OPINION
Marko Bey appeals from the District Court’s denial of his petition for a writ of habeas corpus relating to his 1984 murder conviction, and argues that the jury instructions given in that case violated his federal due process rights. We will affirm.
*909I.
On April 26,1988, Bey approached Carol Peniston as she returned home to her apartment building in Asbury Park, New Jersey, and demanded money. Interrupted by a person exiting the building, Bey forced Peniston to walk a few blocks, down an alley, to an abandoned industrial shed. Inside the shed, Bey went through her purse and ordered her to disrobe. He beat her, causing blunt trauma injuries to her head and upper body as well as internal bleeding in her head, chest, heart, and lungs. Peniston sustained four broken ribs and was left with a sneaker imprint on her chest. Bey raped her, and then used her belt to strangle her. He stole her purse and car, which he later crashed and abandoned.
A week later, police informed Peniston’s family, who had reported her missing, that her car had been involved in an accident and impounded. Bey’s fingerprint was found on the rearview mirror of the car. Police questioned the man who had found Peniston’s discarded purse (and had attempted to return it to her), and he showed them where he had found it. They then discovered the shed and Peniston’s body inside.
The Monmouth County medical examiner, Dr. Stanley Becker, conducted an autopsy of Peniston’s body and concluded, based on the sneaker imprint, broken ribs, and internal bleeding, that her assailant had probably applied very strong force to her chest. He concluded that the cause of death was ligature strangulation, likely from the belt found tied around her neck. Dr. Becker also observed blunt force trauma to her body, including facial hemorrhaging and a broken dental plate.
Bey was arrested two days later and confessed to the murder. He was indicted for murder, felony murder, kidnapping, aggravated assault, aggravated sexual assault, robbery, and theft. Bey testified at trial and admitted that he killed Peniston. The jury convicted Bey on all counts and he was sentenced to death. On direct appeal, the Supreme Court of New Jersey affirmed Bey’s conviction but vacated his death sentence because the jury instructions did not make clear that it need not find mitigating factors unanimously and that each juror must weigh the aggravating and mitigating factors. State v. Bey, 112 N.J. 123, 548 A.2d 887 (1988).1
Before the new penalty phase began, Bey filed a motion for a new trial on the basis of State v. Gerald, 113 N.J. 40, 549 A.2d 792 (1988), which the Supreme Court of New Jersey decided shortly after it issued its opinion in Bey’s direct appeal. The Gerald Court held, based on state constitutional principles, that a defendant convicted of purposely or knowingly causing serious bodily injury resulting in death (“SBI murder”) — as opposed to purposely or knowingly causing death — cannot be sentenced to death.2 Bey argued that because the jury was not specifically instructed as to the difference between these *910two types of murders, it was not required to find each element of capital murder beyond a reasonable doubt. The trial court denied the motion, finding that “[t]here is nothing in the evidence before this jury from which they could have reasonably concluded that [Bey’s] intent was only to inflict serious bodily injury.” (JA at 83 J
After a seven-day resentencing trial, Bey was again sentenced to death. He appealed, and the Supreme Court of New Jersey affirmed. State v. Bey, 129 N.J. 557, 610 A.2d 814 (1992), cert. denied, 513 U.S. 1164, 115 S.Ct. 1131, 130 L.Ed.2d 1093 (1995). The Court considered Bey’s Gerald argument, and held that the jury instructions and verdict sheet did not distinguish between capital murder and SB I murder. However, because Bey’s “actions, taken as a whole, were so wantonly brutal that he could have intended only to cause death, or knew that death was practically certain to occur,” the Court found that the Gerald error was harmless and affirmed the capital murder conviction and sentence. Id. at 825; but see id. at 849 (Handler, J., dissenting); id. at 868 (O’Hern, J., dissenting).
Bey filed a post-conviction relief petition in state court. The trial judge denied the petition, and the Supreme Court of New Jersey affirmed. State v. Bey, 161 N.J. 233, 736 A.2d 469 (1999), cert denied, 530 U.S. 1245, 120 S.Ct. 2693, 147 L.Ed.2d 964 (2000). In March 2000, Bey filed a petition for habeas corpus in the U.S. District Court for the District of New Jersey, raising twenty claims relating to his conviction and sentence. After several years of proceedings in the District Court, the death penalty was repealed in New Jersey in December 2007 and Bey’s death sentence was commuted to life in prison without parole. See N.J. Stat. Ann. § 2C:ll-3b. Accordingly, Bey withdrew all claims except for two: (1) “[t]he trial judge’s failure to distinguish between death-eligible murder and non-death-eligible ‘serious-bodily-injury’ murder at the 1984 guilt trial violated [his] Sixth, Eighth, and Fourteenth Amendment rights, and retrial counsel’s failure to develop all the facts necessary to obtain a new trial on this ground deprived [him] of the effective assistance of counsel”; and (2) Bey’s confession was obtained in violation of his Fifth and Fourteenth Amendment rights to due process and to remain silent. (JA at 7, 9, 10.) The District Court denied the petition.
