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Geoffrey A. Blake

Publications and source records attributed to Geoffrey A. Blake.

At least 55 records · Page 3Linked to original sources
arXiv2024

The high-contrast performance of the Keck Planet Imager and Characterizer

The Keck Planet Imager and Characterizer (KPIC), a series of upgrades to the Keck II Adaptive Optics System and Instrument Suite, aims to demonstrate high-resolution spectroscopy of faint exoplanets that are spatially resolved from their host stars. In this paper, we measure KPIC's sensitivity to companions as a function of separation (i.e., the contrast curve) using on-sky data collected over four years of operation. We show that KPIC is able to reach contrasts of $1.3 \times 10^{-4}$ at 90 mas and $9.2 \times 10^{-6}$ at 420 mas separation from the star, and that KPIC can reach planet-level sensitivities at angular separations within the inner working angle of coronagraphic instruments such as GPI and SPHERE. KPIC is also able to achieve more extreme contrasts than other medium-/high-resolution spectrographs that are not as optimized for high-contrast performance. We decompose the KPIC performance budget into individual noise terms and discuss limiting factors. The fringing that results from combining a high-contrast imaging system with a high-resolution spectrograph is identified as an important source of systematic noise. After mitigation and correction, KPIC is able to reach within a factor of 2 of the photon noise limit at separations < 200 mas. At large separations, KPIC is limited by the background noise performance of NIRSPEC.

astro-ph.IM↗
arXiv2024

Rotation and Abundances of the Benchmark Brown Dwarf HD 33632 Ab from Keck/KPIC High-resolution Spectroscopy

We present the projected rotational velocity and molecular abundances for HD 33632 Ab obtained via Keck Planet Imager and Characterizer high-resolution spectroscopy. HD 33632 Ab is a nearby benchmark brown dwarf companion at a separation of $\sim$20 au that straddles the L/T transition. Using a forward-modeling framework with on-axis host star spectra, self-consistent substellar atmospheric and retrieval models for HD 33632 Ab, we derive a projected rotational velocity of 53 $\pm$ 3 km/s and carbon/water mass fractions of log CO = $-$2.3 $\pm$ 0.3 and log H$_2$O = $-$2.7 $\pm$ 0.2. The inferred carbon-to-oxygen ratio (C/O = 0.58 $\pm$ 0.14), molecular abundances, and metallicity ([C/H] = 0.0 $\pm$ 0.2 dex) of HD 33632 Ab are consistent with its host star. Although detectable methane opacities are expected in L/T transition objects, we did not recover methane in our KPIC spectra, partly due to the high $v\sin{i}$ and to disequilibrium chemistry at the pressures we are sensitive to. We parameterize the spin as the ratio of rotation over break-up velocity, and compare HD 33632 Ab to a compilation of >200 very low-mass objects (M$\lesssim$0.1 M$_{\odot}$) that have spin measurements in the literature. There appears to be no clear trend for the isolated field low-mass objects versus mass, but a tentative trend is identified for low-mass companions and directly imaged exoplanets, similar to previous findings. A larger sample of close-in gas giant exoplanets and brown dwarfs will critically examine our understanding of their formation and evolution through rotation and chemical abundance measurements.

astro-ph.SR↗
arXiv2024

Are these planets or brown dwarfs? Broadly solar compositions from high-resolution atmospheric retrievals of ~10-30 $M_\textrm{Jup}$ companions

Using Keck Planet Imager and Characterizer (KPIC) high-resolution ($R$~35000) spectroscopy from 2.29-2.49 $μ$m, we present uniform atmospheric retrievals for eight young substellar companions with masses of ~10-30 $M_\textrm{Jup}$, orbital separations spanning ~50-360 au, and $T_\textrm{eff}$ between ~1500-2600 K. We find that all companions have solar C/O ratios, and metallicities, to within the 1-2$σ$ level, with the measurements clustered around solar composition. Stars in the same stellar associations as our systems have near-solar abundances, so these results indicate that this population of companions is consistent with formation via direct gravitational collapse. Alternatively, core accretion outside the CO snowline would be compatible with our measurements, though the high mass ratios of most systems would require rapid core assembly and gas accretion in massive disks. On a population level, our findings can be contrasted with abundance measurements for directly imaged planets with m<10 $M_\textrm{Jup}$, which show tentative atmospheric metal enrichment. In addition, the atmospheric compositions of our sample of companions are distinct from those of hot Jupiters, which most likely form via core accretion. For two companions with $T_\textrm{eff}$~1700-2000 K (kap And b and GSC 6214-210 b), our best-fit models prefer a non-gray cloud model with >3$σ$ significance. The cloudy models yield 2-3$σ$ lower $T_\textrm{eff}$ for these companions, though the C/O and [C/H] still agree between cloudy and clear models at the $1σ$ level. Finally, we constrain 12CO/13CO for three companions with the highest S/N data (GQ Lup b, HIP 79098 b, and DH Tau b), and report $v$sin($i$) and radial velocities for all companions.

