	∷	✓̳	✓̳					✓̳	∷̳
ccsd(t)		CC_TYPE	✓̳	✓̳	✓	✓	✓	✓	∷̳	∷̳	✓	✓	∷	∷	✓̳	✓̳					∷̳	∷̳					✓̳	✓̳					∷̳	∷̳
a-ccsd(t)[10]		CC_TYPE	✓̳	✓̳	✓	✓	✓	✓
bccd(t)		CC_TYPE	✓̳	✓̳											✓̳	✓̳											✓̳	✓̳
cc3		CC_TYPE	✓̳	✓̳											✓̳	✓̳											✓̳	✓̳
omp2		MP2_TYPE	✓		✓̳	✓̳	✓	✓	✓		✓̳	✓̳	∷	∷	✓		✓̳	✓̳	✓	✓	✓		✓̳	✓̳	∷	∷	✓		✓̳	✓̳	✓	✓	✓		✓̳	✓̳	∷	∷
omp2.5		MP_TYPE	✓̳		✓	✓	✓	✓	✓̳		✓	✓	∷	∷	✓̳		✓	✓	✓	✓	✓̳		✓	✓	∷	∷	✓̳		✓	✓	✓	✓	✓̳		✓	✓	∷	∷
omp3		MP_TYPE	✓̳		✓	✓	✓	✓	✓̳		✓	✓	∷	∷	✓̳		✓	✓	✓	✓	✓̳		✓	✓	∷	∷	✓̳		✓	✓	✓	✓	✓̳		✓	✓	∷	∷
oremp2		CC_TYPE	✓̳		✓	✓	✓	✓	✓̳		✓	✓	∷	∷	✓̳		✓	✓	✓	✓	✓̳		✓	✓	∷	∷	✓̳		✓	✓	✓	✓	✓̳		✓	✓	∷	∷
olccd		CC_TYPE	✓̳		✓	✓	✓	✓	✓̳		✓	✓	∷	∷	✓̳		✓	✓	✓	✓	✓̳		✓	✓	∷	∷	✓̳		✓	✓	✓	✓	✓̳		✓	✓	∷	∷
svwn, LSDA DFT		SCF_TYPE	✓		✓̳		✓		✓		✓̳		∷		✓		✓̳		✓		✓		✓̳		∷
pbe, GGA DFT		SCF_TYPE	✓		✓̳		✓		✓		✓̳		∷		✓		✓̳		✓		✓		✓̳		∷
b3lyp, Hybrid DFT		SCF_TYPE	✓		✓̳		✓		✓		✓̳		∷		✓		✓̳		✓		✓		✓̳		∷
wb97x, LRC DFT		SCF_TYPE	✓		✓̳				✓		✓̳				✓		✓̳				✓		✓̳
b2plyp, DH DFT[11]		SCF_TYPE	✓	✓	✓̳	✓̳	✓	✓							✓	✓	✓̳	✓̳	✓	✓

[6]

Algorithm type selection keyword below. Values to the right: conventional CV, density-fitted DF, and Cholesky-decomposed CD.

[7]

Active orbital values to the right: all-electron A and frozen-core F.

[8] (1,2,3)

Methods with no analytic gradients do not have finite difference explicitly marked by “∷”, but the capability can be gleaned from the energy availability.

[9] (1,2,3)

Arbitrary-order n through DETCI is inefficient byproduct of CI

[10]

a-CCSD(T) also known as CCSD(aT), Lambda-CCSD(T), and CCSD(T)_L

[11]

DH-DFT only available with DF-MP2

Technical Support

The PSI4 package is distributed for free and without any guarantee of reliability, accuracy, or suitability for any particular purpose. No obligation to provide technical support is expressed or implied. As time allows, the developers will attempt to answer inquiries on the forum or GitHub. For bug reports, specific and detailed information, with example inputs, would be appreciated.

Where-to-post summary:[12]

• How do I? – ask the forum

• I got this error, why? – ask the forum

• I got this error and I’m sure it’s a bug – file a GitHub issue

• Can I open a discussion on this bit of code? – file a GitHub issue

• I have an idea/request and a plan – file a GitHub issue

• I have an idea/request – ask the forum

• Why do you? – ask the forum

• When will you? – ask the forum

• I have an experience that can improve the build documentation – inform the forum or add to the documentation itself

• Anything you want to share privately – crawdad@vt.edu or sherrill@gatech.edu

[12]

Adapted from here.