We granted a certificate of appealability as to three questions: (1) whether the trial judge’s failure to distinguish between death-eligible murder and non-death-eligible SBI murder at the 1984 guilt-phase trial presents a federal question cognizable on habeas corpus review; (2) if so, whether the jury instructions violated Bey’s Fourteenth Amendment right to have the jury find beyond a reasonable doubt each fact necessary to constitute the charged crime; and (3) if so, whether this error is harmless.
II.3
We conclude, first, that Bey has alleged a violation of his federal constitutional rights such that we may review his claim. Although Gerald — the basis of Bey’s claim — is grounded in state law, “[a] jury instruction that omits or materially misdescribes an essential element of an offense as defined by state law relieves the state of its obligation to prove facts constituting every element of the offense beyond a reasonable doubt, thereby violating the *911defendant’s federal due process rights,” and constitutes an error that may be corrected by a federal habeas court. Smith v. Horn, 120 F.3d 400, 415 (3d Cir.1997); see also In re Winship, 397 U.S. 358, 364, 90 S.Ct. 1068, 25 L.Ed.2d 368 (1970). Bey argued before the District Court, and argues now before us, that the jury instructions given in his case violated his federal due process right requiring proof beyond a reasonable doubt as to each element of the offense. The. State readily concedes that we may review Bey’s claim.
In order for an erroneous jury instruction to constitute a due process violation, the instruction at issue must have “operated to lift the burden of proof on an essential element of an offense as defined by state law.” Smith, 120 F.3d at 416. To determine whether a jury instruction was erroneous, we look at the context of the charge as a whole, and consider “whether there is a reasonable likelihood that the jury has applied the challenged instructions in a way that violates the Constitution.” Goldblum v. Klem, 510 F.3d 204, 236 (3d Cir.2007) (quoting Bronshtein v. Horn, 404 F.3d 700, 710 (3d Cir.2005)).
At Bey’s trial, the judge instructed the jury that it must convict Bey of murder if it found that he “purposely or knowingly causefd] the death of or serious bodily injury resulting in the death of Carol Pen-niston [sic].” (JA at 168.) Throughout the instructions, the judge did not clearly distinguish between purposely/knowingly causing death versus purposely/knowingly causing serious bodily injury resulting in death, likely because Gerald had not yet been decided.
Even assuming, without deciding, that the instructions were flawed in light of Gerald’s holding, any such error was harmless. When a jury returns a general verdict after being instructed on several alternative theories of guilt, one of which is invalid, we examine whether the error was harmless — that is, “whether the flaw in the instructions ‘had substantial and injurious effect or influence in determining the jury’s verdict.’ ” Hedgpeth v. Pulido, 555 U.S. 57, 129 S.Ct. 530, 530, 172 L.Ed.2d 388 (2008) (per curiam) (quoting Brecht v. Abrahamson, 507 U.S. 619, 623, 113 S.Ct. 1710, 123 L.Ed.2d 353 (1993)). If Bey’s conviction rested on a finding that he only intended to cause serious bodily injury to Peniston, he could not have been convicted of capital murder under Gerald.
The Supreme Court of New Jersey concluded that a jury could not reasonably find that Bey intended only to cause serious bodily injury, rather than death, when he beat and strangled Peniston. See Bey, 610 A.2d at 825 (“[W]e find that defendant’s actions, taken as a whole, were so wantonly brutal that he could have intended only to cause death, or knew that death was practically certain to occur.... Overall, we find that defendant’s strangulation of the victim and the degree of force applied to the victim’s head and chest make it simply inconceivable that defendant was not practically certain that his action would kill the victim.”) (internal quotation marks, citations, and alterations omitted).
We agree.4 To review, Bey “not only strangled the victim from behind, he also *912smashed her face hard enough to break her dental plate and cause cerebral hemorrhaging, and he stomped on her chest with enough force to crush her ribs, damage her heart and inscribe his sneaker sole on her chest.” Id. Despite this evidence, Bey suggests that Peniston “could have died relatively quickly and suddenly of the assaults and not the choking,” which would indicate that he intended to beat her but not actually kill her. (Br. at 26.) He also argues that he never admitted to intending to kill her, but he did admit to robbing, beating, raping, and strangling her. We conclude that, given the fact that Peniston was found with a belt tied around her neck with evidence of strangulation, combined with signs of an extremely brutal attack, the jury could have only reasonably concluded that Bey intended to kill her.
III.
Because any instructional error as to the elements of the capital murder offense was harmless in light of the evidence adduced at Bey’s trial, we will affirm.5