astro-ph.EP↗
arXiv2024

Orbital and Atmospheric Characterization of the 1RXS J034231.8+121622 System Using High-Resolution Spectroscopy Confirms That The Companion is a Low-Mass Star

The 1RXS J034231.8+121622 system consists of an M dwarf primary and a directly imaged low-mass stellar companion. We use high resolution spectroscopic data from Keck/KPIC to estimate the objects' atmospheric parameters and radial velocities (RVs). Using PHOENIX stellar models, we find that the primary has a temperature of 3460 $\pm$ 50 K a metallicity of 0.16 $\pm$ 0.04, while the secondary has a temperature of 2510 $\pm$ 50 K and a metallicity of $0.13\substack{+0.12 \\ -0.11}$. Recent work suggests this system is associated with the Hyades, placing it an older age than previous estimates. Both metallicities agree with current $[Fe/H]$ Hyades measurements (0.11 -- 0.21). Using stellar evolutionary models, we obtain significantly higher masses for the objects, of 0.30 $\pm$ 0.15 $M_\odot$ and 0.08 $\pm$ 0.01 $M_\odot$ (84 $\pm$ 11 $M_{Jup}$) respectively. Using the RVs and a new astrometry point from Keck/NIRC2, we find that the system is likely an edge-on, moderately eccentric ($0.41\substack{+0.27 \\ -0.08}$) configuration. We also estimate the C/O ratio of both objects using custom grid models, obtaining 0.42 $\pm$ 0.10 (primary) and 0.55 $\pm$ 0.10 (companion). From these results, we confirm that this system most likely went through a binary star formation process in the Hyades. The significant changes in this system's parameters since its discovery highlight the importance of high resolution spectroscopy for both orbital and atmospheric characterization of directly imaged companions.

astro-ph.SR↗
arXiv2024

Molecular Gas Tracers in Young and Old Protoplanetary Disks

Molecular emission is used to investigate both the physical and chemical properties of protoplanetary disks. Therefore, to accurately derive disk properties, we need a thorough understanding of the behavior of the molecular probes we rely on. Here we investigate how the molecular line emission of N$_2$H$^+$, HCO$^+$, HCN, and C$^{18}$O compare to other measured quantities in a set of 20 protoplanetary disks. Overall, we find positive correlations between multiple line fluxes and the disk dust mass and radius. We also generally find strong positive correlations between the line fluxes of different molecular species. However, some disks do show noticeable differences in the relative fluxes of N$_2$H$^+$, HCO$^+$, HCN, and C$^{18}$O. These differences occur even within a single star-forming region. This results in a potentially large range of different disk masses and chemical compositions for systems of similar age and birth environment. While we make preliminary comparisons of molecular fluxes across different star-forming regions, more complete and uniform samples are needed in the future to search for trends with birth environment or age.

astro-ph.EP↗
arXiv2024

High-contrast JWST-MIRI spectroscopy of planet-forming disks for the JDISC Survey

The JWST Disk Infrared Spectral Chemistry Survey (JDISCS) aims to understand the evolution of the chemistry of inner protoplanetary disks using the Mid-InfraRed Instrument (MIRI) on the James Webb Space Telescope (JWST). With a growing sample of >30 disks, the survey implements a custom method to calibrate the MIRI Medium Resolution Spectrometer (MRS) to contrasts of better than 1:300 across its 4.9-28 micron spectral range. This is achieved using observations of Themis-family asteroids as precise empirical reference sources. High spectral contrast enables precise retrievals of physical parameters, searches for rare molecular species and isotopologues, and constraints on the inventories of carbon- and nitrogen-bearing species. JDISCS also offers significant improvements to the MRS wavelength and resolving power calibration. We describe the JDISCS calibrated data and demonstrate its quality using observations of the disk around the solar-mass young star FZ Tau. The FZ Tau MIRI spectrum is dominated by strong emission from warm water vapor. We show that the water and CO line emission originates from the disk surface and traces a range of gas temperatures of ~500-1500 K. We retrieve parameters for the observed CO and H2O lines, and show that they are consistent with a radial distribution represented by two temperature components. A high water abundance of n(H2O)~10^-4 fills the disk surface at least out to the 350 K isotherm at 1.5 au. We search the FZ Tau environs for extended emission detecting a large (radius of ~300 au) ring of emission from H2 gas surrounding FZ Tau, and discuss its origin.

astro-ph.EP↗
arXiv2023

Atmospheric metallicity and C/O of HD 189733 b from high-resolution spectroscopy

We present high-resolution $K$-band emission spectra of the quintessential hot Jupiter HD 189733 b from the Keck Planet Imager and Characterizer (KPIC). Using a Bayesian retrieval framework, we fit the dayside pressure-temperature profile, orbital kinematics, mass-mixing ratios of H$_2$O, CO, CH$_4$, NH$_3$, HCN, and H$_2$S, and the $\rm ^{13}CO/^{12}CO$ ratio. We measure mass fractions of $\rm \log H_2O = -2.0^{+0.4}_{-0.4}$ and $\rm \log CO = -2.2^{+0.5}_{-0.5}$, and place upper limits on the remaining species. Notably, we find $\rm \log CH_4 < -4.5$ at 99\% confidence, despite its anticipated presence at the equilibrium temperature of HD 189733 b assuming local thermal equilibrium. We make a tentative ($\sim3σ$) detection of $\rm ^{13}CO$, and the retrieved posteriors suggest a $\rm ^{12}C/^{13}C$ ratio similar to or substantially less than the local interstellar value. The possible $\rm ^{13}C$ enrichment would be consistent with accretion of fractionated material in ices or in the protoplanetary disk midplane. The retrieved abundances correspond to a substantially sub-stellar atmospheric $\rm C/O = 0.3\pm0.1$, while the carbon and oxygen abundances are stellar to slightly super-stellar, consistent with core-accretion models which predict an inverse correlation between C/O and metallicity. The specific combination of low C/O and high metallicity suggests significant accretion of solid material may have occurred late in the formation process of HD 189733 b.

astro-ph.EP↗
arXiv2023

Water-Rich Disks around Late M-stars Unveiled: Exploring the Remarkable Case of Sz114

We present an analysis of the JDISC JWST/MIRI-MRS spectrum of Sz~114, an accreting M5 star surrounded by a large dust disk with a shallow gap at $\sim 39$ au. The spectrum is molecular-rich: we report the detection of water, CO, CO$_2$, HCN, C$_2$H$_2$, and H$_2$. The only identified atomic/ionic transition is from [NeII] at 12.81 micron. A distinct feature of this spectrum is the forest of water lines with the 17.22 micron emission surpassing that of most mid-to-late M-star disks by an order of magnitude in flux and aligning instead with disks of earlier-type stars. Moreover, flux ratios of C$_2$H$_2$/H$_2$O and HCN/H$_2$O in Sz~114 also resemble those of earlier-type disks, with a slightly elevated CO$_2$/H$_2$O ratio. While accretional heating can boost all infrared lines, the unusual properties of Sz~114 could be explained by the young age of the source, its formation under unusual initial conditions (a large massive disk), and the presence of dust substructures. The latter delays the inward drift of icy pebbles and help preserve a lower C/O ratio over an extended period. In contrast, mid-to-late M-star disks--which are typically faint, small in size, and likely lack significant substructures--may have more quickly depleted the outer icy reservoir and already evolved out of a water-rich inner disk phase. Our findings underscore the unexpected diversity within mid-infrared spectra of mid-to-late M-star disks, highlighting the need to expand the observational sample for a comprehensive understanding of their variations and thoroughly test pebble drift and planet formation models.

astro-ph.EP↗
arXiv2023

The development of HISPEC for Keck and MODHIS for TMT: science cases and predicted sensitivities

HISPEC is a new, high-resolution near-infrared spectrograph being designed for the W.M. Keck II telescope. By offering single-shot, R=100,000 between 0.98 - 2.5 um, HISPEC will enable spectroscopy of transiting and non-transiting exoplanets in close orbits, direct high-contrast detection and spectroscopy of spatially separated substellar companions, and exoplanet dynamical mass and orbit measurements using precision radial velocity monitoring calibrated with a suite of state-of-the-art absolute and relative wavelength references. MODHIS is the counterpart to HISPEC for the Thirty Meter Telescope and is being developed in parallel with similar scientific goals. In this proceeding, we provide a brief overview of the current design of both instruments, and the requirements for the two spectrographs as guided by the scientific goals for each. We then outline the current science case for HISPEC and MODHIS, with focuses on the science enabled for exoplanet discovery and characterization. We also provide updated sensitivity curves for both instruments, in terms of both signal-to-noise ratio and predicted radial velocity precision.

astro-ph.IM↗
arXiv2023

Keck/KPIC Emission Spectroscopy of WASP-33b

We present Keck/KPIC high-resolution ($R\sim35,000$) $K$-band thermal emission spectroscopy of the ultra-hot Jupiter WASP-33b. The use of KPIC's single-mode fibers greatly improves both blaze and line-spread stabilities relative to slit spectrographs, enhancing the cross-correlation detection strength. We retrieve the dayside emission spectrum with a nested sampling pipeline which fits for orbital parameters, the atmospheric pressure-temperature profile, and molecular abundances.We strongly detect the thermally-inverted dayside and measure mass-mixing ratios for CO ($\log\rm CO_{MMR} = -1.1^{+0.4}_{-0.6}$), H$_2$O ($\log\rm H_2O_{MMR} = -4.1^{+0.7}_{-0.9}$) and OH ($\log\rm OH_{MMR} = -2.1^{+0.5}_{-1.1}$), suggesting near-complete dayside photodissociation of H$_2$O. The retrieved abundances suggest a carbon- and possibly metal-enriched atmosphere, with a gas-phase C/O ratio of $0.8^{+0.1}_{-0.2}$, consistent with the accretion of high-metallicity gas near the CO$_2$ snow line and post-disk migration or with accretion between the soot and H$_2$O snow lines. We also find tentative evidence for $\rm ^{12}CO/^{13}CO \sim 50$, consistent with values expected in protoplanetary disks, as well as tentative evidence for a metal-enriched atmosphere (2--15$\times$ solar). These observations demonstrate KPIC's ability to characterize close-in planets and the utility of KPIC's improved instrumental stability for cross-correlation techniques.

astro-ph.EP↗
arXiv2023

Two-dimensional infrared-Raman spectroscopy as a probe of water's tetrahedrality

Two-dimensional spectroscopic techniques combining terahertz (THz), infrared (IR), and visible pulses offer a wealth of information about coupling among vibrational modes in molecular liquids, thus providing a promising probe of their local structure. However, the capabilities of these spectroscopies are still largely unexplored due to experimental limitations and inherently weak nonlinear signals. Here, through a combination of equilibrium-nonequilibrium molecular dynamics (MD) and a tailored spectrum decomposition scheme, we identify a relationship between the tetrahedral order of liquid water and its two-dimensional IR-IR-Raman (IIR) spectrum. The structure-spectrum relationship can explain the temperature dependence of the spectral features corresponding to the anharmonic coupling between low-frequency intermolecular and high-frequency intramolecular vibrational modes of water. In light of these results, we propose new experiments and discuss the implications for the study of tetrahedrality of liquid water.

physics.chem-ph↗
arXiv2023

Anisotropic Lattice Expansion of Monolayer WSe2 Revealed by Ultrafast Electron Diffraction

Bulk layered MX2 transition metal chalcogenides (M = Mo, W and X = S, Se) are known to exhibit an indirect to direct band gap transition as the number of layers is reduced. Previous time-resolved work has principally focused on the investigation of the transient evolution of the band structure after photo-excitation, but additional information on the dynamics of the concomitant lattice rearrangement is needed to fully understand this phenomenon. Here, ultrafast electron diffraction is used to probe the atomic motion and bond dilation in monolayer WSe2 with femtosecond temporal resolution. The change in the intensity of the Bragg diffraction spots is characterized by single-exponential dynamics, consistent with a collective response of the lattice during electron-phonon and phonon-phonon equilibration that is repeatable over many hours of illumination with ultrafast pulses. Moreover, a transient and highly anisotropic lattice expansion is observed. A possible explanation for this behavior is axial strain induced by the laser excitation that breaks the degeneracy of the in-plane phonon modes, and that strongly influences the electronic band structure. Such degeneracy-breaking induced by distortions in the lattice are well characterized in static strain measurements, and the results presented here provide valuable insights into the nature and time scales of the structural rearrangement that occurs following optical photo-excitation in monolayer tungsten diselenide.

cond-mat.mtrl-sci↗
arXiv2023

Breaking Degeneracies in Formation Histories by Measuring Refractory Content in Gas Giants

Relating planet formation to atmospheric composition has been a long-standing goal of the planetary science community. So far, most modeling studies have focused on predicting the enrichment of heavy elements and the C/O ratio in giant planet atmospheres. Although this framework provides useful constraints on the potential formation locations of gas giant exoplanets, carbon and oxygen measurements alone are not enough to determine where a given gas giant planet originated. Here, we show that characterizing the abundances of refractory elements (e.g., silicon, iron) can break these degeneracies. Refractory elements are present in the solid phase throughout most of the disk and their atmospheric abundances therefore reflect the solid-to-gas accretion ratio during formation. We introduce a new framework that parameterizes the atmospheric abundances of gas giant exoplanets in the form of three ratios: Si/H, O/Si, and C/Si. Si/H traces the solid-to-gas accretion ratio of a planet and is loosely equivalent to earlier notions of 'metallicity'. For O/Si and C/Si, we present a global picture of their variation with distance and time based on what we know from the solar system meteorites and an updated understanding of the variations of thermal processing within protoplanetary disks. We show that ultra-hot Jupiters are ideal targets for atmospheric characterization studies using this framework, as we can measure the abundances of refractories, oxygen and carbon in the gas phase. Finally, we propose that hot Jupiters with silicate clouds and low water abundances might have accreted their envelopes between the soot line and the water snowline.

astro-ph.EP↗
arXiv2022

Retrieving C and O Abundance of HR 8799 c by Combining High- and Low-Resolution Data

The formation and evolution pathway for the directly-imaged multi-planetary system HR 8799 remains mysterious. Accurate constraints on the chemical composition of the planetary atmosphere(s) are key to solving the mystery. We perform a detailed atmospheric retrieval on HR 8799~c to infer the chemical abundances and abundance ratios using a combination of photometric data along with low- and high-resolution spectroscopic data (R$\sim$20-35,000). We specifically retrieve [C/H], [O/H], and C/O and find them to be 0.55$^{+0.36}_{-0.39}$, 0.47$^{+0.31}_{-0.32}$, and 0.67$^{+0.12}_{-0.15}$ at 68\% confidence. The super-stellar C and O abundances, yet a stellar C/O ratio, reveal a potential formation pathway for HR 8799~c. Planet c, and likely the other gas giant planets in the system, formed early on (likely within $\sim$1 Myr), followed by further atmospheric enrichment in C and O through the accretion of solids beyond the CO iceline. The enrichment either preceded or took place during the early phase of the inward migration to the planet current locations.

astro-ph.EP↗
arXiv2022

An unusual reservoir of water emission in the VV CrA A protoplanetary disk

We present an analysis of an unusual pattern of water vapor emission from the $\sim$2 Myr-old low-mass binary system VV CrA, as observed in infrared spectra obtained with VLT-CRIRES, VLT-VISIR, and Spitzer-IRS. Each component of the binary shows emission from water vapor in both the L ($\sim3\,μ$m) and N ($\sim 12\,μ$m) bands. The N-band and Spitzer spectra are similar to those previously observed from young stars with disks, and are consistent with emission from an extended protoplanetary disk. Conversely, the CRIRES L-band data of VV CrA A show an unusual spectrum, which requires the presence of a water reservoir with high temperature ($T\gtrsim1500$ K), column density ($N_\mathrm{H2O}\sim 3\times10^{20}\ \mathrm{cm}^{-2}$), and turbulent broadening ($v\sim 10$ km s$^{-1}$), but very small emitting area ($A\lesssim0.005$ AU$^2$). Similarity with previously observed water emission from V1331 Cyg (Doppmann et al. 2011) and SVS 13 (Carr et al. 2004) suggests that the presence of such a reservoir may be linked to evolutionary state, perhaps related to the presence of high accretion rates or winds. While the inner disk may harbor such a reservoir, simple Keplerian models do not match well with emitting line shapes, and alternative velocity fields must be considered. We also present a new idea, that the unusual emission could arise in a circumplanetary disk, embedded within the larger VV CrA A protoplanetary disk. Additional data are likely required to determine the true physical origin of this unusual spectral pattern.

astro-ph.SR↗
arXiv2022

On the Relationship between CH$_3$OD Abundance and Temperature in the Orion KL Nebula

The relative abundances of singly-deuterated methanol isotopologues, [CH$_{2}$DOH]/[CH$_{3}$OD], in star-forming regions deviate from the statistically expected ratio of 3. In Orion KL, the nearest high-mass star-forming region to Earth, the singly-deuterated methanol ratio is about 1, and the cause for this observation has been explored through theory for nearly three decades. We present high-angular resolution observations of Orion KL using the Atacama Large Millimeter/submillimeter Array to map small-scale changes in CH$_{3}$OD column density across the nebula, which provide a new avenue to examine the deuterium chemistry during star and planet formation. By considering how CH$_{3}$OD column densities vary with temperature, we find evidence of chemical processes that can significantly alter the observed column densities. The astronomical data are compared with existing theoretical work and support D-H exchange between CH$_{3}$OH and heavy water (i.e., HDO and D$_{2}$O) at methanol's hydroxyl site in the icy mantles of dust grains. The enhanced CH$_{3}$OD column densities are localized to the Hot Core-SW region, a pattern that may be linked to the coupled evolution of ice mantel chemistry and star formation in giant molecular clouds. This work provides new perspectives on deuterated methanol chemistry in Orion KL and informs considerations that may guide future theoretical, experimental, and observational work.

astro-ph.GA↗
arXiv2022

A Clear View of a Cloudy Brown Dwarf Companion from High-Resolution Spectroscopy

Direct imaging studies have mainly used low-resolution spectroscopy ($R\sim20-100$) to study the atmospheres of giant exoplanets and brown dwarf companions, but the presence of clouds has often led to degeneracies in the retrieved atmospheric abundances (e.g. C/O, metallicity). This precludes clear insights into the formation mechanisms of these companions. The Keck Planet Imager and Characterizer (KPIC) uses adaptive optics and single-mode fibers to transport light into NIRSPEC ($R\sim35,000$ in $K$ band), and aims to address these challenges with high-resolution spectroscopy. Using an atmospheric retrieval framework based on petitRADTRANS, we analyze KPIC high-resolution spectrum ($2.29-2.49~μ$m) and archival low-resolution spectrum ($1-2.2~μ$m) of the benchmark brown dwarf HD 4747 B ($m=67.2\pm1.8~M_{\rm{Jup}}$, $a=10.0\pm0.2$ au, $T_{\rm eff}\approx1400$ K). We find that our measured C/O and metallicity for the companion from the KPIC high-resolution spectrum agree with that of its host star within $1-2σ$. The retrieved parameters from the $K$ band high-resolution spectrum are also independent of our choice of cloud model. In contrast, the retrieved parameters from the low-resolution spectrum are highly sensitive to our chosen cloud model. Finally, we detect CO, H$_2$O, and CH$_4$ (volume mixing ratio of log(CH$_4$)=$-4.82\pm0.23$) in this L/T transition companion with the KPIC data. The relative molecular abundances allow us to constrain the degree of chemical disequilibrium in the atmosphere of HD 4747 B, and infer a vertical diffusion coefficient that is at the upper limit predicted from mixing length theory.

astro-ph.EP↗
arXiv2022

Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy

Two-dimensional Raman and hybrid terahertz/Raman spectroscopic techniques provide invaluable insight into molecular structure and dynamics of condensed-phase systems. However, corroborating experimental results with theory is difficult due to the high computational cost of incorporating quantum-mechanical effects in the simulations. Here, we present the equilibrium-nonequilibrium ring-polymer molecular dynamics (RPMD), a practical computational method that can account for nuclear quantum effects on the two-time response function of nonlinear optical spectroscopy. Unlike a recently developed approach based on the double Kubo transformed (DKT) correlation function, our method is exact in the classical limit, where it reduces to the established equilibrium-nonequilibrium classical molecular dynamics method. Using benchmark model calculations, we demonstrate the advantages of the equilibrium-nonequilibrium RPMD over classical and DKT-based approaches. Importantly, its derivation, which is based on the nonequilibrium RPMD, obviates the need for identifying an appropriate Kubo transformed correlation function and paves the way for applying real-time path-integral techniques to multidimensional spectroscopy.

physics.chem-ph↗